Solutions of the heat conduction equation in a non‐uniform soil

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Abstract
A class of analytic, periodic solutions of the heat conduction equation in a non‐uniform soil is derived. The class may be characterized by the fact that the speed of the temperature wave varies according to the square root of the soil diffusivity (a function of soil depth). In addition it is shown that the constant soil solution is the limiting case when the rate of change with depth of diffusivity and thermal conductivity become very small. The solutions may be regarded as general whenever temperature analysis is restricted to small values of depth or whenever the soil parameters vary slowly. For all other cases the class of solutions possess the additional property that the rate of change of conductive capacity varies directly as the product of the bulk density and specific heat of the soil. A particular temperature profile is given for the case when the diffusivity varies as the nth power of depth.

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