Quantification of uncertainty propagation due to input parameters for simple heat transfer problems

Abstract

Propagation of uncertainty through the physical model has been investigated in the present paper by solving two specific simple stochastic problems using the Non-Intrusive Spectral Projection method. The uncertain parameters are described by either a Gaussian or a LogNormal probability distribution function. For each of the problems, the stochastic and the deterministic mean solutions have been compared and the respective confidence intervals have been obtained. For the deterministic problems, the confidence intervals have been estimated using both one-dimensional and multi-dimensional bound methods. From the results it has been observed that the differences between the stochastic and the deterministic mean solutions are apparent only when large uncertainties are introduced in the random variables. For both the specific problems, considered in the present study, the confidence intervals for the stochastic problems have been exactly predicted by the deterministic limits when uncertainty is introduced only in one of the parameters. For more than one uncertain parameters, the multi-dimensional bound method produces better agreement with the stochastic confidence intervals than the one-dimensional bound method. The findings are expected to be applicable to problems in heat and mass transfer with similar characteristics or input–output relations.