Uncertainty analysis of PCM-enhanced systems for reliable prediction of thermal capacity using stochastic finite element method

Enhancement of building elements, such as pipes and walls, with PCM can significantly improve the thermal efficiency and/or reduce the energy demand of heating, ventilation and cooling systems. A difficulty in the numerical modelling and design of these systems is that for most available commercial technical grade and mixed PCM there is only limited information on their thermal properties and their phase change behavior available. PCM model parameters are uncertain and consequently the reliability of the outcome of simulation-based studies is limited. This contribution proposes a computationally efficient stochastic mathematical modelling approach for uncertainty analysis in nonlinear heat transfer problems with phase change. In this approach the most important PCM parameters for the characterization of the phase change enthalpy and the solid/liquid transition behavior are considered as random parameters. Case studies are presented where uncertainties in the properties of a commercial paraffin-based PCM are determined from caloric data generated by extensive and systematic Differential Scanning Calorimetry experiments. The identified uncertain PCM properties are then used in numerical analysis of heat transfer in a PCM-enhanced pipe insulation, and a PCM-enhanced multi-layer wall element. The results nicely demonstrate that the stochastic analysis can generate useful insights about the impact of uncertainties on simulation results. The generated information is resolved in time and space and allows for a quantitative analysis of the robustness of design decisions in the engineering process.