Bayesian estimation of heat transport parameters in fixed beds

Abstract An approach based upon Bayes Theorem has been developed to resolve two major difficulties encountered in earlier experimental investigations concerned with the estimation of parameters for heat transfer in fixed beds. The first difficulty is in obtaining estimates of the Nusselt and Peclet groups with appropriate confidence intervals, and the second is the considerable variation found in the Peclet and Nusselt groups in the range of intermediate Reynolds number. In a new experimental investigation it has been found that estimates of the Peclet and Nusselt groups could be changed in a correlated way without changing the variance of experimental error about the theoretical values, an interaction that precluded the accurate estimation of either parameter. The Bayesian approach identified a confidence region linking the Nusselt and Peclet groups from earlier work, and a confidence region for the two parameters obtained in the new investigation; the best estimates were obtained where the two confidence regions overlapped. In the final presentation the parameter values and independent estimates of parameter accuracy were found to be consistent with correlations established on the basis of earlier work, but with greatly improved confidence regions for the Nusselt and Peclet groups expressed as functions of Reynolds number.