In the present study, an analytical solution for 2D vapor flow in flat plate heat pipes is presented. The governing equations are solved analytically using the homotopy perturbation method, and numerically using the finite volume method, based on collocated grids. The analytical results are obtained for nondimensional velocity profiles and axial pressures distribution along the entire length of the heat pipe, and compared with the numerical ones. It is shown that there is a relatively small difference of about 1% in the worst case between the analytical and numerical results. Furthermore, the effects of the Reynolds number and the ratio of condenser to evaporator lengths on the flow variables are discussed.
Issue Section:
Technical Briefs
1.
Basiulis
, A.
, Tanzer
, H.
, and McCabe
, S.
, 1986, “Thermal Management of High Power PWB’s Through the Use of Heat Pipe Substrates
,” Proceedings of the Sixth Annual International Electronics Packaging Conference
, San Diego, CA, Vol. 6
, p. 501
.2.
Rightley
, M. J.
, Tigges
, C. P.
, Givler
, R. C.
, Robino
, C. V.
, Mulhall
, J. J.
, and Smith
, P. M.
, 2003, “Innovative Wick Design for Multi-Source Flat Plate Heat Pipes
,” Microelectron. J.
0026-2692, 34
, pp. 187
–194
.3.
Thomson
, M.
, Ruel
, C.
, and Donato
, M.
, 1989, “Characterization of a Flat Plate Heat Pipe for Electronic Cooling in a Space Environment
,” Proceedings of the 1989 National Heat Transfer Conference, Heat Transfer in Electronics HTD
, Vol. 111
, pp. 59
–65
.4.
Ooijen
, H.
, and Hoogendoorn
, C. J.
, 1979, “Vapor Flow Calculations in a Flat-Plate Heat Pipe
,” AIAA J.
0001-1452, 17
, pp. 1251
–1259
.5.
Vafai
, K.
, Zhu
, N.
, and Wang
, W.
, 1992, “Analysis of Flow and Heat Transfer Characteristics of an Asymmetrical Flat Plate Heat pipe
,” Int. J. Heat Mass Transfer
0017-9310, 35
, pp. 2087
–2099
.6.
Vafal
, K.
, Zhu
, N.
, and Wang
, W.
, 1995, “Analysis of Asymmetrical Disk-Shaped and Flat-Plate Heat Pipes
,” ASME J. Heat Transfer
0022-1481, 117
, pp. 209
–218
.7.
Zhu
, N.
, and Vafai
, K.
, 1998, “Vapor and Liquid Flow in an Asymmetrical Flat Plate Heat Pipe: A Three Dimensional Analytical and Numerical Investigation
,” Int. J. Heat Mass Transfer
0017-9310, 41
, pp. 159
–174
.8.
Zhu
, N.
, and Vafai
, K.
, 1998, “Analytical Modeling of the Startup Characteristics of Asymmetrical Flat Plate and Disk-Shaped Heat Pipes
,” Int. J. Heat Mass Transfer
0017-9310, 41
, pp. 2619
–2637
.9.
Wang
, Y.
, and Vafai
, K.
, 2000, “Transient Characterization of Flat Plate Heat Pipes During Startup and Shutdown operations
,” Int. J. Heat Mass Transfer
0017-9310, 43
, pp. 2641
–2655
.10.
Xuan
, Y.
, Hong
, Y.
, and Li
, Q.
, 2004, “Investigation on Transient Behaviors of Flat Plate Heat Pipes
,” Exp. Therm. Fluid Sci.
0894-1777, 28
, pp. 249
–255
.11.
Chen
, Y. S.
, Chien
, K. H.
, Wang
, C. C.
, Hung
, T. C.
, and Pei
, B. S.
, 2006, “A Simplified Transient Three-Dimensional Model for Estimating the Thermal Performance of the Vapor Chambers
,” Appl. Therm. Eng.
1359-4311, 26
, pp. 2087
–2094
.12.
Sonan
, R.
, Harmand
, S.
, Pellé
, J.
, Leger
, D.
, and Fakès
, M.
, 2008, “Transient Thermal and Hydrodynamics Model of Flat Heat Pipe for the Cooling of Electronics Components
,” Int. J. Heat Mass Transfer
0017-9310, 51
, pp. 6006
–6017
.13.
Koito
, Y.
, Imura
, H.
, Mochizuki
, M.
, Saito
, Y.
, and Torii
, S.
, 2006, “Numerical Analysis and Experimental Verification on Thermal Fluid Phenomena in Vapor Chamber
,” Appl. Therm. Eng.
1359-4311, 26
, pp. 1669
–1676
.14.
Boukhanouf
, R.
, Haddad
, A.
, North
, M. T.
, and Buffone
, C.
, 2006, “Experimental Investigation of a Flat Plate Heat Pipe Performance Using IR Thermal Imaging Camera
,” Appl. Therm. Eng.
1359-4311, 26
, pp. 2148
–2156
.15.
Chien
, L.
, and Chang
, C. C.
, 2002, “Experimental Study of Evaporator Resistance on Porous Surface in Flat Heat Pipes
,” Proceedings of the Inter Society Conference on Thermal Phenomena IEEE
, pp. 1052
–1057
.16.
Simura
, T.
, Sho
, H.
, and Nakamura
, Y.
, 2002, “The Aluminum Flat Heat Pipe Using Cyclopentane as Working Fluid
,” Proceedings of the Inter Society Conference on Thermal Phenomena IEEE
, pp. 224
–229
.17.
Chesser
, J. B.
, Peterson
, G. P.
, and Lee
, S.
, 2000, “A Simplified Method for Determining the Capillary Limitation of Flat Heat Pipes in Electronics Cooling
,” Proceedings of the NHTC ‘00, Thirty-Fourth National Heat Transfer Conference
.18.
Um
, J. Y.
, Chow
, L. C.
, and Baker
, K.
, 1994, An Experimental Investigation of Flat Heat Pipe, Fundamentals of Heat Pipes
, ASME HTD
, New York
, Vol. 278
, pp. 21
–26
.19.
He
, J. H.
, 1998, “Approximate Analytical Solution for Seepage Flow With Fractional Derivative in Porous Media
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 167
, pp. 57
–68
.20.
He
, J. H.
, 1999, “Homotopy Perturbation Technique
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 178
(3–4
), pp. 257
–262
.21.
He
, J. H.
, 2000, “A Coupling Method of Homotopy Technique and Perturbation Technique for Nonlinear Problems
,” Int. J. Non-Linear Mech.
0020-7462, 35
, pp. 37
–43
.22.
He
, J. H.
, 2006, “Homotopy Perturbation Method for Solving Boundary Value Problems
,” Phys. Lett. A
0375-9601, 350
(1–2
), pp. 87
–88
.23.
He
, J. H.
, 2006, “Some Asymptotic Methods for Strongly Nonlinear Equations
,” Int. J. Mod. Phys. B
0217-9792, 20
(10
), pp. 1141
–1199
.24.
Ariel
, P. D.
, 2007, “The Three-Dimensional Flow Past a Stretching Sheet and the Homotopy Perturbation Method
,” Comput. Math. Appl.
0898-1221, 54
, pp. 920
–925
.25.
Ganji
, D. D.
, and Sadighi
, A.
, 2006, “Application of He’s Homotopy Perturbation Method to Nonlinear Coupled Systems of Reaction Diffusion Equations
,” Int. J. Nonlinear Sci. Numer. Simul.
1565-1339, 7
(4
), pp. 411
–418
.26.
Ganji
, D. D.
, 2006, “The Application of He’s Homotopy Perturbation Method to Nonlinear Equations Arising in Heat Transfer
,” Phys. Lett. A
0375-9601, 355
, pp. 337
–341
.27.
Siddiqui
, A. M.
, Mahmood
, R.
, and Ghor
, Q. K.
, 2006, “Thin Film Flow of a Third Grade Fluid on a Moving Belt by He’s Homotopy Perturbation Method
,” Int. J. Nonlinear Sci. Numer. Simul.
1565-1339, 7
(1
), pp. 7
–14
.28.
Patankar
, S. V.
, 1980, Numerical Heat Transfer and Fluid Flow
, Hemisphere
, New York
.29.
Ferziger
, J. H.
and Peric
, M.
, 1999, Computational Methods for Fluid Dynamics
, 2nd ed., Springer
, New York
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