An analytical approach for a Hiemenz flow in a porous medium with heat exchange

In this work, a Hiemenz flow established inside a semi-infinite low porosity medium with heat exchange is analyzed analytically. Heat is supplied to the system through two different wall conditions: a constant wall temperature, and a constant wall heat flux. Local thermal non-equilibrium is considered, and the two-equation model is used to consider heat exchange between gas and solid phases. The flow is analyzed through a non-Darcian model, in which viscous and convective terms are considered in the Darcy pressure equation. The results obtained point out the importance of the inner zone (close to the wall) analysis in the case of a constant wall heat flux. From the analysis, a new dimensionless parameter, κ, emerges, which gathers information of the transport phenomena in gas and solid phases, and it is responsible to determine the flow field.