Transient free convective flow in an annular porous medium: A semi-analytical approach

The transient fully developed free-convective flow of viscous incompressible fluid between two concentric vertical cylinders filled with porous material and saturated with the same fluid have been analysed due to isothermal or isoflux heating of the outer surface of inner cylinder. The governing partial differential equations of motion and energy are transformed into ordinary differential equations using Laplace transform technique. The ordinary differential equations are then solved analytically in Laplace domain. The Riemann-sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by comparison with closed form solution obtained for steady states which has been obtained separately. An excellent agreement was found for transient and steady state solution at large value of time. The governing partial differential equations are also solved by implicit finite difference method to verify the present proposed method. The variation of temperature, velocity, skin-frictions and mass flow rate with dimensionless parameter controlling the present physical situation are illustrated graphically and discussed. It is observed that velocity and temperature increases with time and finally attains its steady state status. Furthermore, both velocity as well as temperature of the fluid is higher in case of isothermal heating of the outer surface of the inner cylinder compared with the isoflux heating case when the gap between the cylinder is less or equal to the radius of inner cylinder while reversed trend is observed when the gap between the cylinders is greater than the radius of inner cylinder for all considered values of time.