Thermal Response of Longitudinal Moving With Stretching/Shrinking Mechanism of Porous Fins Having Concave Parabolic, Trapezoidal, and Convex Profiles

ABSTRACT This paper presents a numerical investigation of transient heat transfer in a longitudinal moving porous fin of varying geometries—trapezoidal, convex, and concave profiles under stretching and shrinking motion. The system operates in a convective‐radiative environment with temperature‐dependent thermal conductivity, surface emissivity, and heat transfer coefficient. A unified mathematical model is developed using a general geometric function that describes concave, convex, and trapezoidal profiles as special cases. The nonlinear energy equation governing transient temperature distribution is nondimensionalized and solved numerically using the PDEPE finite‐difference solver in MATLAB. The results indicate that geometry significantly influences thermal behavior and cooling performance. An increase in the Peclet number reduces the temperature distribution by approximately 12%–18%, indicating enhanced advective heat transport. Similarly, increasing the convection‐conduction parameter improves heat dissipation by about 8%–12%, leading to a noticeable reduction in temperature. Among the considered profiles, the concave parabolic fin exhibits the highest overall thermal efficiency, achieving approximately 10%–15% higher efficiency compared to trapezoidal and convex configurations. In contrast, the convex fin shows lower local temperatures due to enhanced surface heat dissipation, while the trapezoidal profile demonstrates intermediate behavior. Furthermore, shrinking motion enhances the cooling capability, whereas stretching reduces overall thermal efficiency. The study offers valuable insights for aerospace, electronic cooling, and energy system applications, where optimized geometry and transient thermal behavior are crucial for efficient heat dissipation. The proposed model can assist in the design of advanced cooling systems such as heat exchangers, electronic heat sinks, and thermal control components based on porous fins.