Validation of the thermal equilibrium assumption in periodic natural convection in porous domains

The validity of the local thermal equilibrium assumption in the periodic free convection channel flow is investigated analytically. Two cases are considered where in the first case transverse conduction in the solid domain is included while in the second case transverse conduction in the fluid domain is included. The periodic disturbance in the free convection flow is due to a periodic thermal disturbance imposed on the channel walls. The Darcy-Brinkman model is used to model the flow inside the porous domain. It is found that four dimensionless parameters control the local thermal equilibrium assumption in the first case and five parameters control the local equilibrium assumption in the second case. The criteria that secure the validity of the local thermal equilibrium assumption are derived.