Modified effective thermal conductivity due to heat dispersion in fibrous porous media

Abstract

When a fluid flows past an array of cylinders that represent the porous media, the micro convection around the cylinders will contribute to heat dispersion. The modified effective thermal conductivity tensor that includes the microscopic heat dispersion effect is usually calculated by a volume averaging method. This method requires a closure constitutive vector b to simulate the modified effective thermal conductivity tensor. In this paper, a direct temperature solution method to calculate the modified effective thermal conductivity tensor, by solving the temperature field in a unit cell with appropriate boundary conditions, is proposed. This method introduces a moving frame that converts the convective-diffusion equation in a pure conduction equation. Navier–Stokes equations and energy equations are solved in an array of cells and effective thermal conductivity is calculated from the local temperature field. The dependence of the modified effective thermal conductivity tensor on pertinent dimensionless numbers such as Peclet number, thermal conductivity ratio of solid to liquid, and the ratio of solid volume (volume fraction of the cylinders) in the unit cell is discussed.