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Analytical Solution for One-Dimensional Heat Conduction-Convection Equation

Shao, Mingan, Horton, Robert, Jaynes, D. B.
Soil Science Society of America journal 1998 v.62 no.1 pp. 123-128
mathematical models, soil temperature, equations, soil heterogeneity, soil depth, water flow, soil water, heat transfer
Coupled conduction and convection heat transfer occurs in soil when a significant amount of water is moving continuously through soil. Prime examples are rainfall and irrigation. We developed an analytical solution for the heat conduction-convection equation. The solution for the upper boundary of the first type is obtained by Fourier transformation. Results from the analytical solution are compared with data from a field infiltration experiment with natural temperature variations. The predicted temperature values are very similar to the observed values. Temperature changes with time for different soil depths are predicted from conduction-convection theory and from conduction theory alone. During infiltration, convective heat transfer contributed significantly to the temperature changes at all soil depths monitored. The theory also quite accurately predicts temperature effects on surface infiltration. Journal paper no. J-16111 of the Iowa Agriculture and Home Economics Exp. Stn., Ames, IA, project no. 3262 and 3287.