Heat transfer analysis of soil heating systems

Heat transfer from a pipe in a soil heating system has been numerically examined in this study. The Brinkman-extended Darcy equations are used to model the flow in the soil while Navier--Stokes equations are used for that above the soil. A parametric study has been performed to investigate the effects of Rayleigh number, Darcy number, and air layer thickness on the flow patterns and heat transfer rates. The results show that heat transfer increases with the Rayleigh number, but the convective strength decreases with a reduction in the Darcy number. The present results confirm the existence of a critical fluid layer thickness that leads to a minimum heat transfer from the pipe. However, the critical layer thickness is a more complicated function of Rayleigh number and Darcy number than that reported in the previous studies.