An accurate estimate of the heat transfer from a buried pipe to the surrounding ground is essential for the design of the ground loop portion of a ground-source heat pump. Exact analytical solutions to this problem are complicated by the fact that heat pump systems rarely operate continuously. Complete numerical simulations of system designs can be carried out, but these are unwieldy and difficult to justify for initial scoping calculations, or for preliminary performance estimates. The purpose of this paper is to describe the development of simple algebraic correlations that can be used to approximate the intermittent overall heat transfer between a fluid flowing in an isolated buried pipe and the surrounding ground.
The correlations described in this paper were drawn from results of a numerical finite-difference analysis of a fluid flowing intermittently in a single round pipe and exchanging heat with the surrounding ground. The two-dimensional analysis was carried out for ranges of the parameters of intermittence factor, thermal diffusivity of the ground, and convective heat transfer coefficient at the fluid-wall interface. The surrounding ground is unbounded for the purposes of the analysis. The dimensionless heat transfer can be easily related to the overall thermal resistance between the flowing fluid and the ground far from the buried pipe.
It is found that the cycle average heat transfer is always lower for the intermittent case than for the continuous case, but that the average over just the active part of the cycle is always higher for any intermittent case than for the continuous case. The effect of the ground thermal diffusivity is largest when the heat transfer coefficient is large, and decreases with decreasing heat transfer coefficient. The range of heat transfer coefficients where isothermal wall conditions are approached is illustrated. Correlations for the operating average and cycle average total heat transfer are presented as functions of the thermal diffusivity, intermittence factor, and heat transfer coefficient.