Thermal Analysis of Longitudinal Moving Fins With Different Geometries and Internal Heat Generation Using the Clique Polynomial of the Cocktail Party Graph

ABSTRACT Moving fins play a crucial role in various engineering systems for effective thermal management. This study investigates the thermal behavior of concave parabolic, convex, and trapezoidal fin shapes under longitudinal motion, considering combined radiative and convective heat transfer. Key thermal characteristics, such as heat conduction, thermal radiation, convective exchange, internal heat generation, and effects of wet porous media, are modeled as temperature‐dependent. A novel computational technique, the clique polynomial of the cocktail party graph collocation method (CPCPCM), is employed to evaluate the nondimensional temperature variation. Results indicate that increasing the convection () and radiation () parameters reduces approximate 12% the fin temperature. An increase in the wet porous parameter () lowers heat transfer but increases heat absorption, further decreasing the temperature profile. Internal heat generation (), modeled as linearly temperature‐dependent, raises the fin temperature as increases and increasing the Peclet number () from 1 to 3 results in an approximate 5% rise in the temperature. Among all shapes, the convex fin shows the highest temperature profile, suggesting superior thermal performance in engineering applications.