Analysis of gaseous slip flow in a porous micro-annulus under local thermal non-equilibrium condition – An exact solution. (October 2015) - Wang, Keyong; Tavakkoli, Fatemeh; Vafai, Kambiz
Highlights: An exact solution for gaseous slip flow in a porous micro-annulus is proposed. Local thermal non-equilibrium condition considers the temperature difference between the fluid and solid phases. Two distinct thermal boundary conditions, namely constant heat flux at the inner wall and adiabatic outer wall and vice versa are considered. The velocity slip enhances the heat transfer whereas the temperature jump exhibits an opposite effect. Abstract: The phenomenon of rarefaction in a micro-annulus filled with a porous medium is analyzed in the slip-flow regime. A local thermal non-equilibrium (LTNE) model is utilized to represent the energy transport within the porous medium. Exact solutions are derived for both the fluid and solid temperature distributions within the annulus. Two distinct cases of the thermal boundary conditions are considered, namely a constant heat flux at the outer wall and adiabatic inner wall (Case I) and vice versa (Case II). By eliminating the temperature difference between the fluid and solid phases, the local thermal equilibrium (LTE) model is theoretically proved to be a special case of the LTNE counterpart. Analytical predictions indicate that although the rarefaction leads to a reduction in the heat transfer, the effects of other thermophysical parameters such as the Biot number, the effective thermal conductivity ratio, the porous media shape factor and the annulus aspect ratio also play an important role. The results suggest that the configuration of Case II is superior to that of Case I from the heat transfer point of view.