How the behavior of thermal systems depends on uncertainties in properties and boundary conditions is an important aspect of simulation. This dependence is usually judged by the statistics of the response, i.e., the mean response and its standard deviation which are often determined by perturbation methods, ranging from 1st to 3rd order. The aim of this paper is to be a tutorial for those interested in estimating uncertainties by summarizing the author’s experience in using higher order perturbation analysis for thermal problems, detailing the underlying assumptions, and presenting several examples. Problems involving correlated parameters, which occur in almost all thermal experiments, are also treated. It is shown that the scale of correlation has a strong effect upon the statistics of the response and that such correlation should not be ignored. It is recommended that the 1st order estimates of the standard deviation and 2nd order estimates of the mean response be used when characterizing thermal systems with random variables, regardless of the degree of correlation.
Multiple-time higher-order perturbation analysis of the regularized long-wavelength equation