A correlation for Nusselt number under turbulent mixed convection using transient heat transfer experiments

This paper reports the results of an experimental investigation of transient, turbulent mixed convection in a vertical channel in which one of the walls is heated and the other is adiabatic. The goal is to simultaneously estimate the constants in a Nusselt number correlation whose form is assumed a priori by synergistically marrying the experimental results with repeated numerical calculations that assume guess values of the constants. The convective heat transfer coefficient "h" is replaced by the Nusselt number (Nu) which is then assumed to have a form NuD= a RiDbReDc where a, b and c are the constants to be evaluated. From the experimentally obtained temperature time history and the simulated temperature time history, based on some guess values of a, b and c, one can define the objective function or the residue as the sum of the square of the difference between experimentally obtained and simulated temperatures. Using Bayesian inference driven by the Markov chain Monte Carlo method, one, more or all of the constants a, b and c are retrieved together with the uncertainty involved in these estimates. Additionally, the estimated parameters are compared with experimental benchmarks.