Heat Transfer Engineering, 32(6):439–454, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2010.506166 Correlations for Natural Convection in Vertical Convergent Channels With Conductive Walls and Radiative Effects LUIGI LANGELLOTTO1 and ORONZIO MANCA2 Centro Sviluppo Materiali S.p.A., Rome, Italy Dipartimento di Ingegneria Aerospaziale e Meccanica Seconda Universit`a degli studi di Napoli, Naples, Italy Natural convection in air, in vertical convergent channels, is analyzed to carry out thermal design and optimization criteria A scale analysis is developed to estimate the optimal geometrical configuration in terms of total volume and average wall temperature The best geometrical configuration obtained by this analysis is the parallel-plates channel New correlations for mass flow rate, radiative heat flux, and dimensionless maximum wall temperature are proposed in the emissivity range from 0.10 to 0.90, convergence angle ranging from 0◦ to 10◦ , ratio between minimum and maximum channel spacing in the range from 0.048 to 1.0, aspect ratio, the ratio between wall length and minimum channel spacing, in the range from 10 to 58, and average channel Rayleigh number in the range from 5.0 to 2.3 × 105 For the same convergence angle and ratio between minimum and maximum channel spacing ranges, new average Nusselt number correlations are also given These correlations are evaluated for emissivity value equal to 0.90, for aspect ratio, referred to the minimum channel spacing, ranging from 10 to 80 and average channel Rayleigh number ranging from 2.5 × 10−2 to 2.3 × 105 INTRODUCTION Cooling technology for electronic equipments and components requires a deep knowledge of heat transfer phenomena The main aim is to maintain a relatively constant component temperature equal to or lower than the manufacturer’s maximum specified service temperature, in order to ensure system performance and reliability [1–3] The design of natural convection thermal control systems using simple relations is certainly appealing Particular interest has been devoted to the channel configuration and several contributions have dealt with this geometry [4] An interesting problem is the heat transfer in a convergent channel with two uniformly heated flat plates [5–11] The first numerical and experimental study of natural convection in water, in a convergent vertical channel, was carried This work was supported by MIUR with Articolo 12 D M 593/2000 Grandi Laboratori “EliosLab.” A special acknowledgment is given to the reviewers; their suggestions have improved the article Address corrrespondence to Professor Oronzio Manca, Dipartimento di Ingegneria Aerospaziale e Meccanica Seconda Universit`a degli studi di Napoli, Via Roma 29–81031, Aversa (CE), Italy E-mail: oronzio.manca@unina2.it out in [5] The converging walls were maintained at the same uniform temperature Natural convection in air in a uniformwall-temperature convergent channel was investigated experimentally in [6], numerically in [7], and both numerically and experimentally in [8] A numerical study on natural convection, in vertical convergent channels, with uniform wall temperature, for different convergence angles was carried out in [9] A Nusselt number composite correlation was proposed for convergence angle in the range 0–60◦ Recently, a numerical simulation and optimization for a vertically diverging and converging channel with laminar natural convection was accomplished in [10] For convergent channels, the results showed that the optimal angle between the two walls was approximately zero when the Rayleigh number was large The configuration of a vertical convergent channel was numerically studied in [11] The two principal flat plates, at uniform heat flux, were considered with finite thickness and thermal conductivity An experimental investigation on natural convection in air, in vertical convergent channels, with uniform wall heat flux was presented in [12] For the lowest spacing, maximum wall temperature decreased significantly, passing from the configurations of the parallel vertical plate to the configurations with convergence angles δ ≥ 2◦ 439 heat transfer engineering Experimental Numerical and experimental Numerical Bianco et al [13, 14] Bianco et al [15] vol 32 no 2011 0◦ to 60◦ bmin 0◦ to 10◦ bmin UWHF + CW + 0◦ to 10◦ bmax RE 10–58 4.4 to 2.9 × 108 4.4 to 2.9 × 108 10–58 θ∗ = f5 bmin , ε, Ra ∗bmax bmax Nu = f3 1/ p p p ;Re = f6 = θ∗ + θ∗ ∞ bmin b , , Ra bmax bmax Lw bav p p , Ra ∗bmax ;θmax = f4 Ra = θ0 + θ∞ /p bmin bav , Ra bmax bmin bmin b qr , , Ra ∗bmax ; = f5 ε, qref , Ra ∗bmax bmax Lw qr + q c bmin , ε, Ra ∗bmax bmax p p Nu = f1 Ra bmax = Nu0 + Nu∞ /p ;Nu = f2 Re = f4 p θ∗max = f2 Ra ∗ = θ∗ + θ∗ ∞ p /p ;θ∗ = f3 p Nu∗ = f1 Ra ∗ = Nu∗ + Nu∗ ∞ p /p Nub = f1 Ra b ; Nu∗ b = f2 Ra ∗b 4.4 to 2.9 × 108 10–58 p p Nu = f Ra , δ = Nu0 + Nu∞ /p Nub = f Ra b Nu = f Ra Correlation Nub = f1 Ra b ; θmax = f2 Ra b to × 106 4.4 to 2.9 × 108 6.4 to 4.8 × 104 × 103 to × 104 Nubmax = f bmax /Lw , Rabmax Ra 4.4 to 2.9 × 108 10–58 0.5–50 10–58 6, 8.5, 12 bmin /2 0◦ to 8◦ L/b 11.4, 22.9 Reference Length 0◦ to 15◦ bmax δ 0◦ to 10◦ bmin and bmax UWHF + CW + 2◦ , 10◦ bmax RE(4) UWHF + CW + 0◦ to 10◦ bmax RE UWT UWHF(2) + CW(3) UWHF + CW UWT UWT(1) B C on channel walls (1) Uniform Wall Temperature; (2) Uniform Wall Heat Flux; (3) Conductive Wall; (4) Radiative Effects Present work Numerical Numerical Numerical Kaiser et al [9] Bianco and Nardini [11] Bianco et al [12] Shalash et al [8] Numerical and experimental Numerical and experimental Type of investigation Sparrow et al [5] Reference Table Comparison among different studies of natural convection in convergent channels 440 L LANGELLOTTO AND O MANCA L LANGELLOTTO AND O MANCA Radiative effects are particularly interesting in convergent channels, due to the large view factor toward the ambient [13, 14] In the first study, a numerical analysis was carried out in laminar, two-dimensional steady-state conditions, with the two principal flat plates at uniform heat flux and taking into account wall conductivity and emissivity Average Nusselt numbers were evaluated and simple monomial correlations for average Nusselt numbers, in terms of channel Rayleigh numbers, were proposed In the second study, an experimental investigation on natural convection in air, in a convergent channel, with uniform heat flux at the walls, was carried out Average Nusselt numbers were evaluated and simple monomial correlations for dimensionless maximum wall temperatures and average Nusselt numbers were proposed in terms of channel Rayleigh numbers in the same ranges given in [13] Numerical results, obtained in [13], were in very good agreement with experimental results given in [14] Design charts for the evaluation of thermal and geometrical parameters, for natural convection in air, were proposed for natural convection in vertical convergent channels in [15] Thermal design and optimization of a channel in stack of convergent channels were obtained employing the correlations among the more significant dimensionless thermal and geometrical parameters Proposed correlations for natural convection in convergent channels, given in the already-mentioned papers, are reported in Table In the present paper, a scale analysis is carried out following the procedure given in references [16–20] New correlations for convective heat transfer contribution in terms of Reynolds numbers, dimensionless wall temperature, and global Nusselt numbers are proposed More accurate new correlations for the ratio between radiative and global heat flux (radiative and convective heat fluxes) are evaluated The new correlations extend the analysis presented in references [15] and [20–23] They are obtained by enlarging the results given in [13] to large values of channel aspect ratio and low Rayleigh numbers This also allows evaluation of the thermal behavior of the convergent channels in a possible fully developed flow The analysis is proposed to evaluate the previously mentioned variable for vertical convergent channel, with surface emissivity ranging from 0.10 to 0.90, for a single assigned wall thickness and thermal conductivity, for convergence angle from 0◦ to 10◦ , ratio between minimum and maximum channel spacing, bmin /bmax , in the range from 0.048 to 1.0, aspect ratio, Lw /bmin , in the range from 10 to 80, and global Rayleigh num∗ bers referred to bmin , Ra bmin , in the range from 2.5 × 10−2 to 2.3 × 105 From a different point of view, the present study may be conceived as an effort to estimate the right balance between the control of the maximum wall temperature and an applied symmetrical wall heat flux Moreover, this attempt can also be viewed as the maximization of heat transfer for an assigned available total volume that is constrained by space heat transfer engineering 441 Figure Sketch of the configuration: (a) physical domain; (b) computational domain limitations This goal has been studied in references [10], [16], [19], and [24], and reviewed lately in [25] and more recently in [26] The present geometry is important in electronic cooling [9, 10, 27] and in solar energy components [28, 29] MODEL DESCRIPTION AND NUMERICAL PROCEDURE Model Description The physical domain under investigation is shown in Figure 1a It consists of two nonparallel plates that form a vertical convergent channel Both plates are thermally conductive, gray, and heated at uniform heat flux The imbalance between the temperature of the ambient air, To , and the temperature of the heated plates draws air into the channel The flow in the channel is assumed to be steady-state, two-dimensional, laminar, incompressible, with negligible viscous dissipation All thermophysical properties of the fluid are assumed to be constant, except for the dependence of density on the temperature (Boussinesq approximation), which gives rise to the buoyancy forces The thermophysical properties of the fluid are evaluated at the ambient temperature, To , which is assumed to be 300 K in all cases The ambient is assumed to be a black body at a temperature of 300 K With the already mentioned assumptions, the governing equations in the conservative form and primitive variables vol 32 no 2011 442 L LANGELLOTTO AND O MANCA Table are: ∂u ∂v + =0 ∂x ∂y (1) ∂u ∂u ∂p ∂ u ∂ u +v =− +ν + ∂x ∂y ρf ∂x ∂x2 ∂y u − gβ (T − To ) (2) Wall∗ T = To HG ∂u =0 ∂x ∂v =0 ∂x T = To AB, EF, IL, OP u=0 v=0 BC, DE, LM, NO u=0 v=0 DN u=0 v=0 u=0 v=0 ∂u =0 ∂x ∂u =0 ∂y ∂v =0 ∂x ∂v =0 ∂y (4) CM where the pressure is referred to the ambient pressure, po A two-dimensional conduction model is employed The heat conduction equations in the steady-state regime with constant thermophysical properties is: RQ ∂ T ∂ T + ∂x2 ∂y ∂ Ts ∂ Ts + =0 ∂x2 ∂y2 (5) (Tmax − To )k ∗ (T − To )k ; θmax = max qc b (qc + qr )b Ra b = Gr Pr = Re = IR, QP ∗ The ∂T =0 ∂x ∂T ∂T = ks kf ∂x ∂x ∂T ∂T = ks + q + qr kf ∂n ∂n ∂T ∂T kf = ks − q + qr ∂n ∂n ∂T =0 ∂x ∂T =0 ∂y letters in the column are in reference to Figure 1b The characteristic variables, for the investigated configuration in this paper, are the dimensionless maximum wall temperature, the channel Rayleigh number, the Reynolds number, and the channel Nusselt number, defined as follows: θmax = T ∂v =0 ∂y ∂T ∂T +v = af ∂x ∂y u v ∂u =0 ∂y (3) u AH and FG ∂v ∂ 2v ∂ 2v ∂v ∂p +v =− +ν + ∂x ∂y ρf ∂y ∂x2 ∂y u Boundary conditions for the fluid domain (6) gβqc b5 gβ(qc + qr )b5 Pr; Ra ∗ = Pr (7) b ν2 kLw ν2 kLw uav,bmin bmin ν Numerical Procedure Since the two plates are placed in an infinite medium, from a numerical point of view the problem has been solved with reference to a computational domain of finite extension, as depicted in Figure 1b, by following the approach given in [11–13] This computational domain allows taking into account the diffusive effects peculiar to the elliptic model The imposed boundary conditions are reported in Table for the fluid domain and in Table for the solid domain The pressure defect is equal to zero at the inlet and outlet boundaries The net radiative heat flux from the surface is computed as a sum of the reflected fraction of the incident and emitted radiative heat fluxes: (8) qr (xw ) = (1 − εw ) qin (xw ) + εw σT4w (xw ) (13) and Nub = qc b Tw,av − To k Nu∗ b = (qc + qr )b Tw,av − To k qin (xw ) = (9) Iin s · nd s·n>0 where b is bmin or bav or bmax , and qc = Lw qr = Lw Tav = Lw Table Boundary conditions for the solid domain Lw qc,x (xw )dxw (10) Wall∗ DN Lw qr,x (xw )dxw kf (11) Tw = Tf CM Lw T(xw )dxw kf (12) BL, OE heat transfer engineering ∂T ∂T = ks − q + qr ∂n ∂n Tw = Tf It is worth noticing that an evaluation of qc separate from qr is very difficult in practice The value of (qc + qr ) is not equal to the dissipated heat flux q due to the conductive heat losses toward the ambient through the lower and upper edges of the walls ∂T ∂T = ks + q + qr ∂n ∂n BC, DE, LM, NO ∂T =0 ∂n ∂T ∂T kf = ks + qr ∂x ∂x Tw = Tf ∗ The letters in the column are in reference to Figure 1b vol 32 no 2011 (14) L LANGELLOTTO AND O MANCA SCALE ANALYSIS For the convergent channel, the total volume (channel total volume) is: Vtot = Wbmax Lw cos δ (15) and it is greater than the channel volume as shown in Figure 1a The geometrical optimization of the convergent channel, in terms of maximum or average wall temperature, should take into account the channel total volume The heat transfer rate in the channel is: Q = 2hWLw Tw (16) In the optimization procedure, the channel total volume is considered: Qbmax = 2hWLw Tw bmax (17) 60 Lw/bmin = 58.0 Tw - T o [K] 40 ε = 0.90 30 20 10 Experimental Numerical 100 (18) heat transfer engineering 200 xw [mm] 300 400 100 10 θ = 0° θ = 2° θ = 5° θ = 10° (b) ε = 0.90 Present numerical data Experimental data [14,31] 0.1 100 101 102 103 104 105 106 107 108 Ra'*bav Figure Comparison between numerical and experimental data: (a) wall temperature profiles, (b) average Nusselt number Combining Eq (18) with the average channel Nusselt number, Eq (9), we get: Vtot Tw ∼ Qbmax b 2kNub (19) for an assigned heat transfer rate The optimal channel configuration that minimizes the product Vtot Tw is the configuration that maximizes the heat transfer as a function of the channel total volume in terms of bmax In laminar, fully developed and two-dimensional natural convection between parallel plates, heated at uniform heat flux, the maximum wall temperature is obtained at the channel outlet section and the minimum Nusselt number is [20]: Nux=L = For small convergent angles Eq (17) becomes: Qbmax ∼ 2hVtot Tw (a) 50 δ = 10° qΩ = 220 W/m2 Nu*bav The computational fluid dynamics code FLUENT [30] was employed to solve the present problem The segregated method was chosen to solve the governing equations, which were linearized implicitly with respect to the equation’s dependent variable The second-order upwind scheme was chosen for the energy and momentum equations The Semi Implicit Method for Pressure-Linked Equations (SIMPLE) scheme was chosen to couple pressure and velocity Similar considerations were made for choice of the discrete transfer radiation model (DTRM), which assumes all surfaces to be diffuse and grey The convergence criteria of 10−6 for the residuals of the velocity components and of 10−8 for the residuals of the energy were assumed A grid dependence test is accomplished to realize the more convenient grid size and radiative subdivisions by monitoring the induced dimensionless mass flow rate and the average Nusselt number, referred to the minimum channel spacing for a convergent channel system with Lw /bmin = 40.6, δ = 10◦ at ∗ Ra bmin = 30 and 220 and with Lw /bmin = 10.2, δ = 10◦ , and ∗ Ra bmin = 3.1 × 104 and 2.25 × 105 as reported in [13] A more detailed description on the numerical model is reported in [13] A comparison between numerical and experimental [31] results is reported in Figure In Figure 2a wall temperature ∗ profiles, obtained for Lw /bmin = 58.0, δ = 10◦ , and Ra bmin = 37, are shown The comparison between the numerical and experimental data showed a good agreement with a maximum percentage discrepancy of about 8% In Figure 2b the comparison, in terms of average Nusselt number, is accomplished A very good accord between the numerical and experimental data is observed Since the numerical results and experimental data are in good agreement, the assumptions of steady-state, two-dimensional, laminar, incompressible, with negligible viscous dissipation are confirmed, as well as the Boussinesq approximation 443 k + hb 48 Rab −1 (20) The average wall temperature is approximately equal to the wall temperature at middle channel length and the average vol 32 no 2011 444 L LANGELLOTTO AND O MANCA Nusselt number is estimated by [20]: Nux=L/2 = k + hb 12 Rab −1 (21) The first term on the right-hand side of the Eqs (20) and (21) is negligible with respect to the square root as given in [20]: Nux=L Rab and Nux=L/2 ∼ 48 Rab 12 Nub xw =Lw bav bmin Rab 12 Nub xw =Lw /2 ∼ 3 (23) For fully developed flow, the comparison between the parallel-plate channel, Eqs (20) and (21), and the convergent channel, Eqs (23), shows that, for the same bmin , the convergent channel has a higher Nusselt number value; i.e., the convergent channel, with the minimum channel spacing, equal to the parallel-plate channel spacing, presents lower maximum and average wall temperature values For the Nusselt number referred to the average channel spacing it is: Rabav bmin and 48 bav Nubav xw =Lw ∼ Nubav xw =Lw /2 ∼ Rabav bmin 12 bav (24) As shown in Eqs (24), the Nusselt number for the convergent channel, referred to bav , is lower than the one for the parallel-plate channel, i.e., the wall temperature in the convergent channel is greater than the one in the parallel-plate channel Further, the convergence angle limit is: bav − Lw sin (δ) = ⇒ δ = arcsin bav Lw (25) NuLw = 0.56 RaLw cos δ Nub max xw =Lw ∼ Nub max xw =Lw /2 ∼ Rabav b2min b3av 12 b5max (27) 0.2 (28) For developing flow in convergent channels as limit condition, Eq (28) is employed in terms of b/Lw with b equal to bmin or bav or bmax : b Lw (29) As suggested in [20], a composite relation is obtained by summing the two expressions, the equation for fully developed limit, indicated with Nu0 [Eqs (23)–(25)], and single-plate limit, indicated with Nu∞ [Eq (29)] The binomial correlation is: −p Nu−p = Nu0 + Nu−p ∞ (30) as a first approximation, the correlation exponent, p, is set equal to The term Vtot Tw is evaluated by means of Eq (30) using bmin , bav , and bmax , respectively: ⎧ −2 Rab bav 3/2 Qbmax bmin ⎨ (Vtot Tw )b ∼ ⎩ 2k 12 bmin + 0.56 Rab cos δ (Vtot Tw )bav ⎫0.5 ⎬ 0.2 −2 + 0.56 Rabav cos δ (Vtot Tw )b max (31) ⎭ ⎧ Qbmax bav ⎨ ∼ ⎩ 2k For the Nusselt number referred to the maximum channel spacing it is: Rabav b2min b3av and 48 b5max bmax 2Lw In laminar, developing, and two-dimensional natural convection along an inclined single plate, heated at uniform heat flux, the average Nusselt number is [32]: Nub ∼ 0.56 (RaLw cos δ)0.2 and bav bmin bmax − 2Lw sin (δ) = ⇒ δ = arcsin (22) In vertical channels, at uniform heat flux, with small convergence angle, the minimum and average Nusselt numbers, referred to the minimum channel spacing, can be evaluated as in [20] It is obtained as: Rab 48 Also in this case, the Nusselt number for the convergent channel, referred to bmax , is lower than the one for the parallelplate channel The convergence angle limit is equal to: Rabav bmin 12 bav −2 ⎫0.5 ⎬ −2 0.2 (32) ⎭ ⎧ Qbmax bmax ⎨ ∼ ⎩ 2k Rabav b2min b3av 12 b5max −2 ⎫0.5 (26) heat transfer engineering + 0.56 Rab max cos δ vol 32 no 2011 ⎬ 0.2 −2 ⎭ (33) L LANGELLOTTO AND O MANCA 445 In Figure 3c, the optimal configuration, in terms of channel spacing, is given as a function of the channel convergence angle, for qc equal to 30 W m−2 The figure shows that the curves tend to an asymptotic value equal to 9.9 × 10−3 m, which represents the optimal configuration for the parallel-plate channel Figure 3c shows that for (Vtot Tw )b , increasing the convergence angle, the minimum channel spacing decreases For fixed convergence angle, decreasing bmin , the total volume decreases and the Nusselt number increases, Eq (31), and then the wall temperature decreases In Vtot Tw referred to bav and bmax , for fixed convergence angle, the Nusselt number and the total volume increase as the reference channel spacing increases ANALYSIS AND PROCEDURES FOR CORRELATIONS The results are obtained by the numerical procedure reported in [13] In this work, the analysis is focused on the radiative effects on natural convection in air, in a convergent channel, uniformly heated at the two principal walls The wall thickness, t, is 3.2 mm, with the ratio t/bmin varying in the range 0.080–0.64 Its thermal conductivity is 0.198 W/m-K, with a solid-to-fluid conductivity ratio ks /kf = 8.18 The input data are ranging from ∗ 10 to 80 for aspect ratios, Lw /bmin ; Rayleigh numbers, Ra bmin , −2 ranging from 2.5 × 10 to 2.3 × 10 ; convergent angles, δ, ranging from 0◦ to 10◦ ; and wall emissivities, ε, ranging from 0.1 to 0.9 The percentage value of the conductive heat flux, qk , referred ∗ to the dissipated heat flux, q , for different Ra bmin values and for the geometry here considered, are given in Table Figure Wall temperature for channel total volume as a function of channel spacing and convergence angle with reference channel spacing equal to: (a) bmin ; (b) bav (c) Optimal geometrical configurations, in terms of bmin , bav and bmax values, as a function of convergence angle The values of Vtot Tw , for qc equal to 30 W m−2, as a function of the convergence angle and the minimum and average channel spacing, are reported in Figures 3a and 3b The contours of Vtot Tw value in the (b,δ) plane are also given It is noted, in Figure 3a, that (Vtot Tw )b , Eq (31), is always defined except for bmin equal to zero The function shows that the absolute minimum value is obtained for δ = 0◦ For the considered convective heat flux the optimal channel spacing is bmin = 9.9 × 10−3 m This value corresponds to the minimum value of Vtot Tw , i.e., the minimum Tw with the minimum compatible total volume Vtot For (Vtot Tw )bav , Eq (32), and Figure 3b, for assigned bav value, the convergence angle limit, δlimit , exists and a vertical asymptotic plane is detected for δ → δlimit , according to Eq (25) The optimal configuration in terms of (Vtot Tw )bav , obtained by Eq (32), is realized for δ = 0◦ and for the considered convective heat flux bav = 9.9 × 10−3 m The same results are obtained for (Vtot Tw )b max , Eq (33), but the results are not reported here heat transfer engineering Mass Flow Rate Mass flow rate, involved in the heat transfer, is an important parameter in design and control of electronic equipment and solar energy in building The following correlations for mass flow rate, in a convergent uniformly heated vertical channel, as a function of thermal and geometrical parameters are proposed The mass flow rate for unit of width is defined as follows: ˙ = ρuav,bmin bmin m (34) where uav,bmin is the mean velocity at the minimum channel section From Eqs (8) and (34): ˙ = Re µ m (35) The Reynolds number, as a function of Ra bmax , is reported in Figure The figure shows that, when the Rayleigh number increases, for fixed aspect ratio and convergence angle, the Reynolds number also increases Decreasing the aspect ratio (increasing the spacing), the Reynolds number increases significantly, whereas there is slight change in the mass flow rate in the emissivity range 0.10–0.90 The maximum percent variation vol 32 no 2011 446 L LANGELLOTTO AND O MANCA Table Conductive heat losses ∗ Ra bmax ≥ 30 ∗ 1.0 ≤ Ra bmax ≤ 30 Ra ∗ bmax Lw /bmin ≤ 58 58 ≤ Lw /bmin ≤ 80 Lw /bmin = 80 Lw /bmin ≥ 80 ≤ 1.0 0.048 ≤ bmin /bmax 0.048 ≤ bmin /bmax 0.048 ≤ bmin /bmax 0.048 ≤ bmin /bmax between emissivity value equal to 0.90 and 0.10 is about 10% Figure shows that the Reynolds number is highly dependent on channel aspect ratio and convergence angle In order to reduce the Reynolds number scattering, the varimin as a function of Ra bmax able Re bbmax Re bmin bmax χ bav Lw = f Ra bmax η is considered: bav Lw ≤ 1.0 ≤ 1.0 ≤ 0.7 ≤ 1.0 qk /q ≈ 3%; qk /q ≤ 5% qk /q ≈ 10%; qk /q ≤ 15% qk /q ≥ 15% A new correlation, in terms of Ra bmax , is evaluated by regression analysis: Re = −4.62 · 103 bmin Lw + 752 bmin Lw + 18.6 bmin Lw η (36) 104 (a) A dependence on is observed and the best correlations Lw for assigned bmin are carried out employing χ = −1 and η = −5/2 The plot of Eq (36) is reported in Figure 5a In this figure, a greater dispersion is observed for high values of Ra bmax ( bLavw )η The dispersion is due to the increase in relevance of the aspect ratio in this zone To obtain a monomial correlation for the mass flow rate, in terms of geometrical and thermal variables, the following relation is proposed in the form [15]: bmax Re bmin Lw =α bmin Ra bmax bav Lw −2.5 β Re(bmax/bmin) Lw bmin Lw bmin 103 102 101 10 (37) 105 106 107 108 109 -2.5 Ra'bmax(bav/Lw) 1010 1011 100 200 300 400 500 Re (numerical) 600 700 700 (b) 600 Re 500 ε = 0.10 ε = 0.50 ε = 0.90 Re (Eq 38) 1000 400 300 100 200 Lw/bmin = 58.0 Lw/bmin = 40.6 δ = 0° δ = 2° δ = 5° δ = 10° Lw/bmin = 20.3 Lw/bmin = 12.6 Lw/bmin = 10.2 10 100 101 102 103 104 105 106 107 108 109 Ra'bmax Figure Reynolds number versus Rayleigh number for various convergence angles and wall emissivity values heat transfer engineering 100 0 Figure (a) Re bbmax as a function of Ra bmax ( bLavw )−2.5 (b) Comparison between numerical Reynolds numbers and Reynolds numbers by correlation given by Eq (38) with a percentage difference in a ±5% range vol 32 no 2011 L LANGELLOTTO AND O MANCA −24.6 bLmin w bmin × ; r = 0.996 bmax Lw/bmin = 12.6 Lw/bmin = 10.2 c (38) and a simpler expression is also proposed: Re = 52.9 −24.6 −2.50 0.249+0.233e bav Lw bmin Lw 0.01 100 (39) bmin + 72.9 Lw bmin + 54.6 Lw −24.5 bLmin w Rab∗max −0.429 Ra bav Lw −2.50 0.242+0.230e bmin ; r = 0.989 bmax (40) Moreover, a new correlation in simplified form, in terms of ∗ bmax , is proposed: Re = 57.4 bmin − 0.454 Lw −24.5 bLmin w × Rab∗max × bav Lw bmin r = 0.988 bmax 101 102 103 104 105 Ra'*bav 106 107 108 ∗ bmin r = 0.990 bmax bmin Re = −499 Lw δ = 0° δ = 2° δ = 5° δ = 10° ε = 0.10 ε = 0.50 ε = 0.90 They present a better regression coefficients than the corre∗ lation presented in [15] in terms of Ra bmax : × 0.1 bmin − 0.436 Lw × Rab max × Lw/bmin = 58.0 Lw/bmin = 40.6 Lw/bmin = 20.3 qr/(q +qr) −0.0248] Rab max −2.50 0.249+0.233e bav Lw 447 −2.50 0.242+0.230e (41) In Figure 5b, a comparison between the Reynolds number value from numerical data and the Reynolds number values calculated by the correlation in Eq (38) are reported together with an error level of ±5% r Figure Radiative heat flux ratio ( qcq+q ), as a function of Ra bav , for three r different wall emissivity values and different convergence angles is very useful when qc + qr is known, thereby allowing for estimation of radiative heat losses The ratios between radiative and total heat fluxes, as a func∗ tion of Ra bav , are reported, for different angles and for three ε values, in Figure It is observed that for fixed Lw /bmin values, ∗ r decreases when Ra bav increases, and the ratio the ratio qcq+q r ∗ variation decreases with increasing Ra bav and decreasing aspect ratio The percentage reduction of heat flux ratio decreases with increasing convergence angle Furthermore, the ratio values increase with decreasing aspect ratio value Increase in the convergence angle produces a significant increase in heat flux ratio For δ = 10◦ , the radiative heat flux ranges between 20% and 40% of the total heat flux Figure shows that, for fixed Rayleigh number, the heat flux ratio decreases with decrease in the wall ∗ emissivity The higher the Ra bav values, the higher is the vari∗ ation of the heat flux ratio In fact, at Ra bav = 20, for ε = 0.10, the heat flux ratio is 0.020, whereas for ε = 0.90, the ratio is ∗ 0.032; at Ra bav = 2.4 × 107, the heat flux ratio is 0.11 and 0.27 for ε = 0.10 and ε = 0.90, respectively The percentage varia∗ tions referred to ε = 0.90 are about 38% and 59% for Ra bav equal to 20 and 2.4 × 10 , respectively For assigned wall length, Figure allows to observe the dependence on the convergence angle and channel spacing when the wall heat flux is fixed Furthermore, the figure shows a data scattering In order to reduce the heat flux ratio scattering, the c is employed as suggested in [15] A new comvariable qrq+q ref posite correlation for ε = 0.90, obtained by means of regression analysis, is proposed: Radiative Heat Flux qr = qc + qr Correlations to evaluate the ratio between radiative heat flux, qr , and total heat flux, qc + qr , for a convergent channel and r , surface emissivity are proposed The heat flux ratio, qcq+q r × heat transfer engineering qr + qc qref 1.12x10−3 0.153Ra ∗ bav −0.26 vol 32 no 2011 + 0.0481Ra ∗ bav qref = W/m2 ; 0.186 r2 = 0.991 1/4 (42) M ESLAMI AND K JAFARPUR 509 Table Upper and lower bounds of BGF for cylinders illustrated in Figure Figure Configuration of the six different cylinders considered in this study Vertical Cylinders A circular cylinder is composed of three distinct surfaces: the cylindrical side and the two end surfaces Using Eq (3), the BGF of the side for a vertical cylinder is easily calculated: G side−ver = P √ A 1/4 = 1.154 D L Body shape Glow Gup Vertical cylinder, L/D = 0.1 Vertical cylinder, L/D = 0.5 Vertical cylinder, L/D = 1.0 Horizontal cylinder, L/D = 0.1 Horizontal cylinder, L/D = 1.0 Inclined cylinder, L/D = 1.0, ϕ = 45◦ 0.758 0.897 0.936 1.088 1.051 0.940 0.900 1.031 1.044 1.115 1.169 1.151 discussed and are reported in Table for the purpose of quick reference Knowing the two bounds, one must now find BFF and Gdyn using Eqs (10)–(13) Figures 2–4 compare the results of the present model, Eq (14), with experimental data of Hassani [35] and Jafarpur [29] for three vertical cylinders of L/D =0.1, 0.5, and 1.0, respectively, as illustrated in Figures 1a–c The experiments were carried out with a heated body suspended inside a pressure vessel containing air at a wide pressure range (from 0.8 to 700 kPa) Hence, Rayleigh number can be changed in the whole range of laminar flow (from Ra of ∼10 to 108) [29, 37] The uncertainty in Ra and Nu is dominated by the uncertainty in pressure measurements (especially at lower pressures) and is less than 10% as reported by Hassani and Hollands [37] To show the dynamic behavior of body gravity function, the modified lower bound and upper bound are also included in Figure The empirical correlation proposed by Kobus and Wedekind [16] is also included It is found that this correlation underestimates the experimental data and the analytical model But excellent agreement between the present model and experimental data is observed for all three cylinders in the whole range of < Ra√ A < 108 This shows that the dynamic BGF is a powerful tool to correlate Nu number over a wide range of Ra 1/8 (16) Obviously, Eq (3) cannot be used to calculate the BGF of horizontal flat surfaces But results of semi-empirical studies are available and can be applied Based on Yovanovich and Jafarpur [34] and Jafarpur [29], body gravity functions for horizontal top and bottom surfaces are obtained by the following equations: G top = 0.952 (17) G top = 0.476 (18) Considering all three surfaces in series and using Eq (6), one can easily obtain the lower bound for body gravity function, Glow Assuming the top surface in parallel with the other two combined in series results in Gup Values of the two bounds for the six circular cylinders shown in Figure are calculated as G bottom = heat transfer engineering Figure Comparison of the results of present model with experiments of Hassani [35] for a vertical cylinder of L/D = 0.1 in air (Pr = 0.72) vol 32 no 2011 510 M ESLAMI AND K JAFARPUR Figure Comparison of the results of present model with experiments of Jafarpur [29] for a vertical cylinder of L/D = 0.5 in air (Pr = 0.72) Horizontal Cylinders Figure Comparison of the results of present model with experiments of Hassani [35] for a horizontal cylinder of L/D = 0.1 in air (Pr = 0.72) can be found using Eqs (6) and (20): The two ends of a horizontal cylinder are vertical circular plates and their BGF is easily obtained from Eq (3): G end = 1.021 (19) Applying Eq (3) to a horizontal circular surface, one can find its BGF as previously derived by Lee et al [31]: G side−hor = 0.891 L D 1/8 (20) Combining these three surfaces as parallel by using Eq (5), the lower bound for body gravity function, Glow , is obtained Also, one may consider top and bottom halves of the horizontal circular side in parallel This idea is supported by investigating streamlines in the numerical solution of Kuehn and Goldstein [8] Therefore, the BGF for a half horizontal circular cylinder Figure Comparison of the results of present model with experiments of Hassani [35] for a vertical cylinder of L/D = 1.0 in air (Pr = 0.72) heat transfer engineering G hal f −hor = 0.972 L D 1/8 (21) Combining the two ends along with the two half circular cylinders all in parallel, Gup is found for a horizontal circular cylinder with active ends Figures and show the results of the present model for two horizontal cylinders of L/D =0.1 and 1, respectively, as illustrated in Figures 1d and e, along with experimental data of Hassani [35] Accurate results for such a large range of aspect ratio and Ra number are observed Inclined Cylinders Stewart [22] and Raithby and Hollands [23] calculated the body gravity function for the circular surface of an isothermal inclined cylinder using equations similar to Eq (4) They have Figure Comparison of the results of present model with experiments of Hassani [35] for a horizontal cylinder of L/D = 1.0 in air (Pr = 0.72) vol 32 no 2011 M ESLAMI AND K JAFARPUR Figure Comparison of the results of present model with experiments of Hassani [35] for an inclined cylinder of L/D = 1.0 and ϕ = 45◦ in air (Pr = 0.72) reported values that cover different inclination angles ϕ and aspect √ ratiosL/D Converting the results to the characteristic length A, the value of BGF for the outer surface of an inclined cylinder of ϕ = 45◦ and L/D = (Figure 1f) is: G side−inc = 1.085 (22) Also, Eq (3) gives the BGF for the two inclined ends: G end = (sin ϕ) /4 × 1.021 (23) Assuming the three surfaces in series, the lower bound is obtained while the upper bound for BGF is calculated by considering these three surfaces in parallel The resulting correlation is compared with experimental work of Hassani [35] in Figure Excellent agreement is again observed between the proposed model and experimental data points It is also interesting to investigate the effect of inclination angle on natural convection heat transfer from isothermal circular cylinders with active ends Figure compares Nusselt number Figure Experimental results of Hassani [35] for three horizontal, inclined and vertical cylinders of L/D = 1.0 in air (Pr = 0.72) from the present analytical method, Eq (14), for three cylinders of L/D = at ϕ = 0, 45, and 90 degrees, respectively It is shown that the horizontal cylinder has the highest rate of heat transfer, but with increasing inclination from horizontal orientation to 45◦ , Nu does not change significantly In other words, the rate of heat transfer decreases mostly when the cylinder is in the near vertical orientation This effect is clear from the lower and upper bounds of body gravity function for the three cylinders as shown in Table It is also confirmed by the available experimental data (Figure 9) Finally, the accurate results of this simple model show that the present method of modeling body gravity function is a powerful tool for calculation of natural convection heat transfer from isothermal bodies of arbitrary shape over a wide range of Ra CONCLUSIONS Evaluation of natural convection heat transfer from isothermal cylinders of arbitrary aspect ratio and inclination with active ends using a new analytical model is presented The method is based on the concept of the dynamic body gravity function, which itself is a function of a new dimensionless parameter the body fluid function Excellent agreement between the results of the present model and available experimental results is observed in the whole laminar flow range (0 < Ra√ A < 108 ) for all the geometries discussed This shows that no accurate result can be obtained unless this dynamic BGF is employed The present model also shows that the rate of heat transfer decreases with increasing inclination angle from horizontal to vertical orientation Due to the presence of F(Pr), the proposed model can be used for fluids of any Prandtl number NOMENCLATURE Figure Comparison of the results of present model for three horizontal, inclined, and vertical cylinders of L/D = 1.0 in air (Pr = 0.72) heat transfer engineering 511 A ˜ A total surface area, m2 fraction of sectional area defined by Eq (7) vol 32 no 2011 512 M ESLAMI AND K JAFARPUR BFF BGF C D F(Pr) g G√A G low hx , hω L N N u√ A N u 0√ A P Pr Ra√ A x body fluid function body gravity function universal correction factor diameter of circular cylinder, m Prandtl number function defined by Eq (2) gravitational acceleration, m/s2 body gravity function based on characteristic length √ A modified lower bound scale factors length of cylinder, m number of distinct surfaces of a body shape √ Nusselt number based on characteristic length A √ conduction limit based on characteristic length A local perimeter of body with respect to gravity vector, m Prandtl number √ Rayleigh number based on characteristic length A surface coordinate line [5] [6] [7] [8] [9] [10] Greek Symbols ω θ ϕ surface coordinate line angle between normal to the surface and gravity vector, radians inclination angle, radians [11] [12] Subscripts cyl dyn hor i inc low up ver cylindrical surface dynamic horizontal surface number i inclined lower bound upper bound vertical [13] [14] [15] REFERENCES [1] Morgan, V T., Heat Transfer by Natural Convection From a Horizontal Isothermal Circular Cylinder in Air, Heat Transfer Engineering, vol 18, pp 25–33, 1997 [2] Morgan, V T., The Overall Convective Heat Transfer From Smooth Circular Cylinders, Advances in Heat Transfer, vol 11, pp 199–263, 1975 [3] Kuehn, T H., and Goldstein, R J., Correlating Equations for Natural Convection Heat Transfer Between Horizontal Circular Cylinders, International Journal of Heat and Mass Transfer, vol 19, pp 1127–1134, 1976 [4] Raithby, G D., and Hollands, K G T., Natural Convection, in Handbook of Heat Transfer Fundamentals, ed W M heat transfer engineering [16] [17] [18] Rohsenow, J P Hartnett, and E N Ganic, pp 6.25–6.26, McGraw-Hill, New York, 1985 McAdams, W H., Heat Transmission, 3rd ed., McGrawHill, New York, pp 176–177, 1954 Churchill, S W., and Chu, H H S., Correlating Equations for Laminar and Turbulent Free Convection From a Horizontal Cylinder, International Journal of Heat and Mass Transfer, vol 18, pp 1049–1053, 1975 Clemes, S B., Hollands, K G T., and Brunger, A P., Natural Convection Heat Transfer From Long Horizontal Isothermal Cylinders, ASME Journal of Heat Transfer, vol 116, pp 96–104, 1994 Kuehn, T H., and Goldstein, R J., Numerical Solution to the Navier–Stokes Equations for Laminar Natural Convection About a Horizontal Isothermal Circular Cylinder, International Journal of Heat and Mass Transfer, vol 23, pp 971–979, 1980 Farouk, B., and Guceri, S I., Natural Convection From a Horizontal Cylinder–Laminar Regime, ASME Journal of Heat Transfer, vol 103, pp 522–527, 1981 Minkowycz, W J., and Sparrow, E M., Local Nonsimilar Solutions for Natural Convection on a Vertical Cylinder, ASME Journal of Heat Transfer, vol 96, pp 178–183, 1974 Sparrow, E M., and Gregg, J L., Laminar Free Convection Heat Transfer From the Outer Surface of a Vertical Circular Cylinder, ASME Journal of Heat Transfer, vol 78, pp 1823–1829, 1956 Fujii T., and Uehara H., Laminar Natural Convective Heat Transfer From the Outer Surface of a Vertical Cylinder, International Journal of Heat and Mass Transfer, vol 13, pp 607–615, 1970 Popiel, C O., Wojtkowiak, J., and Bober, K., Laminar Free Convective Heat Transfer From Isothermal Vertical Slender Cylinder, Experimental Thermal and Fluid Sciences, vol 32, pp 607–613, 2007 Oosthuizen, P H., Free Convective Heat Transfer From Vertical Cylinders With Exposed Ends, Tranactions of the Canadian Society of Mechanical Engineering, vol 5, pp 231–234, 1978 Jafarpur, K., and Yovanovich, M M., Natural Convection from Horizontal Isothermal Elliptic Disks: Models and Experiments, Proc 35th Aerospace Sciences Meeting & Exhibit, AIAA, Reno, NV, 1997 Kobus, C J., and Wedekind, G L., An Experimental Investigation Into Natural Convection Heat Transfer From Horizontal Isothermal Circular Disks, International Journal of Heat and Mass Transfer, vol 44, pp 3381–3384, 2001 Krysa, J., and Wragg, A A., Free Convective Mass Transfer at Vertical Cylindrical Electrodes of Varying Aspect Ratio, Journal of Applied Electrochemistry, vol 22, pp 429–436, 1992 Wragg, A A., and Krysa, J., Modelling Natural Convection at Complex Surfaces and Solid Bodies Using vol 32 no 2011 M ESLAMI AND K JAFARPUR [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] Electrochemical Techniques and Flow Visualisation, Journal of Applied Electrochemistry, vol 37, pp 33–39, 2007 Oosthuizen, P H., Experimental Study of Free Convective Heat Transfer From Inclined Cylinders, ASME Journal of Heat Transfer, vol 98, pp 672–674, 1976 Al-Arabi, M., and Khamis, M., Natural Convection Heat Transfer From Inclined Cylinders, International Journal of Heat and Mass Transfer, vol 25, pp 3–15, 1982 Oosthuizen, P H., and Mansingh, V., Free and Forced Convection Heat Transfer From Short Inclined Circular Cylinder, Chemical Engineering Communications, vol 42, pp 333–348, 1986 Stewart, W E., Asymptotic Calculation of Free Convection in Laminar Three-Dimensional Systems, International Journal of Heat and Mass Transfer, vol 14, pp 1013–1031, 1971 Raithby, G D and Hollands, K G T., Analysis of Heat Transfer by Natural Convection (or Film Condensation) for Three Dimensional Flows, Proc 6th International Heat Transfer Conference, Toronto, Ontario, pp 187–192, 1978 Kobus, C J., and Wedekind, G L., An Empirical Correlation for Natural Convection Heat Transfer From Thin Isothermal Circular Disks at Arbitrary Angles of Inclination, International Journal of Heat and Mass Transfer, vol 45, pp 1159–1163, 2002 Kobus, C J., Investigation of Natural Convection Heat Transfer From Uniformly Heated (Isoflux) Thin Stationary Circular Disks at Arbitrary Angles of Inclination, Experimental Thermal and Fluid Sciences, vol 31, pp 191–195, 2007 Wragg, A A., Use of Electrochemical Techniques to Study Natural Convection Heat and Mass Transfer, Journal of Applied Electrochemistry, vol 21, pp 1047–1057, 1991 Krysa, J., Reuter, W., and Wragg, A A., Free Convective Mass Transfer at Circular Thin Disk Electrodes With Varying Inclination, International Journal of Heat and Mass Transfer, vol 48, pp 2323–2332, 2005 Yovanovich, M M., On the Effect of Shape, Aspect Ratio and Orientation upon Natural Convection From Isothermal Bodies of Complex Shape, ASME HTD, vol 82, pp 121–129, 1987 Jafarpur, K., Analytical and Experimental Study of Laminar Free Convective Heat Transfer From Isothermal Convex Bodies of Arbitrary Shape, Ph.D thesis, University of Waterloo, Waterloo, ON, Canada, 1992 Eslami, M., Dynamic Behavior of Body Gravity Function in Laminar Free Convection Heat Transfer From Isothermal Convex Bodies of Arbitrary Shape, M.Sc thesis, Shiraz University, Shiraz, Iran, 2008 heat transfer engineering 513 [31] Lee, S., Yovanovich, M M., and Jafarpur, K., Effects of Geometry and Orientation on Laminar Natural Convection from Isothermal Bodies, Journal of Thermophysics and Heat Transfer, vol 5, pp 208–216, 1991 [32] Bigdely, M R., Calculation of Conduction Limit Using Panel Method, M.Sc thesis, Shiraz University, Shiraz, Iran, 1998 [33] Churchill, S W., and Churchill, R U., A Comprehensive Correlating Equation for Heat and Component Transfer by Free Convection, AICHE Journal, vol 21, pp 604–606, 1975 [34] Yovanovich, M M., and Jafarpur, K., Bounds on Laminar Natural Convection From Isothermal Disks and Finite Plates of Arbitrary Shape for All Orientations and Prandtl Numbers, ASME HTD 264, pp 93–110, 1993 [35] Hassani, A V., An Investigation of Free Convection Heat Transfer from Bodies of Arbitrary Shape, Ph.D thesis, University of Waterloo, Waterloo, ON, Canada, 1987 [36] Yovanovich, M M., New Nusselt and Sherwood Numbers for Arbitrary Isopotential Geometries at Near Zero Peclet and Rayleigh Numbers, Proc 22nd Thermophysics Conference, AIAA, Honolulu, HI, 1987 [37] Hassani, A V., and Hollands, K G T., On Natural Convection Heat Transfer From Three-Dimensional Bodies of Arbitrary Shape, Journal of Heat Transfer, vol 111, pp 363–371, 1989 Mohammad Eslami is a Ph.D student in mechanical engineering at Shiraz University, Shiraz, Iran He worked on analytical modeling of natural convection heat transfer for his master’s thesis and received his M.S at Shiraz University in June 2008 His research interests have included convection and conduction heat transfer, numerical modeling of heat and fluid flow, electrokinetic flow in microchannels, and solar energy measurements and applications Khosrow Jafarpur is an associate professor of mechanical engineering at Shiraz University, Shiraz, Iran He received his Ph.D at the University of Waterloo, Canada, in 1992 and joined Shiraz University in the same year His research includes free convection heat transfer, solar energy measurement, and solar stills, as well as heat transfer (and optimization) in welding, porous media, and nanosystems He is the author or co-author of about 70 papers on these topics vol 32 no 2011 Heat Transfer Engineering, 32(6):514–520, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2010.506383 Temperature Determination Using Multispectral Radiation Thermometry Algorithms for Aluminum Alloys CHANG-DA WEN Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan Multispectral radiation thermometry (MRT) was applied to predict the aluminum surface temperature Experiments were conducted to measure the spectral intensity values for five different aluminum alloys, AL1100, AL2024, AL5083, AL6061, and AL7005, at 600 K, 700 K, and 800 K The experimental work is coupled with six MRT emissivity models encompassing mathematical and analytical functions to infer surface temperature Assessment of the MRT emissivity model is subject to parametric effects of number of wavelengths, alloy composition, and temperature Results show that increasing wavelength number does not significantly improve measurement accuracy while applying MRT If the emissivity model can represent well the real emissivity behaviors, a more accurate inferred temperature can be achieved Overall, most models achieve high accuracy in temperature prediction, except two emissivity models One particular emissivity model provides the best compensation for the aforementioned parametric influences INTRODUCTION Most processes in aluminum production require one to accurately measure the surface temperature For example, achieving superior microstructure and mechanical properties during extrusion requires precise knowledge of the part’s temperature during transit Therefore, accurate temperature determination and control are of paramount importance to attain desired mechanical properties, ensure product quality and reproducibility, and reduce cost Sensors requiring physical contact with a surface, such as thermocouples, are commonly used to measure the surface temperature in many industries However, the contact sensors may not be feasible for the fast transit of parts in processes such as extrusion and rolling and may change the surface physically or chemically Therefore, accurate, noncontact radiation thermometry is highly desired for aluminum production The author is grateful for the support of the National Science Council of Taiwan (with project number NSC-95-2221-E-006-393) The author also thanks J King Aluminum, Inc (JKAI), in Taiwan for the supply of steel samples and Dr Jongmook Lim of the Spectraline, Inc., for technical assistance and instrument support Address correspondence to Dr Chang-Da Wen, Department of Mechanical Engineering, National Cheng Kung University, No 1, University Road, Tainan 701,Taiwan E-mail: alexwen@mail.ncku.edu.tw Radiation thermometry is a popular alternative for temperature measurement This noncontact measurement method utilizes spectral radiance observation from the target surface to infer the surface temperature Determining the temperature can be accomplished by three categories of radiation thermometry that utilize radiance measurement at different number of wavelengths: spectral, dual-wavelength, and multispectral Spectral radiation thermometry requires radiance measurement at one wavelength and a constant emissivity value to infer the surface temperature Dual-wavelength radiation thermometry (DWRT) utilizes radiance measurements at two wavelengths and an emissivity compensation algorithm Multispectral radiation thermometry (MRT) employs radiance measurements at three or more wavelengths and an emissivity model Due to their inability to adequately compensate for the complex emissivity characteristics of aluminum alloys, the spectral and dual-wavelength radiation thermometry methods have limited use in specific applications and well defined situations The present study is based on the MRT method In this study, test samples encompassing a variety of aluminum alloys, AL1100, AL2024, AL5083, AL6061, and AL7005, were studied Spectral intensity values were first measured for aluminum alloys over the wavelength range of 2.91 to 4.13 µm and temperatures of 600, 700, and 800 K The experimental work was then complemented by six MRT emissivity models encompassing mathematical and analytical 514 C.-D WEN 515 Table Aluminum alloys tested in present study Alloy AL 1100 AL 2024 AL 5083 AL 6061 AL 7005 Applications Foil, cladding, surface finishing, sheet metal, spun hollow ware, and decorative parts Aircraft structures, truck wheels, and domestic products Small boats or larger yachts, and vehicle armor Aircraft structures, such as wings and fuselages, yacht construction, and bicycle frames or components Aircraft structures, keys,and Alclad product surfaces Heat treatability No Yes No Yes No Figure Temperature measurement facility functions to explore the accuracy of these models at inferring surface temperature subject to the interdependent parametric effects of the number of wavelengths, alloy composition, and temperature EXPERIMENTAL METHODS An experimental apparatus was configured and fabricated to facilitate intensity measurements for aluminum alloys at different temperatures As shown in Figure 1, this apparatus included a spectrometer (radiation thermometer), test sample heating assembly, temperature controller, power supply, translation stage, data acquisition system, and a blackbody for calibration A fast infrared array spectrometer (FIAS) model ES100 made by Spectraline, Inc., was used to simultaneously measure 160 discrete spectral radiation intensity values over a wavelength range of 1.2 to 4.8 µm The spectrometer was optically aligned in front of the test sample with the aid of an HeNe laser The radiation intensity from the target is incident on the entrance slit, and then ultimately dispersed over a staggered 160-element linear array PbSe detector The spectrometer software converted the voltages and pixel numbers from the linear array into wavelengths and intensities The intensity data collected in each spectrum is stored at 390 Hz The data acquisition is controlled by the drive circuit on the spectrometer A Windows-based graphic user interface (GUI), Infraspec Version 2, designed by Spectraline, Inc., is available for basic spectrometric functions The FIAS output can be either displayed with the aid of a graphical user interface or stored for data analysis As shown in Figure 2, the sample heating assembly consisted of cartridge heaters, heating block, test sample, and ceramic fiber blanket insulation The whole sample heating assembly was fastened by the aluminum frame and situated on a two-dimensional translation stage The aluminum test sample was held in contact with a heating block In order to minimize the temperature gradient, the heating block was fabricated from copper and surheat transfer engineering rounded by a thick blanket of high-temperature ceramic fiber insulation Three embedded cartridge heaters as the heat source were embedded in the heating block and a temperature controller with a type K thermocouple attached on the sample surface was used to heat the sample to the desired test temperature The thermocouple was inserted mm behind the test surface to monitor the sample’s temperature The temperature gradient between the thermocouple bead and the surface was negligible because of the high conductivity of the aluminum samples As shown in Table 1, five aluminum alloys that span a broad range of domestic and aerospace applications were supplied from J King Aluminum, Inc (JKAI), and machined to the size of 30 mm × 30 mm × 10 mm After the samples were machined to size, the test surface was cleaned in succession with acetone and methanol to get rid of oils, grease, or dirt The samples were handled with great care, and wrapped in fine tissue to protect them from any contact with roughening agents following the surface preparation The experiments were initiated by preheating the heating block to a temperature slightly above the desired value Next, a chromel-alumel (type K) thermocouple was inserted into the sample’s thermocouple hole, which was prepacked with high-thermal-conductivity boron nitride powder in order to ensure good thermal contact between the thermocouple bead and the sample The test sample was then pressed against the preheated heating block to initiate heat-up The desired sample temperature was achieved by manipulating the power input to the cartridge heaters Once the sample temperature reached steady state, the intensity data were recorded by the spectrometer MULTISPECTRAL RADIATION THERMOMETRY (MRT) Two different mathematical techniques of multispectral radiation thermometry are used to infer the temperature The first method is the exact technique, which employs an emissivity model with m unknown coefficients and radiation intensity measurements at m + wavelengths to infer temperature Coates [1] and Doloresco [2] concluded that the exact technique vol 32 nos 2011 516 C.-D WEN Figure Construction of aluminum test sample and heating assembly might cause over-fitting and result in large errors for using more than three wavelengths The other method, which can overcome the over-fitting problem, is the least-squares technique It employs least-squares fitting of the measured intensities to simultaneously deduce the best-fit values of emissivity and temperature The least-squares technique requires spectral intensity measurements at a minimum of m + wavelengths to use an emissivity model with m unknown coefficients This technique is commonly used in MRT The rationale is to determine the inferred temperature and the unknown emissivity coefficients by minimizing the chi-squared (χ2) value of the following equation: n χ2 = L λ,meas,i − L λ,gen,i (1) i=0 where Lλ,meas,i and Lλ,gen,i are the measured and generated values of spectral intensity, respectively Neglecting the intensity of irradiation from the surroundings that is reflected by the target surface and applying a Planck blackbody distribution, the generated spectral intensity can be simplified as L λ,gen (λ, T ) ∼ = ελ (λ) L λ,b (λ, T ) = ελ (λ) c1 c λ5 (e /λ T − 1) (2) heat transfer engineering where c1 = 1.191062 × 108 W-µm4-m−2-sr−1 and c2 = 1.438786 × 104 µm-K For emissivity models with exponential form, the linear leastsquares technique can be used to determine the inferred temperature and the unknown emissivity coefficients by minimizing the magnitude of χ2 in the following equation: n χ2 = ln L λ,meas,i − ln L λ,gen,i (3) i=0 In addition, the Planck blackbody distribution used in Eq (2) to determinate the generated value of spectral intensity, Lλ,gen,i, is approximated by Wien’s formula, L λ,b (λ, T ) = c1 c1 ∼ (4) = c c2 λ5 (e /λ T − 1) λ5 (e /λ T ) Therefore, a set of equations that is linear with respect to the temperature and the unknown emissivity coefficients can be created to simplify the computation The unfixed coefficient values in the emissivity model allow the multispectral radiation methods to have enough selectivity to represent the variable emissivity behaviors and are less affected by noise Moreover, the increased number of wavelengths also allows for the statistical reduction in temperature errors from measurement noise vol 32 nos 2011 C.-D WEN IST∗ , IWS, WLT, and WLT∗ Values exceeding ±50 K have been purposely deleted to help point out accurate models and their predictive trends The results are shown for five different aluminum alloys—AL1100, AL2024, AL5083, AL6061, and AL7005—two different numbers of wavelengths (n and N), and three different temperatures (600, 700, and 800 K) The value n is the required minimum number of wavelengths using leastsquares technique, which is equal to the number of unknown coefficients in the emissivity model plus two, and N is the total number of wavelengths available in the examined wavelength range A comprehensive analysis of these results yields some useful conclusions and trends Following is a discussion of the effects of the number of wavelengths, alloy composition, and temperature, as they relate to temperature prediction for the MRT emissivity models A first look at the table appears to be somewhat puzzling However, half of the temperature predictions by MRT emissivity models provide the absolute temperature error under ±50 K and a quarter of the results are under ±20 K The occurrence of the accurate measurements that have errors below K is random They are the HRR model for AL1100 and AL5083 at 700 K, and AL2024 at 600 K; the IST model for AL1100 and AL6061 at 600 K; the IST∗ model for AL2024 at 600 K, and AL5083 at 700 K; and the WLT∗ model for AL1100 and AL6061 at 600 K Statistically, most models achieve high accuracy in temperature prediction, except the IWS and WLT models The HRR model gives the largest number of good results and provides the best overall compensation for different alloys, number of wavelengths, and temperatures Figure provides an alternative representation of temperature errors (abbreviated “ T E.”) In addition to Table 3, most models have many data points falling within a ±50 K error band The HRR model provides the small deviation and shows the best agreement with the data The IWS and WLT models generally underpredict the temperature Table Mathematical form of emissivity models examined in present study Emissivity model Mathematical function T 1/2 λ Hagen–Ruben relation (HRR) ελ = a × Inverse spectral temperature-1 (IST) ελ = exp Inverse spectral temperature-2 (IST∗ ) Inverse wavelength squared (IWS) Wavelength temperature-1 (WLT) ελ = exp a0 + Wavelength temperature-2 (WLT∗ ) ελ = a0 Tλ a1 Tλ 1+a0 λ2 ελ = exp (a0 λ + a1 T ) a1 Tλ ελ = exp a0 λ + n N 65 65 65 65 65 65 Note n is the minimum number of wavelength required in MRT model and N is the total number of wavelengths available in the examined wavelength range Tλ is the spectral radiance temperature, which is the equivalent blackbody temperature of the measured spectral intensity; a0 and a1 are the unknown coefficients in the emissivity model As shown in Table 2, six selected MRT emissivity models encompassing mathematical and analytical functions are examined in this study for accuracy in temperature determination They are the Hagen–Rubens relation (HRR) model [3–9], inverse spectral temperature (IST) model [6–9], inverse wavelength squared (IWS) model [7–10], and wavelength temperature (WLT) model [6, 8, 9, 11], and two variations to IST and WLT models (IST∗ and WLT∗ ) RESULTS AND DISCUSSION Table provides absolute errors in the inferred temperature predicted by six MRT emissivity models, HRR, IST, Table Absolute temperature error (K) in inferred temperature by MRT for aluminum samples at 600, 700, and 800 K, from 2.91 to 4.13 µm, for six models HRR T (K) n N AL 1100 600 700 800 600 700 800 600 700 800 600 700 800 600 700 800 –47 –5 –19 –30 –13 18 –39 –36 AL 5083 AL 6061 AL 7005 13 32 –37 –43 –15 –40 –44 IST∗ IST Sample AL 2024 517 n N n –46 –38 –10 –33 –11 –9 –26 –18 –14 23 –43 –50 –23 –48 –42 –22 –36 21 –46 –24 –1 –14 –29 –48 –16 46 –9 IWS N WLT∗ WLT n N n N n –45 –37 –37 –46 12 –30 –6 –34 –13 –44 –19 –44 –24 19 11 –35 21 –4 –21 –42 –30 –50 –47 N 32 –19 30 –44 –23 –43 –32 46 –50 –26 –35 –39 –23 –40 Note Missing values correspond to errors beyond ±50 K Numbers of wavelengths are given as n, the minimum number of wavelengths required in MRT model, and N, the total number of wavelengths available in the examined wavelength range heat transfer engineering vol 32 nos 2011 518 C.-D WEN Table The best model and the inferred temperature error for each aluminum sample Minimum absolute temperature error (K) 600 Sample AL 1100 AL 2024 AL 5083 AL 6061 AL 7005 n 13 15 (IST) (IST∗ ) (HRR) (IST) (HRR) 700 N (WLT∗ ) (HRR) 19 (HRR) (IST) 23 (HRR) 800 n 19 35 40 N (HRR) (HRR) (IST∗ ) (WLT∗ ) (HRR) 39 32 44 39 (HRR) (IWS) (HRR) (HRR) (IST∗ ) n 13 43 (IST∗ ) (IST∗ ) (HRR) (HRR) (IST∗ ) N 33 (IST) 42 (IST) (HRR) 70 (IST) 23 (IST∗ ) Note n is minimum number of wavelengths required in MRT model; N is total number of wavelengths available in the examined wavelength range Figure Comparison of real temperature with inferred temperature by MRT emissivity models of (a) HRR, (b) IST, (c) IST∗ , (d) IWS, (e) WLT, and (f) WLT∗ for all test alloys at three different temperatures heat transfer engineering vol 32 nos 2011 C.-D WEN One feature that makes MRT more preferred than SRT and DWRT is that an increase in the number of wavelengths allows for the statistical reduction in temperature errors from measurement noise However, as the results show in Table 3, increasing the number of wavelengths doesn’t significantly enhance measurement accuracy for most models The required minimum number of wavelengths n actually gives satisfactory results either using linear or nonlinear least-squares technique in this study Similar results also have been reported by Doloresco [2], Gathers [12], and Gardner et al [13] Therefore, it is sufficient to employ the required minimum number of wavelengths to infer the temperature The percentages of inferred temperature error predicted by the best model for each alloy at different temperatures and numbers of wavelengths are shown in Table Statistics show that the HRR model is most frequently the best This similar result was also found earlier in Table This coincidence shows that the HRR emissivity model not only achieves good temperature predictions for different alloys, number of wavelengths, and 519 temperatures, but also provides the smallest inferred temperature errors How an emissivity model affects the accuracy of temperature prediction is demonstrated here through the following example As shown in Table 3, for AL5083 at 800 K with number of wavelengths n, three representative emissivity models, HRR, IST, and IST∗ , have temperature errors, 13 K, 23 K, and –14 K, respectively In other words, in this case the HRR model is the most accurate MRT emissivity model in temperature determination, followed by the IST∗ model, and then the IST model Figure 4a shows the comparison of the measured spectral intensity for AL5083 at 800 K and the generated spectral intensity in Eq (2), which is inferred by the emissivity models HRR, IST, and IST∗ There is not much difference among them since the leastsquares technique in Eq (1) is applied The generated spectral intensity value, Lλ,gen,i, from each emissivity model should be in between the measured spectral intensity values, Lλ,meas,i in order to minimize the chi-squared (χ2) value and determine the inferred temperature and the unknown emissivity coefficients However, in Figure 4b, there is a big difference between the real emissivity value and that inferred from each model The emissivity distribution inferred by the HRR model, which has the most accurate temperature prediction, is the closest one to the real emissivity distribution The next closest to the real emissivity spectrum is the one inferred by the IST∗ model, which has the second best temperature prediction The furthest one away from the real emissivity values is inferred by the IST model, which has the worst temperature prediction Therefore, we can find that the closer the generated emissivity spectrum and the measured one, the more accurate is the inferred temperature; i.e., if the emissivity model can represent well the real emissivity behaviors, a more accurate inferred temperature can be achieved CONCLUSIONS Figure Comparison between experimental data and predictions of HRR, IST, and IST∗ model for (a) radiation intensity and (b) spectral emissivity of AL5083 at 800 K heat transfer engineering Experiments were conducted to measure the spectral intensity values for five different aluminum alloys, AL1100, AL2024, AL5083, AL6061, and AL7005, at 600, 700, and 800 K The experimental work is coupled with six multispectral radiation thermometry (MRT) emissivity models encompassing mathematical and analytical functions to infer surface temperature Assessment of MRT emissivity models is subject to parametric effects of the number of wavelengths, alloy composition, and temperature The present findings show that (1) half of the temperature predictions by MRT emissivity models provide the absolute temperature error under ±50 K and a quarter of the results are under ±20 K; (2) every model also produces its good temperature prediction (under K) in certain conditions; and (3) increasing the number of wavelengths doesn’t significantly improve measurement accuracy for most models It is sufficient to employ the required minimum number of wavelengths to infer the temperature while using MRT least-squares technique (4) Overall, most models achieve high accuracy in temperature vol 32 nos 2011 520 C.-D WEN prediction, except the IWS and WLT models The HRR model gives good results most frequently and provides the best overall compensation for different alloys, number of wavelengths, and temperatures (5) The closer the inferred emissivity value and real one, the more accurate is the inferred temperature; i.e., if the emissivity model can represent well the real emissivity behaviors, a more accurate inferred temperature can be achieved [4] [5] NOMENCLATURE c1 c2 DWRT HRR IST IWS Lλ,b Lλ,gen Lλ,meas MRT m n N SRT T Tλ WLT first thermal radiation constant second thermal radiation constant dual-wavelength radiation thermometry Hagen–Rubens relation emissivity model inverse spectral temperature emissivity model inverse wavelength squared emissivity model spectral intensity of blackbody radiation generated spectral intensity of radiation measured spectral radiation intensity multispectral radiation thermometry number of unknown coefficients of emissivity model required minimum number of wavelengths total number of wavelengths available in the examined wavelength range spectral radiation thermometry surface temperature spectral radiance temperature wavelength temperature emissivity model [6] [7] [8] [9] [10] [11] Greek Symbols ελ λ χ2 spectral emissivity wavelength least-squares error [12] Subscripts b gen meas λ [13] blackbody generated measured spectral REFERENCES [1] Coates, P B., Multi-Wavelength Pyrometry, Metrologia vol 17, pp 103–109, 1981 [2] Doloresco, B K., Review of Multispectral Radiation Thermometry and Development of Constrained Minimization Method, M.S thesis, Purdue University, West Lafayette, IN, 1986 [3] Dmitriev, V D., and Kholopov, G K., Radiant Emissivity of Tungsten in the Infrared Region of the Spectrum, Zhurheat transfer engineering nal Prikladnoi Spektroskopii, vol 2, no 6, pp 481–488, 1965 Haugh, M J., Radiation Thermometry in the Aluminum Industry, in Theory and Practice of Radiation Thermometry, eds D P DeWitt and G D Nutter, John Wiley and Sons, New York, pp 905–971, 1988 Mihalow, F A., Radiation Thermometry in the Steel Industry, in Theory and Practice of Radiation Thermometry, eds D P DeWitt and G D Nutter, John Wiley and Sons, New York, pp 861–904, 1988 Pellerin, M A., Multispectral Radiation Thermometry: Emissivity Compensation Algorithm, M.S thesis, Purdue University, West Lafayette, IN, 1990 Pellerin, M A., Multispectral Radiation Thermometry for Industrial Application, Ph.D thesis, Purdue University, West Lafayette, IN, 1999 Wen, C., and Mudawar, I., Emissivity Characteristics of Roughened Aluminum Alloy Surfaces and Assessment of Multispectral Radiation Thermometry (MRT) Emissivity Models, International Communications in Heat and Mass Transfer, vol 47, pp 3591–3605, 2005 Wen, C., Emissivity Characteristics of Aluminum Alloy Surfaces and Assessment of Multispectral Radiation Thermometry (MRT) Emissivity Models, Ph.D thesis, Purdue University, West Lafayette, IN, 2005 Duvaut, T., Georgeault, D., and Beaudoin, J L., Multiwavelength Infrared Pyrometer: Optimization and Computer Simulations, Infrared Physics & Technology, vol 36, pp 1089–1103, 1995 Dail, G J., Fuhrman, M G., and DeWitt, D P., Evaluation and Extension of the Spectral-ratio Radiation Thermometry Method, Proc 4th Int Aluminum Extrusion Technology Seminar, Chicago, vol 2, pp 209–213, 1988 Gathers, G R., Analysis of Multiwavelength Pyrometry Using Nonlinear Chi-Square Fits and Monte Carlo Methods, International Journal of Thermophysics, vol 13, no 3, pp 539–554, 1992 Gardner, J L., Jones, T P., and Davies, M R., A SixWavelength Radiation Pyrometer, High Temperatures– High Pressures, vol 13, pp 459–466, 1981 Chang-Da Wen is an assistant professor of mechanical engineering at the National Cheng Kung University, Taiwan He received his M.S degree in mechanical engineering from the University of Michigan, Ann Arbor, MI, USA, and the Ph.D degree in mechanical engineering from Purdue University, West Lafayette, IN, USA His research interests are in the areas of thermal/fluid sciences Special interests include radiation thermometry, electronic cooling, two-phase flow and heat transfer, thermal management, material processing, surface analysis, and specialized heat transfer projects He is a member of ASME, CSME, and STAM and was a recipient of the NCKU ME Excellent Teacher Award for 2007 and 2008 vol 32 nos 2011 Heat Transfer Engineering, 32(6):521–523, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2011.542085 book review corner Ralph L Webb Book Review Editor The present “Books Received” listing contains several interesting new titles, heat transfer and refrigeration/air-conditioning Brief content description is given of all listed books Also, note that the 41st edition of the book, Steam: Its generation and use, published by The Babcock & Wilcox Co is a new release If you would like to prepare a detailed review of one of the books listed below, please e-mail me (Ralph.Webb@psu.edu) The book is yours to keep for preparing the review books received (with brief content description) Mechanical Engineering Advanced Heat and Mass Transfer, Amir Faghri, Yuwen Zhang, John Howell, 956 pages, Global Digital Press, 2010, ISBN: 978–0-9842760–0-4, $89.95 The chapters of this text book can be viewed on-line at The Thermal Fluids Central website https://www.thermalfluidscentral.org/ebooks/book-intro.php?b=37 In addition one may access, and download, 130 different pdf files of ppt lectures of the book at website https://www.thermalfluidscentral.org/eresources/handle/item/2 The number on each pdf file corresponds to the chapter/section addressed Brief Content Review This textbook provides a uniqueness not found in other competing books This book covers the subjects of conduction, convection, boiling, condensation, and thermal radiation in a single course at the intermediate or advanced level This approach is in contrast to the traditional approach of having a course and textbook for the separate subjects of single-phase, two-phase convection, conduction, and radiation Thus, this textbook seeks to present the subject of heat and mass transfer with a focus on the significant advances in the field in the last decade, while emphasizing the basic, fundamental principles A closely related key objective is to provide focus on modern applications of heat and mass transfer (e.g., nano-technology, biotechnology, energy, material processing, etc.), all of which are emphasized via examples and homework problems Further examples of modern topics are heat and mass transfer applications such as gas turbines, electronic cooling, heat pipes, and food processing equipment, and emerging technologies in sustainable energy including biological systems, security, information technology and nanotechnology This is in addition to traditional topics in heat exchange technology Other topics, which are lacking in most other textbooks, are integrated in the present book (e.g., porous media, micro-scale, heat transfer, and multi-phase, multi-component systems) Thus, this single volume advanced book provides both basic and advanced application materials to senior undergraduate and graduate students instead of relying upon several books Also, professional engineers will find this book an up-to-date important reference for a wide range of topics—from traditional to emerging heat and mass transfer systems In addition, the book addresses phase change processes, including boiling, condensation, melting, solidification, sublimation, and vapor deposition from one perspective in the context of the fundamental treatment Although there are separate chapters on boiling and condensation, the reviewer saw very little material typically addressed in a course on forced convection two-phase flow and heat transfer The book presents the generalized integral, differential, and average formulations for the governing equations of transport phenomena The book employs a top-down approach that first emphasizes the basic physics of the problem by beginning with a general governing equation and then reducing it for the particular problems or analysis addressed In addition, the foundations of numerical solutions of convective flow are concisely discussed, to provide understanding of the basis and limitations of these methods The book is not narrowly focused on traditional issues in mechanical engineering Rather it is applicable to a wide variety of engineering disciplines—from mechanical and chemical to biomedical and materials engineering—who must master the principles of heat and mass transfer in analyzing and designing any system or systems wherein heat and mass are transferred This textbook provides a clear presentation of the fundamentals, focused homework problem sets, and tangible examples of how this knowledge is put to use in traditional and modern engineering design Professional engineers, too, will find this 521 522 book review corner book invaluable as reference for everything from traditional to emerging heat and mass transfer system A solution manual is available to instructors, who use the book for course instruction Summary of Book Chapters: Introduction; Generalized Governing Equations; Heat Conduction; External Convective Heat and Mass Transfer; Internal Convective Heat and Mass Transfer; Natural Convection; Condensation and Evaporation; Boiling; Fundamentals of Thermal Radiation; Heat Transfer by Radiation Rather than being contained in an individual chapter, mass transfer is integrated throughout the book Springer Handbook of Mechanical Engineering, Grote, KarlHeinrich; Antonsson, Erik K (Eds.), 2009, XXVIII, 1580 p 1822 illus., 1551 in color With DVD., Hardcover, ISBN: 978-3-540-49131-6 Brief Content Review This is a massive 1551 page handbook! Mechanical Engineering handbooks typically cover application of principles of physics, design, manufacturing, and maintenance of mechanical systems In addition to these main areas, specialized fields are necessary to prepare future engineers for their positions in industry, such as mechatronics and robotics, transportation and logistics, fuel technology, automotive engineering, biomechanics, vibration, optics and others The Springer Handbook of Mechanical Engineering devotes its contents to all areas of interest for the practicing engineer Authors from all over the world have contributed with their expertise and support the globally working engineer in finding a solution for today’s mechanical engineering problems Each subject is discussed in detail and supported by numerous figures and tables DIN standards are retained throughout and ISO equivalents are given where possible The text offers a concise but detailed and authoritative treatment of the topics with full references Key Topics Include: • • • • • • • • • • • • • Engineering Mathematics Mechanics Materials Science and Tribology Thermodynamics Design of Machine Elements Manufacturing Engineering Measuring and Quality Control Engineering Design Pressure Vessels and Heat Exchangers Turbomachinery Transportation Systems Construction and Earth Moving Equipment Power Generation heat transfer engineering • Electrical Engineering • Enterprise Organization and Operation Refrigeration Cycles and Systems, Ibrahim Dincer, Mehmet Kanoglu, John Wiley and Sons, 2010—480 pages, US $120.00, 2010 480 Pages, Hardcover, ISBN-10: 0-47074740-4, ISBN-13: 978-0-470-74740-7 Also published online: JUL 2010 Brief Content Review Refrigeration Systems and Applications, 2nd edition offers a comprehensive treatise that addresses real-life technical and operational problems, giving the reader an understanding of the fundamental principles and the practical applications of refrigeration technology New and analysis techniques (including exergy as a potential tool), models, correlations, procedures and applications and recent developments in the field are included—many of which are taken from the author’s research activities in this area The book also includes discussion of global warming issues and its potential solutions The book discusses industrial technical and operational problems, as well as new performance improvement techniques and tools for better design and analysis The contents include fundamental aspects of thermodynamics, fluid flow, and heat transfer; refrigerants; refrigeration cycles and systems; advanced refrigeration cycles and systems, including some novel applications; heat pumps; heat pipes; and many more It provides explanations, numerous new chapter-end problems and worked-out examples as learning aids for students and instructors Refrigeration applications include the cooling of electronic devices to food cooling processes This 2nd edition forms a useful reference source for graduate and postgraduate students and researchers in academia and as well as practicing engineers, who are interested in refrigeration systems and applications, and the methods and analysis tools for their analysis, design and performance improvement The Chapters address: • • • • • • • • • • refrigeration cycles and systems; vapor-compression refrigeration systems; energy analysis of vapor-compression refrigeration cycle; practical vapor-compression refrigeration cycle; air purging methods—two ways to purge systems of air, manual or automatic; air-standard refrigeration cycles—also as reverse Brayton cycles; Absorption–Refrigeration Systems (ARSs)—ups and downs; basic ARS using ammonia–water solution; two-stage or two-effect ARS—vapors driven off by heating first-stage concentrator, driving off more water; absorption-augmented engine-driven refrigeration system Chapter is published on line at http://onlinelibrary wiley.com/doi/10.1002/9780470661093.ch4/summary vol 32 no 2011 book review corner Thermal Design: Heat Sinks, Thermoelectrics, Heat Pipes, Compact Heat Exchangers, and Solar Cells, HoSung Lee, Hardcover, ISBN: 978-0-470-49662-6, 648 pages, November 2010 US $150.00 Brief Content Review This book is written as a senior undergraduate or the firstyear graduate textbook, covering modern thermal devices such as heat sinks, thermoelectric generators and coolers, heat pipes, and heat exchangers as design components in larger systems These devices are becoming increasingly important and fundamental in thermal design across such diverse areas as microelectronic cooling, green or thermal energy conversion, and thermal control and management in space, etc However, there is no textbook available that specifically covers this range of topics The book may be used as a capstone design course after the fundamental courses such as thermodynamics, fluid mechanics, and heat transfer The underlying concepts in this book cover 1) the understanding of the physical mechanisms of the thermal devices with the essential formulas and detailed derivations, and 2) designing the thermal devices in conjunction with mathematical modeling, graphical optimization, and occasionally computational-fluid-dynamic (CFD) simulation Important design examples are developed using the commercial software, MathCAD, which allows the students to easily reach the graphical solutions even with highly detailed processes Hence, the design concept is embodied through the example problems The graphical presentation generally provides designers or students with the rich and flexible solutions toward achieving the optimal design A solutions manual will be provided Steam: Its generation and use, 41st Edition, Eds, J B Kitto and S C Stultz, 2005, The Babcock & Wilcox Co With DVD., Hardcover, ISBN: 0-9634570-1-2 The book may be heat transfer engineering 523 ordered from the Babcock & Wilcox Co website for $105 http://www.babcock.com/library/steam.html Brief Content Review The 41st Edition of this book published by The Babcock & Wilcox Company, details advances in the production of steam and the utilization of all fuel types This massive, 45 mm thick, 50 chapter edition has been updated and revised and includes rewritten sections on emissions control, environmental protection, and advanced steam generator designs for the 21st century Book includes a CD, which contains all chapters and appendices in the book in pdf format Twisted-Tape-Generated Single-Phase Swirl Flow Through Ducts, Sujoy Saha, paperback, ISBN 13:978-3-639-269413, 284 pages, VDM Verlag Dr Muller Aktiengesellschaft & Co KG, 2010, $98.00 Brief Content Review Professor Saha is an internationally recognized researcher on the subject of twisted-tapes Different types of twisted-tape inserts in internal flow through ducts of different cross-sectional geometry are one such passive heat transfer technique (it does not require additional expenditure of external energy) This book provides distinctly different instances of using variants of twisted tapes, for laminar and turbulent flow, either alone or in combination with other enhancement techniques such as ribs and corrugations The book provides the professional engineer essential tools, heat transfer and pressure drop characteristics and correlations to design more energy-efficient and less costly heat exchangers Researchers and academics will also find the book useful for their research vol 32 no 2011 [...]... Convergent Channel With Uniformly Heated Conductive Walls, International Communications in Heat and Mass Transfer, vol 32, no 6, pp 758–769, 2005 [12] Bianco, N., Manca, O., and Nardini, S., Experimental Investigation on Natural Convection in a Convergent Channel With Uniformly Heated Plates, International Journal of Heat and Mass Transfer, vol 50, pp 2772–27 86, 2007 [13] Bianco, N., Langellotto, L., Manca,... 135–1 46, 2007 [30] Fluent 6.2 User Manual, Fluent, Inc., Lebanon, NH, 2006 [31] Bianco, N., Langellotto, L., Manca, O., Nardini, S., and Naso, V., Converging on New Cooling Technology, Fluent News, p 28, summer, 2005 [32] Fujii, T., and Imura, H., Natural Convection Heat Transfer from a Plate With Arbitrary Inclination, International Journal of Heat and Mass Transfer, vol 15, p 752, 1972 heat transfer engineering. .. American Society of Mechanical Engineering, and Unione Italiana di Termofluidodinamica UIT He has co-authored more than 270 refereed journal and conference publications He is currently a member of the editorial advisory boards for The Open Thermodynamics Journal, The Open Fuels & Energy Science Journal, and Advances in Mechanical Engineering vol 32 no 6 2011 Heat Transfer Engineering, 32(6):455–4 66, 2011. .. Manca, O., and Naso, V., Numerical Analysis of Radiative Effects on Natural Convection in Vertical Convergent and Symmetrically Heated Channels, Numerical Heat Transfer Part A, vol 49, pp 369–391, 2006 [14] Bianco, N., Langellotto, L., Manca, O., and Nardini, S., An Experimental Study of Radiative Effects On Natural Convection in Air in Convergent Channels, International Journal of Heat and Mass Transfer, ... systems engineering, heat exchanger networks, refinery process design, surfactant enhanced oil recovery, membrane technology, and electrodeless plating vol 32 no 6 2011 Heat Transfer Engineering, 32(6):467–475, 2011 Copyright C Taylor and Francis Group, LLC ISSN: 0145-7632 print / 1521-0537 online DOI: 10.1080/01457632.2010.506169 The Effect of Tube Flattening on Flow Boiling Heat Transfer Enhancement... heat transfer The authors express their thanks to the School of Mechanical Engineering, College of Engineering, University of Tehran, for financial support of the present experimental work Address correspondence to Professor M A Akhavan-Behabadi, School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran E-mail: akhavan@ut.ac.ir performance for the mass velocity ranges... 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