Free convection stagnation-point boundary-layer flow in a porous medium with a density maximum

The steady free convection boundary-layer flow near a stagnation point in a fluid-saturated porous medium is considered when the convecting fluid is close to its maximum density. Three forms for the wall boundary condition are treated, a prescribed wall temperature, prescribed wall heat flux and Newtonian heating. In each case the flow and heat transfer characteristics are determined by a dimensionless parameter δ   that measures the difference between the ambient temperature and the temperature at which the fluid attains its density maximum. We find that solutions are possible for δ≥0δ≥0 for each case. For δ<0δ<0 there is a critical value δc of δ  , the value of which depends on the boundary conditions applied, with solutions possible only for δ≥δcδ≥δc. The nature of this critical value, as well as other limiting asymptotic forms is discussed.

► Free convection in a porous medium near a density maximum with a nonlinear density-temperature relation. ► Comparison of different boundary conditions, prescribed surface temperature, heat flux and newtonian heating. ► Similarity solutions with ranges of dual solutions Critical parameter values with possible non-existence of solution.