Optimizing the cooling efficiency of a convex spine fin with wetted characteristics beneficial in automotive components: an execution of Charlier polynomial collocation method

• Published in: Applied mathematics and mechanics Vol. 46; no. 8; pp. 1609 - 1630
• Main Authors: Mallikarjuna, A. N., Abhilasha, S. K., Varun Kumar, R. S., Gamaoun, F., Prasannakumara, B. C.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2025; Springer Nature B.V
• Edition: English ed.
• Subjects: Ambient temperature; Applications of Mathematics; Automotive parts; Classical Mechanics; Collocation methods; Cooling; Fluid- and Aerodynamics; Heat; Heat exchangers; Heat generation; Industrial applications; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nonlinear differential equations; Ordinary differential equations; Parameters; Partial Differential Equations; Performance enhancement; Polynomials; Radiation; Radiators; Temperature profiles; wet fin; 65L06; O357; Charlier polynomial collocation method; 65L60; fin; spine; internal heat generation; 80A20; O242.21; 65L10
• DOI: 10.1007/s10483-025-3278-9
• ISSN: 0253-4827

Fins are extensively utilized in heat exchangers and various industrial applications as they are lightweight and can benefit in various systems, including electronic cooling devices and automotive components, owing to their adaptable design. Furthermore, spine fins are introduced to improve performance in applications such as automotive radiators. They can be shaped in different ways and constructed from a collection of materials. Inspired by this, the present model examines the effects of internal heat generation and radiation-convection on the thermal distribution in a wetted convex-shaped spine fin. Using dimensionless terms, the proposed fin model involving a governing nonlinear ordinary differential equation (ODE) is transformed into a dimensionless form. The study uses the operational matrix with the Charlier polynomial collocation method (OMCCM) to ensure precise and computationally efficient numerical solutions for the dimensionless equation. In order to aid in the analysis of thermal performance, the importance of major parameters on the temperature profile is graphically illustrated. The main outcome of the study reveals that as the radiation-conductive, wet, and convective-conductive parameters increase, the heat transfer rate progressively improves. Conversely, the ambient temperature and internal heat generation parameters show an inverse relationship.