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Solutions of the heat conduction equation in a non‐uniform soil
Author(s) -
Wiltshire R. J.
Publication year - 1982
Publication title -
earth surface processes and landforms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.294
H-Index - 127
eISSN - 1096-9837
pISSN - 0197-9337
DOI - 10.1002/esp.3290070303
Subject(s) - thermal diffusivity , thermal conduction , heat equation , thermal conductivity , constant (computer programming) , thermodynamics , heat capacity , limiting , function (biology) , soil science , materials science , mathematics , environmental science , mathematical analysis , physics , mechanical engineering , evolutionary biology , biology , computer science , engineering , programming language
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 n th power of depth.