Investigations of Couette Flow Unsteady Radiative Convective Heat Transfer in a Vertical Channel Using the Generalized Method of Lines (MOL)

Abstract

This study describes a very efficient and fast numerical solution method for the non-steady free convection flow with radiation of a viscous fluid between two infinite vertical parallel walls. The method of lines (MOL) is used together with the Runge-Kutta ODE Matlab solver to investigate this problem numerically. The presence of radiation adds more stiffness and numerical complexity to the problem. A complete derivation in dimensionless form of the governing equations for momentum and energy is also included. A constant heat flux condition is applied at the left wall and a transient numerical solution is obtained for different values of the radiation parameter (<i>R</i>). The results are presented for dimensionless velocity, dimensionless temperature and Nusselt number for different values of the Prandtl number (<i>Pr</i>), Grashof number (<i>Gr</i>), and the radiation parameter (<i>R</i>). As expected, the results show that the convection heat transfer is high when the Nusselt number is high and the radiation parameter is low. It is also shown that the solution method used is simple and efficient and could be easily adopted to solve more complex problems.