Slip and no-slip temperature boundary conditions at interface of porous, plain media: conduction

Abstract

The phase distribution nonuniformities near bounding surfaces result in anisotropy and nonuniformity of the effective thermal conductivity tensor. For a two-dimensional porous medium made of cylindrical particles, we evaluate the properties of this tensor for cases where the medium is bounded by the fluid saturating it or by a solid surface. The use of a uniform effective conductivity, such as the bulk (far from the surface) value, along with the near surface temperature distribution results in an error in the calculated heat flux. We examine this error and the errors resulting from the use of other approximations of the effective conductivity near the surface. We also point out a slip in the surface temperature occurring when the bulk effective conductivity and the temperature distribution away from the surface are used to extrapolate the temperature at the interface. A slip coefficient is used to account for this slip in temperature.