Saturday, 15 July 2006
116-4

The Analytical Solutions of Three Dimensional Heat Equation for Thermal Pulse Method.

Gang Liu Sr., China Agricultural Univ, Room223, Building Xinxuekezonghe, College of Resource and Environment, No.2 Yuan-ming-yuan Xilu, Haidian district, 100094, Beijing, China

The heat pulse method enables estimation of the thermal diffusivity, volumetric heat capacity (r c), and thermal conductivity of soils. It has been much employed for moisture estimation because of the strong dependence of (rc on soil water content. The present study investigates the influence of boundary conditions and soil column's geometry on temperature measured by thermocouple. Analytical solutions are found for three kinds of boundary conditions. One is the zero temperature boundary conditions which mean that all boundaries are in thermal equilibrium with the environment. The other is the adiabatic boundary conditions, for which no heat exchange occurs with the environment. The third is the more general case, the radiation boundary. We solve three dimensional heat conduction equations in homogeneous and isotropic medium. The heater of finite length and the soil sample of finite size were considered. For both adiabatic,zero surface temperature and radiation boundary conditions, we obtained the analytical solutions of heat equation for thermal pulse method with short-duration of heat released. Different conformations of the heater due to the distortion of the heater and sensor probes were also taken into account. The analytical solutions agree rather well with the experiment result. Based on these theoretical models, we evaluated the error of volumetric heat capacity caused by adopting the commonly used infinite linear heat resource in infinite solid. We find that the error of adiabatic boundary condition is larger than that of zero surface boundary condition. For soil sample with fixed height, the shorter heater will introduce bigger error comparing with the opponent of it, which is the result of more inhomogeneous temperature distribution in soil sample. For typical probe spacing and probe length, soil column geometry, the error is <5%, thus, the infinite line source model is a good approximation.

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