On the use of Laplace and Warburg variables for heat diffusion modeling

The modeling of heat diffusion phenomena is important to develop optimal control strategies for ground coupled heat pump systems. This paper will discuss different model extraction techniques for such heat diffusion problems, namely using rational transfer function models in both the Laplace and the Warburg domain. The experimental verification is done using measurements on the heat diffusion problem in an isolated bar. The best rational transfer function models in the Laplace variable s and in the Warburg variable √s are compared, demonstrating that the Warburg domain has better predicting capabilities when it comes to predicting the lower frequency behavior of the system.