Natural-convection heat transfer from a cylinder embedded vertically in water-saturated Ottawa sand was investigated experimentally and numerically under temperatures relevant to ground heat exchangers for heat pumps. Measurements were made of the steady-state temperature field in an annular region bounded by a vertical constant-heat-flux inner cylinder and a constant-temperature concentric outer cylinder. The measured temperature profiles were found to deviate significantly from conduction-only solutions, to deviate significantly from conduction-only, indicating the importance of natural convection. Comparisons between measured temperatures and numerical prediction obtained using a finite-difference solution technique in Fortran developed by the authors showed good agreement. Using this computer program, numerical solution points are obtained and plotted in terms of average Nusselt numbers vs. Rayleigh numbers for an isothermal cylinder embedded vertically in an infinite water-saturated permeable sand for a range of temperature differentials and length-to-radius ratios typical of ground heat exchangers for heat pumps.

KEYWORDS: convection, heat flow, heat exchangers, heat pumps, vertical, cylinders, experiment, computer programs, measuring, steady state, temperature, conduction loss, soil heat pumps, soil heat pumps, Rayleigh number, Nusselt number