Comparison of heat diffusion model in Laplace and Warburg variable

Research output: Chapter in Book/Report/Conference proceedingMeeting abstract (Book)


The modeling of heat diffusion is important, for example, for the development of an efficient control strategy of a geothermal heat pump. Heat diffusion processes are typically described by parabolic partial differential equations, leading to transfer functions that can be described as rational transfer functions in the Warburg variable ?s. Small thermal structures, on the other hand, are often modeled as a series of connected RC networks. This poster discusses these two different rational transfer function models used for the dynamic modeling of a simple heat diffusion problem. The heat diffusion in an isolated iron construction is considered as a test case. A comparison is made between the modeling using rational transfer function models in the Laplace variable s and in the Warburg variable ?s. First, a rational model in the Laplace domain is fitted on the measured data. By limiting the possible rational models to the ones for which the poles and zeros are real we find a model that can be interpreted as a combination of resistors and capacitors. Since diffusion phenomena can only be approximately described by a rational form in the s-domain we also fit a rational model in the ?s-domain. Then we try to interpret model in the ?s-domain as a combination of two rational models, namely one in the s-domain and one in the ?s-domain. The first model in the s-domain describes the heat transport over a short distance whereas the latter model in the ?s-domain describes the heat diffusion over large distances. Finally, we compare the results in both domains in order to choose the best suited model.
Original languageEnglish
Title of host publicationERNSI Workshop Cambridge,UK, September 26-29, 2010
Publication statusPublished - 26 Sep 2010
EventUnknown -
Duration: 26 Sep 2010 → …


Period26/09/10 → …


  • Laplace variable
  • Warburg variable
  • heat diffusion


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