Role of heat source/sink on time dependent free convective flow in a coaxial cylinder filled with porous material: a semi analytical approach

In this article, the semi analytical solution for a fully developed time dependent free convective flow of a viscous incompressible fluid with heat source/sink in an infinite vertical coaxial cylinder saturated with porous material has been analyzed. The flow was induced by buoyancy forces due to temperature differences caused by the thermal insulation of the inner wall and constant heating of the outer wall. The Laplace transform technique was employed to transform the governing equation from time domain to the Laplace domain. Notwithstanding, a numerical inversing scheme known as Riemann-sum approximation (RSA), renowned for its precision has been utilized to transform the Laplace domain solution to time domain. The accuracy of the numerical technique employed was tested by presenting a comparison with the numerical values obtained using RSA, PDEPE, and steady state solution at large time. The effects of the various flow parameters on the flow formation are exhibited graphically. It is interesting to note that the fluid temperature and velocity increases as time passes. In addition, the velocity can be enhanced and minimized by gradually increasing Darcy number and the viscosity ratio respectively. However, the increase is seen to be more prominent when heat source is applied. The drag on both walls are seen to increase with increase in Darcy number, the reverse trend is observed with increase in the viscosity ratio.