UNSTEADY NATURAL CONVECTION FLOW THROUGH A VERTICAL POROUS CHANNEL FILLED WITH POROUS MATERIALS UNDER THE EFFECT OF THERMAL RADIATION
Abstract
The paper examines the velocity and heat transfer on unsteady natural convection flow through a vertical porous channel filled with porous materials under the effect of thermal radiation. The study considered the fluid flow to be through an infinite vertical porous channel filled with porous materials and the energy
equation in the flow model is examined using non-linear Rosseland heat diffusion. The partial differential equations associated with the flow formation are transformed into ordinary differential equations (ODEs) using similarity variables and the resulting ODEs are solved by Adomian decomposition method (ADM).
Finally, the results are presented on graphs as velocity and temperature profiles for various values of the controlling physical parameters involved in the problem. In the course of investigation, it was found that; the fluid velocity increases with increase in thermal radiation and Darcy number and the fluid temperature was seen to increase with increase in thermal radiation.
References
Abdul-Hakeem,A.K. and Sathiyanathan, K. (2009). An analytic solution of an oscillatory flow through a porous medium with radiation. Journal of Nonlinear Analysis:
Hybrid System. 3: 288-295.
Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Boston.MA Kluwer.
Ajibade, A.O., (2010). Entropy generation in a horizontal micro channel with a moving boundary. Int. J. of energy and Tech., 2(21): 2-8.
Al-Sanea, S.A. (2004).Mixed convection heat transfer along a continuous moving heated vertical plate with suction or injection. Int. J. Heat Mass Transfer. 47:145 146.
Braslow, A.L. (1999). A History of Suction-type Laminar Flow Control with Emphasis on Flight Research American Institute of Aeronautics and Astronautics, Washington D.C.
Cortell, R. (2007a). Effects of heat source/sink, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet. Comput. Math. Appl. 53:305-316
Cortell, R. (2008b). Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys. Lett. A., 372:631-636.
Cheng, P. (1978). Heat transfer in geothermal systems. Adv. Heat Transfer. 4:1-105.
Cherruault, Y. (1990). Convergence of Adomian’s method. J. of Mathematical and Computer Modelling. 14:83-86.
Hossain, M.A.and Takhar H.S. (1996). Radiation effect on mixed convection along a vertical plate with uniform surface temperature. Int. Journal of Heat and Mass Transfer, 2: 185-198.
Hossain, M.A., Alim, M.A. and Rees, D. (1999a). The effect of radiation on free convection from a porous vertical plate. Int.J. HeatMass Transfer, 42:181-191.
Hossain, M.A., Khanafer, K., and Vafai, K. (2001b). The effect of radiation on free convection flow of fluid with variable viscosity from a porous vertical plate. Int. J. Therm. Sci. 40:115-124.
Ingham, D.B. and Pop, I. (1998) Transport phenomena in porous media. Pargamon. Oxford.
Ishak, A., Merkin, I.H., Nazar, R., and Pop, I. ((2008). Mixed convection boundary layer flow over a permeable vertical surface with prescribed wall heat flux. ZAMP
,100-123.
Jha, B.K. (1997). Transient natural convection through vertical porous stratum. Heat and Mass transfer. Germany. 33,261-263.
Jha, B.K. (2003). Transient free-convective flow in a vertical channel with heat sink. Int. J. of Applied Mechanics and Engineering. 8(3):497-502.
Jha, B.K., Yabo, I.B. and Lin, J. (2017). Transient Natural Convection in an Annulus with Thermal Radiation. Journal of Applied Mathematics. 8: 1351-1366.
Magyari, E. and Pantokratoras, A. (2011). Note on the effect of thermal radiation in the linearized Rossseland approximation on the heat transfer characteristics of various boundary layer flows. International Communications in Heat and Mass Transfer. 38:554-556.
Makinde, O.D., and Ogulu, A. (2011). The effect of thermal radiation on the heat and mass transfer flow of a variable viscosity fluid past a vertical porous plate permeated by a transverse magnetic field, J. Chem. Eng. Comm.195:1575-1584.
Makinde, O.D., Olajuwon, B.I. and Gbolagade A.W. (2007). Adomian Decomposition Approach to a Boundary Layer Flow with Thermal Radiation past a Moving Vertical Porous Plate. International Journal of Applied Mathematics and Mech. 3(3):62-70.
Makinde, O.D. and Ibrahim, S.Y. (2011). Radiation effect on chemically reacting magneto hydrodynamics (MHD) boundary layer flow of heat and mass transfer through a porous vertical flat plate. Int. Journal of Physical Sciences. 6(6): 1508-1516.
Mansour, M.A. (1990). Radiative and Free- convection Effects on the Oscillating flow past a Vertical Plate. Journal of Astrophysics and Space Science. 166: 269-275.
Neild, D.A. and Bejan, A. (2013). Convection In porous media. 4th edition. Springer, New York.
Robert, W. and Murray, R. S. (2010). Schaum’s Oulines Series “Advanced Calculus”. Third Edition.
Singh, A.K. (1984).Stokes problem for a porous vertical plate with heat sink by finite difference method. Astrophys. Space Sci. 103:241-248.
Shojaefard, M.H., Noopoor, A.R., Avanesians, A. and Ghaffapour, M. (2005). Numerical investigation of flow control by suction and injection on a subsonic airfoil.
American Journal of Applied Sciences. 20(10):1474-1480.
Rapist, A, Perdikis, C. and Takhar, H.S. (2004). Effect of thermal radiation on MHD flow. Appl. Math. Comp., 153:645-1584.
Sparrow, E.M. and Cess, R.D. (1978).Radiation heat transfer. Hemisphere Publishing Corporation. Washington.
Vafai, K. (2000). Hand book of porous media. Mercel Dekker, New York.
Yabo, I.B., Jha, B.K.and Lin, J. (2016). Combined Effects of Thermal Diffusion and Diffusion-Thermo Effects on Transient MHD Natural Convection AND Mass Transfer
Flow in a vertical Channel with Thermal Radiation. Journal of Applied Mathematics. 6: 2354-2373.
Copyright (c) 2023 FUDMA JOURNAL OF SCIENCES
This work is licensed under a Creative Commons Attribution 4.0 International License.
FUDMA Journal of Sciences
