Time-Dependent Natural Convection Couette Flow of Heat Generating/Absorbing Fluid between Vertical Parallel Plates Filled With Porous Material

Abstract

This paper, investigates the time-dependent behavior of natural convection Couette flow of a viscous and incompressible heat generating/absorbing fluid in a porous medium bounded by two infinite vertical parallel plates. The Brinkman-extended Darcy model is considered to simulate the momentum transfer within the porous medium. The flow is generated by the asymmetric heating and the impulsive motion of one of the infinite vertical parallel plates. Laplace transform techniques is used to obtain the analytical solutions for the temperature and the velocity profiles while the rate of heat transfer as well the skin friction are consequently derived. The numerical simulation conducted for some saturated liquids reveled that at t ≥ Pr the steady and unsteady state velocities (as well as the temperature of the fluid) coincide. It is also observed that the temperature as well as the velocity of the fluid can be improved by increasing the gap between the plates. For Gr = 0, indicating the absence of convection current, the results are comparable to the results obtained in Schlichting (1979) as Da → ∞ and γ = 1.0.

Keywords: heat generating/absorbing fluid, natural convection Couette flow, porous material asymmetric heating and impulsive motion

Journal of the Nigerian Association of Mathematical Physics, Volume 19 (November, 2011), pp 233 – 248