Restrictions on the Validity of the Thermal Conditions at the Porous-Fluid Interface—An Exact Solution

Thermal conditions at the porous-fluid interface under local thermal nonequilibrium (LTNE) conditions are analyzed in this work. Exact solutions are derived for both the fluid and solid temperature distributions for five of the most fundamental forms of thermal conditions at the interface between a porous medium and a fluid under LTNE conditions and the relationships between these solutions are discussed. This work concentrates on restrictions, based on the physical attributes of the system, which must be placed for validity of the thermal interface conditions. The analytical results clearly point out the range of validity for each model for the first time in the literature. Furthermore, the range of validity of the local thermal equilibrium (LTE) condition is discussed based on the introduction of a critical parameter. The Nusselt number for the fluid at the wall of a channel that contains the fluid and porous medium is also obtained. The effects of the pertinent parameters such as Darcy number, Biot number, $Bi$⁠, Interface Biot number, $Biint$⁠, and fluid to solid thermal conductivity ratio are discussed.