Application of Green’s Function to Establish a Technique in Predicting Jet Impingement Convective Heat Transfer Rate from Transient Temperature Measurements

Abstract

Jet impingement heat transfer has gained attention of the researchers due to its very high rate of convective heat transfer. The objective of this study is to establish an analytical technique to predict the convective heat transfer coefficient and the reference temperature over a surface being impinged. This technique is based on the fundamental mathematical concept of Green’s function. A code in MATLAB is developed to predict both local convective heat transfer coefficient and reference temperature over the impinging surface, which requires the transient temperature data at both faces of the impinging plate as input. Radiation correction is also considered to incorporate radiation losses in high-temperature applications. This code works on the principle of one-dimensional heat transfer across the impinging plate, for known dimensions, thermal diffusivity, and surface emissivity. A numerical simulation of hot jet at Reynolds number equal to 1000, over a cold plate of thickness 10 mm, is carried out for a given set of spatially varying convective heat transfer coefficient and reference temperature values, along the impinging surface. The impinging plate is considered to be orthotropic to ensure one-dimensional heat conduction across the plate thickness. Transient temperature at both the faces for a duration of 10 s with an interval of one second was recorded and used as input to the code to validate the proposed technique. Local heat transfer coefficient and the reference temperature predicted are in good agreement with those input values for numerical analysis using ANSYS, having a maximum deviation of 2 and 10%, respectively. Further, it is observed that estimated values of convective heat flux at a given location on the impinging surface varies linearly with temperature at the same location, which confirms Newton’s law of cooling.