Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

ANALYTICAL SOLUTION OF COUPLED RADIATION-CONVECTION DISSIPATIVE NON-GRAY GAS FLOW IN A NON-DARCY POROUS MEDIUM

  • Darvishi, Mohammad Taghi (Department of Mathematics, Razi University) ;
  • Khani, Farzad (Department of Mathematics, Bakhtar Institute of Higher Education) ;
  • Aziz, Abdul (Department of Mechanical Engineering, School of Engineering and Applied Science, Gonzaga University)
  • 투고 : 2009.12.07
  • 심사 : 2010.05.27
  • 발행 : 2010.09.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The homotopy analysis method (HAM) has been applied to develop an analytic solution for the coupled radiation-convection dissipative non-gray gas flow in a non-Darcy porous medium. Results are presented for the surface shear and temperature profiles are presented to illustrate the effect of various parameters appearing in the analytical formulation. The accuracy and convergence of the method is also discussed.

키워드

참고문헌

  1. R.D. Cess, Radiation effects upon boundary layer ow of an absorbing gas, ASME J Heat Transfer 86c (1964), 469-475.
  2. I.S. Habib and R. Grief, Heat transfer to a flowing non-gray radiating gas: an experimental and theoretical study, Int. J. Heat Mass Transfer 21 (1978), 477. https://doi.org/10.1016/0017-9310(78)90081-9
  3. R. Grief, Laminar convection with radiation: experimental and theoretical results, Int J. Heat Mass Transfer 21 (1978), 477. https://doi.org/10.1016/0017-9310(78)90081-9
  4. S. Kubo, Stagnation-point flow of a radiating gas of a large optical thick ness, J. Phys. Soc. Japan 36 (1974), 293-297. https://doi.org/10.1143/JPSJ.36.293
  5. J.L. Novotny and M.D. Kelleher, Free convection stagnation flow of an absorbing-emitting gas, Int. J. Heat Mass Transfer 10 (1967), 1171-1178. https://doi.org/10.1016/0017-9310(67)90082-8
  6. A.T. Mattick, Coaxial radiative and convective heat transfer in gray and non-gray gases, J. Quantitative Spectroscopy and Radiation Transfer 15 (1981), 1071-1081.
  7. C.L. Tien and M.M. Abu-Romai, Perturbation solutions in the differential analysis of radiation interaction with conduction and convection, AIAA J. 4 (1966), 732-733. https://doi.org/10.2514/3.3526
  8. F.H. Azad and M.F. Modest, Combined radiation and convection flow in absorbing, emmitting and anisotropically scattering gas-particulate tube flow, Int. J. Heat Mass Transfer 24 (1981), 1681-1698. https://doi.org/10.1016/0017-9310(81)90077-6
  9. B.W. Webb and R. Viskanta, Radiation-induced buoyancy-driven flow in rectangular enclosures: experiment and analysis, ASME J. Heat Transfer 109 (1987), 427-433. https://doi.org/10.1115/1.3248099
  10. A. Yucel, H. Kehtarnavaz and Y. Bayazitoglu, Boundary layer flow of a non-gray radiating fluid, Int. Comm. Heat Mass Transfer 16(3) (1989), 415-425. https://doi.org/10.1016/0735-1933(89)90089-4
  11. H.S. Takhar and O.A. Beg, Thermal radiation, thermal conductivity and non-Darcy effects on laminar convective boundary layer flow of an optically dense fluid in a saturated porous medium, 9th Int. Symp. on Transport Phenomena in Thermal Fluids, ISTP 9, Singapore, June 1996, pp. 1093-109.
  12. P. Cheng, Geothermal heat transfer, In Handbook of Heat Transfer Applications,W.M. Rohsenow, J.P. Hartnett and E. Ganic (Eds), McGraw Hill, New York, 1985.
  13. J.P. Sauty Sensible energy storage in aquifers, 1, theoretical study, Water Resourc. Res. 18 (1982).
  14. H.S. Takhar and O.A. Beg Numerical analysis of non-Darcy radiative hydromagnetic free convective flow through a fluidfilled porous medium, J. Math. Phys. Sci. (1996).
  15. H.S. Takhar, O.A. Beg and M. Kumari, Computational analysis of coupled radiation-convection dissipative non-Gray gas flow in non-Darcy porous medium using the Keller-Box implicit differential scheme, Int. J. Energy Res. 22 (1998), 141-159. https://doi.org/10.1002/(SICI)1099-114X(199802)22:2<141::AID-ER340>3.0.CO;2-F
  16. S.J. Liao, An explicit, totally analytic approximate solution for Blasius-viscous flow problems, Int J Nonlinear Mech 34(4) (1999), 759-78. https://doi.org/10.1016/S0020-7462(98)00056-0
  17. S.J. Liao Beyond perturbation: introduction to the homotopy analysis method, Boca Raton: Chapman & Hall/CRC Press, (2003).
  18. S.J. Liao and Y. Tan, A general approach to obtain series solutions of nonlinear differential equations, Stud. Appl. Math. 119 (2007), 297-355. https://doi.org/10.1111/j.1467-9590.2007.00387.x
  19. S.J. Liao, Notes on the homotopy analysis method: some definitions and theorems, Commun. Nonlinear Sci. Numer. Simulat. 14(4) (2009), 983-97. https://doi.org/10.1016/j.cnsns.2008.04.013
  20. A. Molabahrami and F. Khani, The homotopy analysis method to solve the Burgers-Huxley equation, Nonlinear Anal. Real World Appl. 10(2) (2009), 589-600. https://doi.org/10.1016/j.nonrwa.2007.10.014
  21. F. Khani and A. Aziz, Thermal analysis of a longitudinal trapezoidal fin with temperature-dependent thermal conductivity and heat transfer coefficient, Commun. Nonlinear Sci. Numer. Simulat. (in press), doi:10.1016/j.cnsns.2009.04.028.
  22. M.T. Darvishi and F. Khani, A series solution of the foam drainage equation, Comput. Math. Appl. 58 (2009), 360-368. https://doi.org/10.1016/j.camwa.2009.04.007
  23. A. Aziz and F. Khani, Analytic solutions for a rotating radial ¯n of rectangular and various convex parabolic profiles, Commun. Nonlinear Sci. Numer. Simulat. (in press), doi:10.1016/j.cnsns.2009.07.008.
  24. S.J. Liao, A new branch of solutions of boundary-layer flows over an impermeable stretched plate, Int. J. Heat Mass Transfer 48 (2005), 2529-2539. https://doi.org/10.1016/j.ijheatmasstransfer.2005.01.005
  25. S.J. Liao and E. Magyari, Exponentially decaying boundary layers as limiting cases of families of algebraically decaying ones, ZAMP 57(5) (2006), 777-792. https://doi.org/10.1007/s00033-006-0061-x
  26. A.C. Cogley, W.G. Vincenti and S.E. Giles, Differential approximation for near-equilibrium flow of a non-gray gas, AIAA J. 6 (1968), 551. https://doi.org/10.2514/3.4538
  27. B. Gebhart, Y. Jaluria, R.L. Mahajan and B. Sammakia, Buoyancy-Induced Flows and Transport, Hemisphere, Washington, 1988.