Errors Incurred in Local Convective Heat Transfer Coefficients Obtained through Transient One-Dimensional Semi-Infinite Conduction Modeling: A Computational Heat Transfer Study

Abstract

In typical turbulent flow problems, detailed heat transfer coefficient (h) maps obtained through short-duration experiments are based on inverse heat transfer methods that take the wall temperatures measured via liquid crystals or infrared thermography as input, and an error minimization routine is adopted to determine the best value of h that satisfies the wall temperature temporal evolution under a certain change in fluid temperature. A common practice involves modeling the solid as a one-dimensional semi-infinite medium by selecting the solid material that has low thermal conductivity and low thermal diffusivity. However, in certain flow scenarios, the neglection of the lateral heat diffusion may lead to significant errors in the deduced h values. It is imperative to understand the reasons behind large errors that may be incurred by using the 1D heat conduction assumption in order to accurately determine high-resolution h maps for better heat exchanger designs in a wide range of thermal management applications. This paper presents a computational heat transfer study on different jet impingement scenarios to demonstrate the errors incurred in the determination of h when calculated under the assumption of one-dimensional (1-d) heat conduction into a solid. To this end, three different cases are studied: (a) single jet, (b) array jet (theoretical distribution), (c) array jet (experimental distribution), along with three different mainstream temperature evolution profiles representing step change, moderately fast transient and slow transient nature of flow driving the heat transfer in the solid. A known distribution of heat transfer coefficient (“true h”) for each of the three cases is considered, and three-dimensional transient heat diffusion equations were solved to populate temperatures of each node in the solid at every time step. It is found that stagnation zones’ h1d calculations were lower than the “true h” while the low heat transfer zones exhibited significantly higher h1d compared to the “true h”. For the array jet (experimental distribution) case, it was observed that errors can be as high as 10% in certain low heat transfer zones. Different data reduction procedures, configurations, and conditions explored in this study indicate that a suitable balance can be achieved if shorter time durations in transient experiments are used as a reference for tracking in h1d calculations to keep the deviations from the “true h” low.