Impact of heat generation/absorption on transient natural convective flow in an annulus filled with porous material subject to isothermal and adiabatic boundaries

Abstract

This article deliberated the effects of heat generation/absorption on transient natural convective flow in infinite vertical concentric cylinder filled with a porous material. The natural convective flow is as a result of constant heating at the inner cylinder while the inner surface of the outer cylinder is thermally insulated. A combination of Laplace transform technique and Riemann-sum approximation approach has been used to transform and invert the governing equation from the Laplace domain to the time domain respectively. The numerical values obtained from the Riemann-sum approximation excellently agree with the steady state solution at large time. The obtained results are represented graphically and the effects of the governing parameters on the velocity field, temperature field, mass flow rate, heat transfer as well as the skin-friction on both surfaces of the annulus are studied in detail. In the course of numerical computations, it is found that the fluid velocity and temperature both increases with time, while the fluid velocity and skin friction on both walls are seen to be proportional to Darcy number but inversely proportional to the viscosity ratio. Furthermore, it is found that the mass flow rate can be controlled by increasing/decreasing the heat generation/absorption parameter.