Computational analysis of wetted triangular spine fin using Lerch polynomial collocation method

Fins are widely applied in heat exchanging systems to increase the heat transmission between a primary surface and the surrounding fluid. The employment of optimized fin model is a highly efficient method for enhancing the overall efficiency of fin-integrated heat exchangers, which are extensively utilized in the refrigeration and air-conditioning operations. Motivated by these facts, the modified configuration of triangular spine fin is considered to analyze its efficiency and enhancement of heat transfer. Also, the existing study explores the temperature dispersion in a rectangular and triangular porous wet spine fin, influenced by both convection and radiation. To describe radiation heat exchange, the Rosseland approximation is taken to consideration. By introducing non-dimensional terms, the governing equation is transformed into its dimensionless form. The resulting nonlinear ordinary differential equation is solved via Lerch polynomial collocation method (LHPCM). The precision of the LHPCM is depicted by the execution of error analysis between the exact solution and numerical results provided in the literature. Furthermore, the results of these comparisons confirm that the proposed algorithm provided the accurate solutions. The demonstrated approach exhibits detailed procedures, which are highly accurate, reliable, and require minimized computational efforts. Moreover, graphical analysis is presented to highlight the influence of different non-dimensional parameters on the thermal distribution, heat transfer, and efficiency of both rectangular and triangular spine fins. The pertinent results disclose that, the rate of heat is transferred progressively with an increase in porous parameter, wet parameter, and convective-conductive parameter.