Analytical Solution for One-Dimensional Heat Conduction-Convection Equation
Jaynes, D. B.
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.
This article is published as Shao, Mingan, Robert Horton, and D. B. Jaynes. "Analytical solution for one-dimensional heat conduction-convection equation." Soil Science Society of America Journal 62, no. 1 (1998): 123-128. doi; 10.2136/sssaj1998.03615995006200010016x. Posted with permission.