Thermal Stress Analysis and Heat Transfer Optimization in Functionally Graded Annular Fin With Memory‐Dependent Effects

ABSTRACT This study examines the thermal stress behavior of functionally graded material (FGM) rectangular‐shaped annular fins, utilizing memory‐dependent derivatives (MDDs) as an alternative framework to traditional fractional‐order theory. The MDD approach enhances physical interpretability and adaptability by incorporating single‐phase‐lag (SPL) and kernel functions, allowing for more accurate modeling of transient thermoelastic behavior. Material properties, including thermal conductivity, specific heat capacity, heat transfer coefficient, and modulus of elasticity, are expressed as power‐law functions along the radial direction, while Poisson's ratio remains constant. Analytical solutions are derived for specific parameter values, and a detailed parametric study evaluates the influence of time delay, kernel functions, and inhomogeneity parameters on thermal stress distribution. The analysis focuses on an FGM structure composed of partially stabilized zirconia (PSZ) particles dispersed within a SUS304 matrix, emphasizing the importance of composition selection in reducing thermal stress. Its ability to withstand high‐temperature gradients while minimizing thermal stress enhances durability and performance. Future research can explore advanced computational techniques and experimental validation to optimize its thermal efficiency and mechanical stability further.