Forced Convection in a Transpired Passage With a Porous Medium Insert

Forced convective heat transfer in a passage with a porous medium matrix subjected to uniform blowing has been fully analyzed, using a local thermal nonequilibrium approach, in application of transpiration systems on the basis of porous medium. An exact solution was found for the asymptotic case of infinitely high interstitial Biot number. In order to extend the problem to general local nonthermal equilibrium cases, an analytical solution procedure has been developed, introducing six unknown parameters to describe both fluid and solid temperature profiles, which are then determined by solving six independent differential and integral equations based on the two energy equations for individual phases and their corresponding boundary conditions. The important performance index for the problem, namely, the overall cooling effectiveness is found quite sensitive not only to the blowing ratio, but also to the interstitial Biot number and fluid to solid effective thermal conductivity ratio. It rises with the blowing ratio and effective thermal conductivity ratio, while it drops as increasing the interstitial Biot number toward the local thermal equilibrium. The present analysis reveals that the local nonthermal equilibrium analysis is definitely needed for accurate estimation of the transpiration-cooled wall temperature.