OJFD  Vol.5 No.4 , December 2015
Non-Darcy Mixed Convection between Differentially Heated Vertical Walls Filled with a Porous Material: Application of New Modified Adomian Decomposition Method
ABSTRACT
This paper presents non-Darcy mixed convective flow of an incompressible and viscous fluid in a differentially heated vertical channel filled with a porous material in the presence of a temperature dependent source/sink. The analytical solution of fourth order non-linear ordinary differential equation for temperature field, which is formed by eliminating velocity field from system of governing equations in non-dimensional form, is obtained by using new modified Adomian decomposition method (NMADM) in terms of various parameters. In order to illustrate the interactive influences of governing parameters on the temperature and velocity fields, a numerical study of the analytical solution is performed with respect to three categories of transport processes i) when forced convection is dominated, ii) when forced and natural convection are equal and iii) when natural convection is dominated. Analysis of all categories has revealed that the temperature and velocity profiles are increasing function of modified Darcy number while decreasing function of Forchheimer number.

Cite this paper
Tiwari, A. and Singh, P. (2015) Non-Darcy Mixed Convection between Differentially Heated Vertical Walls Filled with a Porous Material: Application of New Modified Adomian Decomposition Method. Open Journal of Fluid Dynamics, 5, 380-390. doi: 10.4236/ojfd.2015.54037.
References
[1]   Szeri, A.Z. and Rajagopal, K.R. (1985) Flow of a Non-Newtonian Fluid between Heated Parallel Plates. International Journal of Non-Linear Mechanics, 20, 91-101.
http://dx.doi.org/10.1016/0020-7462(85)90003-4

[2]   Aung, W. and Worku, G. (1986) Theory of Fully Developed Combined Convection Including Flow Reversal. ASME Journal of Heat Transfer, 108, 485-488.
http://dx.doi.org/10.1115/1.3246958

[3]   Nelson, D.J. and Wood, B.D. (1989) Fully Developed Combined Heat and Mass Transfer Natural Convection between Parallel Plates with Asymmetric Boundary Conditions. International Journal of Heat and Mass Transfer, 32, 1789-1792.
http://dx.doi.org/10.1016/0017-9310(89)90060-4

[4]   Hamadah, T.T. and Wirtz, R.A. (1991) Analysis of Laminar Fully Developed Mixed Convection in a Vertical Channel with Opposing Buoyancy. ASME Journal of Heat Transfer, 113, 507-510.
http://dx.doi.org/10.1115/1.2910593

[5]   Kou, H.S. and Huang, D.K. (1997) Fully Developed Laminar Mixed Convection through a Vertical Annular Duct Filled with Porous Media. International Journal of Heat and Mass Transfer, 24, 99-110.
http://dx.doi.org/10.1016/S0735-1933(96)00109-1

[6]   Boulama, K. and Galanis, N. (2004) Analytical Solution for Fully Developed Mixed Convection between Parallel Vertical Plates with Heat and Mass Transfer. ASME Journal of Heat Transfer, 126, 381-388.
http://dx.doi.org/10.1115/1.1737774

[7]   Umavathi, J.C. and Malashetty, M.S. (2005) Magnetohydrodynamic Mixed Convection in a Vertical Channel. International Journal of Non-Linear Mechanics, 40, 91-101.
http://dx.doi.org/10.1016/j.ijnonlinmec.2004.05.018

[8]   Chen, Y.C., Chung, J.N., Wu, C.S. and Lue, Y.F. (2000) Non-Darcy Mixed Convection in a Vertical Channel Filled with a Porous Medium. International Journal of Heat and Mass Transfer, 43, 2421-2429.
http://dx.doi.org/10.1016/s0017-9310(99)00299-9

[9]   Muralidhar, M. (1989) Mixed Convection Flow in a Saturated Porous Annulus. International Journal of Heat and Mass Transfer, 32, 881-888.
http://dx.doi.org/10.1016/0017-9310(89)90237-8

[10]   Hadim, A. and Chen, G. (1994) Non-Darcy Mixed Convection in a Vertical Porous Channel. Journal of Thermophysics and Heat Transfer, 8, 805-808.

[11]   Vafai, K. and Kim, S.J. (1989) Forced Convection in a Channel with a Porous Medium: An Exact Solution. Journal of Heat Transfer, 111, 1103-1106.
http://dx.doi.org/10.1115/1.3250779

[12]   Nadeem, S. and Akbar, N.S. (2009) Effects of Heat Transfer on the Peristaltic Transport of MHD Newtonian Fluid with Variable Viscosity: Application of Adomian Decomposition Method. Communications in Non-Linear Sciences and Numerical Simulation, 14, 3844-3855.
http://dx.doi.org/10.1016/j.cnsns.2008.09.010

[13]   Nield, D.A., Junqueira, S.L.M. and Large, J.L. (1996) Forced Convection in a Fluid-Saturated Porous-Medium Channel with Isothermal or Isoflux Boundaries. Journal of Fluid Mechanics, 322, 201-214.
http://dx.doi.org/10.1017/S0022112096002765

[14]   Beckett, P.M. (1980) Combined Natural and Forced Convection between Parallel Vertical Walls. SIAM Journal on Applied Mathematics, 39, 372-384.
http://dx.doi.org/10.1137/0139031

[15]   Chamkha, A.J. (2002) On Laminar Hydromagnetic Mixed Convection Flow in a Vertical Channel with Symmetric and Asymmetric Wall Heating Conditions. International Journal of Heat and Mass Transfer, 45, 2509-2525.
http://dx.doi.org/10.1016/S0017-9310(01)00342-8

[16]   Khan, M., Hyder Ali, S., Hayat, T. and Fetecau, C. (2008) MHD Flows of a Second Grade Fluid between Two Side Walls Perpendicular to a Plate through a Porous Medium. International Journal of Non-Linear Mechanics, 43, 302-319.
http://dx.doi.org/10.1016/j.ijnonlinmec.2007.12.016

[17]   Wazwaz, A.M. and El-Sayed, S.M. (2001) A New Modified of the Adomian Decomposition Method for Linear and Nonlinear Operators. Applied Mathematics and Computation, 122, 393-405.
http://dx.doi.org/10.1016/S0096-3003(00)00060-6

[18]   Wazwaz, A.M. (2006) The Modified Decomposition Method for Analytic Treatment of Differential Equations. Applied Mathematics and Computation, 173, 165-176.
http://dx.doi.org/10.1016/j.amc.2005.02.048

[19]   Barletta, A. and Zanchini, E. (1999) On the Choice of Reference Temperature for Fully Developed Mixed Convection in a Vertical Channel. International Journal of Heat and Mass Transfer, 42, 3169-3181.
http://dx.doi.org/10.1016/S0017-9310(99)00011-3

 
 
Top