Transport in Porous Media, Vol.69, No.3, 359-372, 2007
Steady mixed convection boundary layer flow over a vertical flat plate in a porous medium filled with water at 4 degrees C: case of variable wall temperature
The problem of steady mixed convection boundary layer flow over a vertical impermeable flat plate in a porous medium saturated with water at 4 degrees C (maximum density) when the temperature of the plate varies as x(m) and the velocity outside boundary layer varies as x(2m), where x measures the distance from the leading edge of the plate and m is a constant is studied. Both cases of the assisting and the opposing flows are considered. The plate is aligned parallel to a free stream velocity U-infinity oriented in the upward or downward direction, while the ambient temperature is T-infinity = T-m (temperature at maximum density). The mathematical models for this problem are formulated, analyzed and simplified, and further transformed into non-dimensional form using non-dimensional variables. Next, the system of governing partial differential equations is transformed into a system of ordinary differential equations using the similarity variables. The resulting system of ordinary differential equations is solved numerically using a finite-difference method known as the Keller-box scheme. Numerical results for the non-dimensional skin friction or shear stress, wall heat transfer, as well as the temperature profiles are obtained and discussed for different values of the mixed convection parameter lambda and the power index m. All the numerical solutions are presented in the form of tables and figures. The results show that solutions are possible for large values of lambda and m for the case of assisting flow. Dual solutions occurred for the case of opposing flow with limited admissible values of lambda and m. In addition, separation of boundary layers occurred for opposing flow, and separation is delayed for the case of water at 4 degrees C (maximum density) compared to water at normal temperature.