Numerical Solution of Energy Equation in Porous Channels under Effects of Radiation Field

Ala'a A.  Hammodat; Osama T.  Al-Bairaqdar; Abida T.  Hammodat

doi:10.24996/ijs.2021.62.10.20

Authors

Ala'a A. Hammodat Department of Mathematics, College Education of Pure Science, Mosul University, Nineveh, Iraq
Osama T. Al-Bairaqdar Department of Mathematics, Faculty of Science and Health, Koya University, KOY45 Kurdistan Region F.R. Iraq
Abida T. Hammodat Department of Physics, College of Science, Mosul University, Nineveh, Iraq

DOI:

https://doi.org/10.24996/ijs.2021.62.10.20

Keywords:

Heat transfer, Porous medium, Brinkman number, Pouger number, Boltzmann number, Reynolds number

Abstract

In this paper, we built a mathematical model for convection and thermal radiation heat transfer of fluid flowing through a vertical channel with porous medium under effects of horizontal magnetic field (MF) at the channel. This model represents a 2-dimensional system of non-linear partial differential equations. Then, we solved this system numerically by finite difference methods using Alternating Direction Implicit (ADI) Scheme in two phases (steady state and unsteady state). Moreover, we found the distribution and behaviour of the heat temperature inside the channel and studied the effects of Brinkman number, Reynolds number, and Boltzmann number on the heat temperature behaviour. We solved the system by building a computer program using MATLAB.