Experimental validation of an inverse method for bottom heat flux determination in a heat sink

A transient Inverse Conjugate Heat Transfer Problem (ICHTP) is experimentally investigated to estimate the spatially and temporally varying applied bottom heat flux in a three-dimensional plate-fin heat sink using infrared thermography. In this framework, the interface between the heat sink and the air domain is assumed to exhibit perfect thermal contact, thereby defining the problem as a transient conjugate heat transfer formulation. Unlike conventional inverse heat conduction problems, this approach necessitates the simultaneous solution of the continuity, momentum, and energy equations in the air domain, coupled with the heat conduction equation in the heat sink domain, significantly increasing its complexity. To the best of the authors’ knowledge, this work represents the first experimental investigation of an ICHTP aimed at estimating the unknown heat flux of a heat sink. The accuracy of the estimated heat flux is verified experimentally under a prescribed inlet air velocity. Results indicate that, due to the singularity of the cost-function gradient at the terminal time, estimates near the final time must be discarded. For numerical simulations with error-free measurements and an inlet velocity of 5 m/s, highly accurate bottom-surface heat fluxes are recovered. The effect of measurement noise (σ = 0.3) is further examined in both numerical simulations and experimental evaluations. The average relative errors of the estimated heat fluxes are 2.82 % in the simulations and 9.6 % in the experiments, both achieved with only six iterations. The discrepancy arises because measurement noise in simulations can be precisely controlled, whereas experimental measurements inherently exhibit greater uncertainty. This underscores the inherent challenges associated with inverse problems and highlights the importance of obtaining accurate measurement data in the problem domain. Moreover, if the discrepancy principle is not employed as the stopping criterion, the estimation of heat flux deteriorates with additional iterations, despite the apparent reduction in temperature residuals between measured and estimated values.