Solution by operational matrix based Vieta-Lucas collocation method to analyze the thermal performance of the convex spine fin applicable in air conditioning systems

Finned surfaces are commonly used for enhancing the heat transfer rate between the ambient surroundings and the system. Numerous technical applications, including industrial cooling systems, cryogenics, and air conditioning, utilize finned surfaces. Specifically, spine fins are employed in cooling systems to increase heat transmission in the air ducts, resulting in enhanced effectiveness of temperature regulation inside buildings. Thus, the present investigation analyzes the thermal distribution in a convex-shaped porous spine fin wetted with a ternary hybrid nanofluid with the effect of radiation and internal heat generation. The phenomenon of thermal dispersal is described by nonlinear differential equations with pertinent boundary conditions. These equations are transformed into dimensionless forms using appropriate non-dimensional variables, and the convergent series solution is obtained by applying the shifted Vieta-Lucas polynomials-based collocation technique with the integration matrix. The convective-conductive parameter, porosity parameter, wetted parameter, and radiative-conductive factors are shown to rise in correlation with the decrease in temperature distribution. Furthermore, a 50 % increase in the wet parameter values elevates 3.28 % of heat transfer in the convex spine. The porous fin wetted with a hybrid nanofluid exhibits more heat-transferring characteristics than the dry fin.