Impact of Thermal Stratification on Unsteady Natural Convection Couette Flow Formation in a Vertical Channel Filled with Anisotropic Porous Material

Abstract

Recently, heat transfer problems where anisotropic porous medium or stably stratified fluid are taken into account have been separately studied. Developing a mathematical model that combines these physical quantities naturally results to complex coupled differential equations. In this paper, a fully developed time dependent natural convection Couette flow of stably stratified fluid between vertical parallel channels filled with anisotropic porous material is investigated. The governing partial differential equations are transformed into ordinary differential equations using Laplace transform techniques and then decoupled using D’Alembert method. Exact solutions in Laplace domain for the velocity and temperature equations are then obtained. A numerical method: Riemann-sum approximation is then used to invert the expressions for the velocity and temperature profiles, as well as the resulting skin friction, rate of heat transfer and volumetric mass flow rate into their corresponding time domain. The research establishes that both the anisotropic and the stratification parameters aid in regulating the fluid temperature and velocity. The research further reveals that the fluid velocity attains its maximum (or minimum) velocity when θ = 900 (or θ = 00) for k*<1 and when k*>1, the fluid velocity is least (or maximum) when θ = 900 (or θ = 00).