Transient-free convective flow with heat generation/absorption in an annular porous medium: A semi-analytical approach

Abstract

This article presents the impact of heat-generating/absorbing fluid on fully developed transient free convective flow of a viscous and an incompressible fluid bounded by two concentric vertical cylinders filled with isotropic porous materials and saturated with the same fluid. In the present model, the convective current is setup due to internally generated heat and either isothermal or isoflux heating of the outer surface of the inner cylinder. The transport equations concerned with the model under consideration are rendered nondimensional and transformed into ordinary diffferential equation using Laplace transform technique. The solution of the momentum and energy equation obtained separately in Laplace domain is transformed into time domain using the Riemann-sum approximation approach, this is later validated by numerical comparisons at large time with the closed form solution obtained for steady flow. The accuray of this approach has further been extablished by presenting a numerical solution using implicit finite difference method. The effect of the various physical parameters entering into the model is demostrated with the aid of tables and line graphs. During the course of numerical computations, it is found that the effect of heat generation/absorption can be controlled by increasing/decreasing the viscosity ratio. The system can also be maintained by varying the annular gap and applying approprate phenomenon of heating.

Keywords

Transient free convection Darcy number isothermal isoflux Riemann-sum approximation heat generation/absorption

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