The precision of estimates of system performance and parameter estimation is often based upon the standard deviation obtained from the usual equation for the propagation of variances derived from a Taylor series expansion [1]. With increasing computing power, it is often suggested that the more complex Bayesian inference approach may yield improved estimates of the precision. The Bayesian approach has not been widely used in the heat transfer and fluid mechanics communities. The paper develops the necessary equations and applies them to two typical heat transfer problems. It is shown that, even for the simple problem of heat loss from a fin, that the predicted performance can be a strong function of relatively minor changes in the heat transfer coefficients or the thermal conductivity and as a consequence that the form of the parameter variability has a substantial effect.

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