A hybrid optimization technique for developing heat transfer correlations based on transient experiments

A new approach for developing a Nusselt number correlation, in terms of relevant non-dimensional parameters, for turbulent forced convection flows in vertical channels using a judicious combination of transient cooling experiments with a hybrid optimization technique is reported. The temperature–time history, during the cooling of a heated plate, idealized as a lumped capacity heat transfer model, is recorded using a PC based data acquisition system. A numerically computed temperature–time history of the plate is then compared with the experimentally known temperature–time history to estimate the residual. The minimization of sum of the squares of the residual is done using a hybrid numerical optimization technique, i.e. a combination of Genetic Algorithm and the Levenberg–Marquardt method, in order to obtain the coefficient and the exponents of the pertinent non-dimensional parameters in the Nusselt number correlation. The parameters in the correlation are also retrieved using another global optimization technique, the Simulated Annealing (SA), for evaluating the consistency in parameter estimation. As a validation exercise, Nusselt number values estimated using the proposed correlation are compared with steady state experimental results and a good agreement of results endorses the efficacy of this approach.