CONDUCTIVE HEAT TRANSFER FROM HEMISPHERICAL, BURIED TANKS WITH APPLICATION TO SOLAR HEATING
Buried thermal storage tanks can permit the storage of solar collected thermal energy from the summer, when it is most readily available, to the winter, when it is most needed for building heating. Both the tank temperature and the ambient temperature vary in a quasi-cyclic manner, with a period of one year. This paper first presents a mathematical formulation of the problem of assessing the heat transfer from the tank to its ambient environment. The tank geometry considered is a buried hemisphere with its equatorial plane coplanar to the ground surface. The total problem is divided into three separate boundary-value problems, and general analytical solutions to two of the problems are given in terms of Bessel function and Legendre polynomial series. The two boundary value problems solved correspond to the case where: (a) both the tank temperature and the ambient temperature are static; and (b) the case where the tank temperature is cyclic and the ambient temperature is static. The series solutions are summed for the heat transfer in both of these cases and the results given in generalized plots of the dimensionless heat transfer as a function of the relevant Biot and Fourier numbers.