Effects of viscous dissipation and boundary wall thickness on steady natural convection Couette flow with variable viscosity and thermal conductivity

Abstract

Abstract This study theoretically examines the effects of boundary plate thickness and viscous dissipation on a steady natural convection flow of an incompressible viscous fluid of variable properties. This is due to the fact that several investigations in literature have neglected the thickness and material composition of the boundary plates and as such, their results are either over-determined or under-determined. The viscosity and thermal conductivity of the heat generating/absorbing fluid were assumed to be functions of temperature. Due to the nonlinearity and coupling nature of the governing flow equations, homotopy perturbation method (HPM) has been used to solve the problem. The effects of the thermophysical and flow parameters were captured in graphs and tables. It has been discovered from the study that the velocity profile increases with increase in thermal conductivity. Increase in boundary plate thickness ( d ) was found to boost the fluid flow across the medium while the temperature decreases near the heated plate. It’s further observed that the skin friction decreases on both plates with increase in fluid viscosity and boundary plate thickness ( d ) while the rate of heat transfer decreases on both the plates with an increase in boundary plate thickness ( d ). The volume flow rate is discovered to increase with increase in Brinkman number ( B r ) while a decrease was observed with increase in boundary plate thickness ( d ).