Transient Heat Transfer from a Buried Pipe

Figure 1. Computational domain and parameters

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.  It was desirable to  develop  simple algebraic correlations that could be used to approximate the intermittent overall heat transfer between a fluid flowing in an isolated buried pipe and the surrounding ground.

Figure 2. Sample heat flow results

A finite difference model of this transient problem was developed in a SINDA-like numerical package.  Figure 1 shows the computational domain and system and material parameters that were used in the numerical model.  The model was exercised over a wide range of ground and fluid properties and operating conditions.  Figure 2 presents one sample set of results showing  dimensionless heat flow as a function of time at the pipe wall.  Algebraic correlations of the results were developed in order to provide readily accessible and simple design equations.  Figure 3 demonstrates the agreement between the dimensionless average heat transfer and the algebraic correlation as a function of dimensionless time.

Figure 3. Sample average heat flow results with algebraic correlation

References

J.W. Stevens, 2002, “Coupled Conduction and Intermittent Convective Heat Transfer From a Buried Pipe,”  Heat Transfer Engineering, Vol 23, n. 4, pp. 34-43.

J. W. Stevens, 2000, “Intermittent Convective Heat Transfer for Ground-source Heat Pump Design,”  Proceedings of the ASME Advanced Energy Systems Division – 2000, AES-Vol. 40, pp. 147-152.

J.W. Stevens, 1998, "Transient Heat Transfer Approximations for Ground-source Heat Pump Design,"  Proceedings of the ASME Advanced Energy Systems Division – 1998, AES-Vol. 38, pp. 415-424.