Analysis of an Impinging Two-Dimensional Jet

Heat transfer in jet impingement is a complicated phenomenon and a general analytical solution is not available. Typical jet impingement studies are conducted experimentally and best-fit correlations are proposed (Beitelmal, Saad, and Patel [2]; Beitelmal [3]; Beitelmal, Saad, and Patel [4]; Schauer and Eustis [7]; McMurray, Myers, and Uyehara [8], Gardon and Akfirat [9]). Separate solutions for the stagnation region and the wall jet region are then combined to determine the overall heat transfer solution for the impinging jet. In this paper, stagnation and wall jet region solutions for a two-dimensional jet normally impinging on a flat surface are developed using heat transfer relations available in the literature. These solutions are analyzed and compared to previous experimental results (Beitelmal, Saad, and Patel [2]; Beitelmal [3]). The potential flow assumption is used for the fluid dynamics analysis at the stagnation region. For the wall jet region, a comparison was achieved through consideration of the classical analytical solution for parallel flow over a flat plate. Analytical solutions as well as semiempirical solutions for the stagnation region and the wall jet reported by previous investigators were also considered. Predictions for heat transfer in the stagnation region using potential flow assumptions were found to be accurate to within 20%. For the wall jet region, previous correlations predicted by McMurray, Myers, and Uyehara [8] and Nizou [10] were found to be the most accurate. At large values of $x∕D$⁠, the heat transfer properties in the wall jet are shown to be very similar to those of a turbulent boundary layer over a flat plate. Such a simplified analysis in different regions of an impinging jet using some basic fluid dynamics assumptions can greatly facilitate a prediction of the local Nusselt number.