TRANSIENT PRESSURE DRIVEN FLOW IN A COMPOSITE CHANNEL PARTIALLY FILLED WITH POROUS MATERIAL- A SEMI-ANALYTICAL APPROACH

This work is to investigate the transient fully developed flow in a horizontal channel formed by two infinite parallel plates due to sudden application of constant pressure gradient in horizontal direction. Momentum transfer in the porous medium is simulated using the Brinkman - extended Darcy model. The fluid and porous regions are joined together by equating their velocities and incorporating the shear stress jump conditions at the interface. With the application of Laplace transform technique, the governing partial differential equations are changed into ordinary differential equations which are solved exactly in the Laplace domain. The Riemann-sum approximation method is then applied to the exact solution in Laplace domain to invert result to time domain. Validation of the Riemann-sum approximation method is achieved by comparing numerical values obtained with those of closed form solution obtained for steady state flow and transient solution obtained by implicit finite difference method. At large values of time, transient solution obtained using Riemann-sum approximation method and implicit finite difference method coincide with closed form solution obtain exactly for steady state flow showing excellent agreement between the methods. Line graphs are used to discuss the effect of the different flow parameters involved in the flow formation. The variations in velocity, skin friction and volumetric flux with respect to time, and the adjustable coefficient in the stress jump condition have been discussed. Fluid velocity increases with time, Darcy number and thickness of clear fluid.