INVERSE HEAT CONDUCTION PROBLEM OF ESTIMATING TIME-VARYING HEAT TRANSFER COEFFICIENT

Abstract

An inverse heat conduction problem is solved by using Alifanov's iterative regularization method to estimate the time-varying heat transfer coefficient of forced-convective flow boiling over the outer surface of a heater tube. The estimation is based on transient temperature measurements taken by a thermocouple on the inner surface of the circular tube on which the flow boiling occurs. The inverse problem is solved as an optimization problem in which a squared residue functional is minimized with the conjugate gradient method. A sensitivity problem is solved to determine the step size in the direction of descent, and an adjoint problem is solved to determine the gradient of the functional. No prior information is used in the functional form of the heat transfer coefficient variation with time. Numerical experiments are performed to test the proposed mathematical model of the measurement of flow boiling heat transfer coefficient. Effects of the time scale of the heat transfer coefficient variation, the measurement errors, and the data acquisition rates on the inverse solution are investigated. We found that for a given experimental configuration there is a physical limitation on the time scale of the heat transfer coefficient variation that can be estimated by the inverse analysis.