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

Abstract

Near the interface of porous plain media, convective heat transfer may be noticeably affected by the nonuniformity of the phase distributions. The boundary effects are modeled by using interfacial slip or no-slip temperature boundary conditions. The latter uses a variable transverse total diffusivity giving a continuous variation of the temperature near and across the interface. The former uses a constant transverse total diffusivity which requires a temperature slip cross the interface (in order to obtain accurate heat flux calculations). In this study these boundary conditions are examined by the direct simulation of the momentum and energy equations for a model porous medium made of two-dimensional periodic arrangements of cylinders. The slip coefficient is found to depend on the bulk Peclet number Pe I , the ratio of solid to fluid conductivity k s k f , and the gap size h. For the no-slip boundary condition, the magnitude and the distribution of D 1 (y) α f also depend on Pe I , k s k f , and h. For a solid bounding surface, and when k s k f> 1 , the effective transverse conductivity k e1 k f dominates over the hydrodynamic dispersion, and therefore, the accurate description of the variation of k e1 ( y) k f , becomes critical. For a fluid bounding medium, the results show that D 1 ( y) is nonuniform on both sides of the interface. The nonuniformity of D 1( y) in the fluid medium is due to the local two dimensionality of the flow. The total diffusivity tensor D in the bulk of a two-dimensional periodic structure is also examined. The effects of the Reynolds number, Prandtl number, particle shape, particle arrangement, and flow direction, on the bulk value of D are examined. It is found that for oblique flows, the ensemble-averaged longitudinal total diffusivity D 1 α f , over the tilt angle, approaches a Pe 1, relation instead of a Pe 2 1 relation expected for periodic structures.