Lawrence Berkeley National Laboratory

We present a simple analytical solution for one dimensional steady heat transfer with convection and conduction through a multi-layer system such as a vadose zone. We assume that each layer is homogenous and has a constant thermal diffusivity. The mass/heat flow direction is perpendicular to the layers, and the mass flow rate is a constant. The analytical solution presented in this study also assumes constant known temperatures at the two boundaries of the system. Alhough the analytcal solution gives the temperature as a function of a few paramters, we focus on the inverse application to estimate the percolation rate to high degree of accuracy (e.g., to mm/y). In some other cases the solution may also be helpful in characterizing potential lateral flow along layer divides.