Significance of Rosseland’s radiative process in magnetohydrodynamic Darcy–Forchheimer non-Newtonian fluid flow in a parabolic trough solar collector: Probable error

Thermal energy is produced from sunlight through solar thermal collectors, with the parabolic trough solar collector (PTSC) playing a crucial role in concentrated solar power (CSP) technologies by capturing solar energy at temperatures between 325 and 700 K. The tangent hyperbolic fluid model, a non-Newtonian fluid model, effectively predicts shear thinning behavior, as shown in experimental studies. This model’s rheological properties at varying shear rates contribute to its superior heat transmission performance. This study investigates the thermal efficiency of Darcy–Forchheimer magnetohydrodynamic tangent hyperbolic fluid flow in inclined cylindrical films, incorporating a non-uniform heat source/sink in the PTSC framework. The analysis considers the effects of radiation alongside the non-uniform heat source or sink on thermal phenomena. By applying relevant transformations, the governing equations are reformulated into a nonlinear ordinary differential system, solved using the Runge–Kutta fourth-order method with the shooting technique. Results are analyzed mathematically and graphically. The correlation coefficient is used as a statistical metric to examine the relationship between key parameters and their effect on the skin friction coefficient (SKF) and local Nusselt number (LNN). This approach evaluates potential errors to determine statistical significance. Findings show that Reynolds number exhibits a strong correlation of 0.8828 with SKF and 0.9769 with LNN, suggesting significant effects on heat transfer. Notably, parameters such as local porosity number and magnetic number affect SKF, while local porosity and mixed convection parameters strongly correlate with LNN, indicating that utilizing such fluids in PTSCs can enhance heat transmission rates and optimize solar energy utilization, ultimately improving system efficiency.