Investigation of turbine cooling using semi-analytical methods in non-Newtonian fluid flow with porous wall

This study explores non-Newtonian fluid dynamics in an axisymmetric channel with a porous boundary, focusing on its relevance to turbine cooling systems in engineering and industry. Managing fluid flow in such systems is crucial. To address the complexity, mathematical tools like the Homotopy Perturbation Method, Variational Iteration Method, and Runge-Kutta 4th numerical method are used to solve nonlinear differential equations governing momentum and heat transfer. The investigation primarily aims to elucidate relationships in system parameters, including the Power Law index, Reynolds number, and Prandtl number. These relationships are compared with numerical techniques, assessing the precision and simplicity of the employed methods. The inquiry goes beyond conventional research paradigms, exploring constant parameters and trial function steps. The proposed solution reveals a theme of precision, simplicity, and efficient convergence. The correlation between the Reynolds number and the thermal boundary layer is a significant finding. Increasing the Reynolds number and adjusting the Power Law index results in a noticeable reduction in the thermal boundary layer. This has substantial implications for temperature profiles in coupled systems, potentially enhancing cooling effectiveness in various industrial applications.