Mixed thermal convection heat transfer to an ultralarge heat pipe placed in geothermal reservoirs has been investigated both analytically and numerically. The heat pipe axis was assumed to be oriented vertically (parallel to the gravitational acceleration) and subjected to uniform upwelling flows. The buoyancy effects are taken into account through the Boussinesq approximation. First similar transformations were implemented locally with the boundary layer aproximation. The fully two dimensional solutions were also computed numerically by means of finite differences in order to test the validity of the locally similar solutions. Both of them were fair in agreement. In general it is found that the buoyancy effects on the rate of heat transfer are weak within a presently studied parametric range.

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Using a numerical simulator, a parametric study was carried out to investigate the longterm thermal output characteristics of a downhole coaxial heat exchanger. The effects of flow rate, inlet water temperature, well depth, undisturbed temperature distribution, and effective thermal conductivity of the formation were evaluated. The possible advantage of insulating the upper part of the casing were also studied. The following results were obtained: (1) For a given inlet water temperature, the outlet water temperature decreases but the net thermal output becomes higher with increasing flow rate. There appear to be limiting value of net thermal output, even when the flow rate is substantially increased. The effect of flow rate on the net thermal output is amplified by an increase of effective thermal conductivity of the formation. (2) The outlet water temperature is raised linearly with the inlet water temperature, whereby the coefficient of linearity is larger for a larger flow rate. The net thermal output is inversely proportional to the increase of inlet water temperature, where the coefficient is proportionately smaller for larger flow rates. (3) If heat transfer in the formation is purely conductive, there is no significant advantage of adopting an “insulated casing” to prevent heat loss. (4) For a fixed total borehole depth, the net thermal output increases linearly with increasing geothermal gradient, Heat extractivity index as defined by the following formula correlated very well with the net thermal output after 1 year of heat extraction:Heat extractivity index (°Ckm)=∫₀ ^b{t(z)-t_in}dzwhre b is the depth of borehole in km, t_in is inlet water temperature in °C, and t (z) is undisturbed formation temperature at depth z in °C. Hence, the heat extractivity indexmay be useful for preliminary evaluation of thermal energy extractivity at each borehole and site-selection.(5) Greater thermal output could be obtained in the case of high effective thermal conductivity, or in the convective case rather than the purely conductive case. The present system is expected to perform better for boreholes drilled in permeable, high-temperature formations where convective heat transfer is expected.

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