Analytical Solutions for Heat Transfer in Saturated Soil with Effective Porosity

Closed-form analytical solutions are presented for one-dimensional heat transfer through saturated soil with effective porosity and steady fluid flow. The solutions yield distributions of temperature and total heat flux for both transient and steady-state conditions within a soil block having constant temperature boundaries. The analysis adopts a series–parallel approach for heat transfer and accounts for advection, conduction, and thermal mechanical dispersion assuming local thermal equilibrium between solid and fluid phases. Solutions are first developed and experimental data are provided to highlight the significance of effective porosity with regard to soil thermal conductivity. Numeric examples are presented to illustrate the effects of the thermal Peclet number, thermal dispersivity, and effective porosity on heat transfer behavior. Depending on conditions, each parameter can affect heat transfer in saturated soil significantly. The solutions also demonstrate the requisite uniqueness when cast in terms of dimensionless parameters.