Natural convection from avertical ground heat exchanger embedded in a semi-infinite porous medium

The heat-transfer process from a vertical ground heat exchanger to the surrounding soil is simulated by natural convection from a vertical cylinder embedded in a semi-infinite porous medium and is investigated numerically. Steady as well as transient behaviors were studied. The governing equations are expressed in the stream function-temperature formulation, and an explicit finite-difference technique was developed to solve the coupled nonlinear equations. Results are presented for a vertical cylinder with uniform heat flux at different Rayleigh numbers and aspect ratios for typical ground heat exchanger conditions. The thermal interaction with the atmosphere represented by Biot number at the ground surface is taken into consideration. The numerical results are used to obtain simple correlations for the average Nusselt number in the transient and steady-state phases, which can be used for simulation as well as sizing of ground heat exchangers.