Analytical Solution for Two‐Dimensional Heat Conduction beneath a Partial Surface Mulch

Abstract

Abstract Models describing heat conduction in materials subjected to periodically varying surface temperatures are important in agricultural physics and other disciplines of applied physics. To date, most attempts to model soil heat conduction in two dimensions have relied on methods of numerical approximation to solve the heat‐conduction equation. We have developed an exact analytical solution to the heat‐conduction equation in a two‐dimensional region of constant thermal properties. The surface temperature is described by a wave that varies sinusoidally with time and that has mean temperature, amplitude, and phase constant as arbitrary functions of space. In addition to a general solution, a particular solution is presented for a surface temperature pattern corresponding to a partial surface mulch. Calculated temperature and heat‐flux profiles beneath a partial surface mulch indicate that, at certain times of the day, there are large vertical and horizontal spatial variations in temperature and heat flux but, at other times, temperatures are uniform and heat fluxes have similar magnitude and direction. The calculations also show that, near the soil surface, the horizontal component of the heat flux can be quite large.