An Apparent Interface Location as a Tool to Solve the Porous Interface Flow Problem

A new approach for solving the laminar flow problem above a porous medium is presented here, using an apparent interface for which both superficial velocity and intrinsic shear stress are continuous. The derivation of this approach is based on a detailed investigation of the Ochoa-Tapia and Whitaker (Int. J. Heat Mass Transfer 38:2635–2646, 1995a) jump condition and its sensitivity to the value of β (the jump condition coefficient) and to an error in the interface location. While the value of the jump condition coefficient is highly sensitive to the interface location, the new apparent interface approach does not require an a priori information about the location of the interface. This approach can be easily used knowing only one measurable parameter—the maximum velocity or the flow rate. Validation of the apparent interface approach against measurements from other works shows that it can be successfully used to predict the velocity profile for different geometrical models.