Applying a full implicit finite-difference method in jet impingement heat transfer studies

Jet impingement heat transfer is an effective and practical approach that is employed in many industrial processes where heating, cooling, or drying is required. Details of the heat or mass transfer rate have been investigated both experimentally and numerically and can be found in the published literature. In most of the numerical studies, control-volume approach has been employed to solve the governing equations of the thermal and flow fields. Using this numerical approach, a pressure correction equation is usually developed from the conservation equations in a rigorous manner to obtain the pressure distribution. Avoiding the complexities encountered in the traditional manner, a full implicit finite-difference method was developed for the first time and applied for studying jet impingement heat transfer. Similar to the velocity components, static pressure was also treated as an unknown variable in this approach. Specifications of both flow and thermal fields were obtained for two cases of confined and unconfined jets by the proposed numerical method. It was demonstrated that this novel numerical approach was a straightforward method, which required no additional equation for pressure calculation, and had the potential use in other two- or three-dimensional flow and thermal field analysis.