Statistical Validation for Heat Transfer Problems: A Case Study

This paper presents a proposed methodology for applying statistical techniques as the basis for validation activities of a computer model of heat transfer. To demonstrate this approach, a case study of a Ruggedized Instrumentation Package subject to heating from battery discharge and electrical resistance during normal operations is considered. First, the uncertainty in the simulation due to the discretization of the governing partial differential equations is quantified. This error is analogous to the measurement error in an experiment in that it is not representative of actual physical variation, and is necessary to completely characterize the range of simulation outcomes. Secondly, physical uncertainties, such as unknown or variable material properties, are incorporated into the model and propagated through it. To this end, a sensitivity study enables exploration of the output space of the model. Experiments are considered to be a realization of one of these possible outcomes, with the added complication of containing physical processes not included in the model. Statistical tests are proposed to quantitatively compare experimental measurements and simulation results. The problem of discrepancies between the computational model and tests is considered as well.