Similarity solutions for flows and heat transfer in microchannels between two parallel plates

International Journal of Heat and Mass Transfer

Volumn 54, Issue 11-12, 2011, Pages 2349-2354

  Wang, Z C ^a,b   Tang, D W ^a   Hu, X G ^a  

^a INSTITUTE OF ENGINEERING THERMOPHYSICS   (China)

^b UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Homotopy analysis method; Temperature jump; Velocity slip; Viscous dissipation

Indexed keywords

ANALYTICAL EXPRESSIONS; BRINKMAN NUMBER; CONSTANT HEAT FLUX; CONSTANT WALL TEMPERATURE; ENERGY EQUATION; FLOW FRICTIONS; GOVERNING EQUATIONS; HOMOTOPY ANALYSIS METHODS; INTERACTIVE EFFECT; KNUDSEN NUMBERS; NEWTONIAN FLUIDS; NONLINEAR DIFFERENTIAL EQUATION; PARALLEL PLATES; POISEUILLE NUMBERS; SIMILARITY SOLUTION; SIMILARITY TRANSFORMATION; TEMPERATURE JUMP; THERMAL BOUNDARY CONDITIONS; VELOCITY SLIP; VELOCITY SLIPS; VISCOUS DISSIPATION;

BOUNDARY CONDITIONS; FORCED CONVECTION; HEAT FLUX; MICROCHANNELS; MIXED CONVECTION; NONLINEAR EQUATIONS; NUSSELT NUMBER; PLATES (STRUCTURAL COMPONENTS); TABLE LOOKUP; VELOCITY; VELOCITY DISTRIBUTION; VISCOUS FLOW;

NAVIER STOKES EQUATIONS;

EID: 79953055208     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2011.02.027     Document Type: Article

References (31)

1. A. Beskok, and G.E. Karniadakis Simulation of heat and momentum transfer in complex micro-geometries AIAA J. Thermophys. Heat Transfer 8 4 1994 355 370
2. Y. Zhang, R. Qin, and D.R. Emerson Lattice Boltzmann simulation of rarefied gas flows in microchannels Phys. Rev. E 71 4 2005 047702
3. G.H. Tang, W.Q. Tao, and Y.L. He Lattice Boltzmann method for gaseous microflows using kinetic theory boundary conditions Phys. Fluids 17 5 2005 058101
4. E.G.R. Eckert, and R.M. Drake Jr. Analysis of Heat and Mass Transfer 1972 McGraw-Hill New York pp. 467-486
5. H.S. Tsien Superaerodynamics, mechanics of rarefied gases J. Aerosp. Sci. 13 12 1946 653 664
6. F.S. Sherman The transition from continuum to molecular flow Annu. Rev. Fluid Mech. 1 1969 317 340
7. J.Q. Liu, Y.C. Tai, C.M. Ho, MEMS for pressure distribution studies of gaseous flows in microchannels, in: Proceedings of the Micro Electro Mechanical Systems, IEEE, 1995, pp. 209-215.
8. E.B. Arkilic, K.S. Breuer, M.A. Schmidt, Gaseous flow in microchannels, in: First ASME Symposium on Application of Micro-fabrication to Fluid Mechanics, 1997, pp. 57-66.
9. Z.Y. Guo, and Z.X. Li Size effect on microscale single-phase flow and heat transfer Int. J. Heat Mass Transfer 46 1 2003 59 149
10. H.Y. Wu, and P. Cheng An experimental study of convective heat transfer in silicon microchannels with different surface conditions Int. J. Heat Mass Transfer 46 14 2003 2547 2556 (Pubitemid 36610809)
11. G. Hetsroni, A. Mosyak, E. Pogrebnyak, and L.p. Yarin Fluid flow in micro-channels Int. J. Heat Mass Transfer 48 10 2005 1982 1998
12. M. Gad-el-Hak The fluid mechanics of microdevices-the freeman scholar lecture J. Fluid Eng. 121 1 1999 5 33
13. E.B. Arkilic, M.A. Schimidt, and K.S. Breuer Gaseous slip flow in long micro-channels J. Microelectromech. Syst. 6 2 1997 167 178 (Pubitemid 127607048)
14. T.T. Zhang, L. Jia, and Z.C. Wang Validation of Navier-Stokes equations for slip flow analysis within transition region Int. J. Heat Mass Transfer 51 25-26 2008 6323 6328
15. X. Zhu, M.D. Xin, and Q. Liao Analysis of heat transfer between two unsymmetrically heated parallel plates with microspacing in the slip flow regime Microscale Thermophys. Eng. 6 4 2002 287 301
16. O. Aydin, and M. Avci Analysis of laminar heat transfer in micro-Poiseuille flow Int. J. Therm. Sci. 46 1 2007 30 37 (Pubitemid 44708801)
17. O. Aydin, and M. Avci Heat and fluid flow characteristics of gases in micropipes Int. J. Heat Mass Transfer 49 9-10 2006 1723 1730
18. S.J. Liao, Proposed Homotopy Analysis Techniques for the Solution of Nonlinear Problems, PhD Thesis, Shanghai Jiao Tong University, Shanghai, 1992.
19. S.J. Liao An approximate solution technique which does not depend upon small parameters: a special example Int. J. Non Linear Mech. 30 3 1995 371 380
20. S.J. Liao An approximate solution technique which does not depend upon small parameters (Part 2): an application in fluid mechanics Int. J. Non Linear Mech. 32 5 1997 815 822
21. S.J. Liao An explicit, totally analytic approximation of Blasius' viscous flow problems Int. J. Non Linear Mech. 34 4 1999 759 778
22. S.J. Liao On the homotopy analysis method for nonlinear problems Appl. Math. Comput. 147 2 2004 499 513
23. S.J. Liao A new branch of solutions of boundary-layer flows over an impermeable stretched plate Int. J. Heat Mass Transfer 48 12 2005 2529 2539
24. S.J. Liao An analytic solution of unsteady boundary-layer flows caused by an impulsively stretching plate Commun. Nonlinear Sci. Numer. Simul. 11 2006 326 339
25. F.M. Allan, and M.I. Syam On the analytic solution of non-homogeneous Blasius problem J. Comput. Appl. Math. 182 2 2005 362 371 (Pubitemid 40736811)
26. S. Abbasbandy The application of the homotopy analysis method to nonlinear equations arising in heat transfer Phys. Lett. A 360 1 2006 109 113 (Pubitemid 44634988)
27. S. Abbasbandy The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation Phys. Lett. A 361 6 2007 478 483
28. T. Hayat, and M. Sajid On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder Phys. Lett. A 361 4 2007 316 322 (Pubitemid 44894740)
29. T.T. Zhang, L. Jia, and Z.C. Wang Analytic solution for steady slip flow between parallel plates with micro-scale spacing Chin. Phys. Lett. 25 1 2008 180 183
30. S.J. Liao A general approach to get series solution of non-similarity boundary-layer flows Commun. Nonlinear Sci. Numer. Simul. 14 2009 2144 2159
31. J.V. Rij, T. Harman, and T. Ameel The effect of creep flow on two-dimensional isoflux microchannels Int. J. Therm. Sci. 46 11 2007 1095 1103 (Pubitemid 47444533)