Analytical investigation of temperature‐dependent thermal conductivities in functionally graded conical shells: General thermal boundary conditions

Abstract This investigation, for the first time, analytically provides a solution for steady‐state heat conduction in 2D functionally graded conical shells under general boundary conditions (BCs). The material properties vary in both angular and longitudinal directions according to an arbitrary power‐law function of the longitudinal variable. Furthermore, the thermal conductivity coefficients are assumed to be linearly dependent on temperature, providing a more realistic understanding of heat transfer in functionally graded materials (FGMs). To derive the temperature distribution, this study employs the Kirchhoff transformation, the finite integral transform, and Green's function. An excellent agreement is observed when comparing the results of the present study with available analytical data. To demonstrate the practical applicability of the solution in various industrial scenarios, such as cooling pin fins and spacecraft heat shields, a typical industrial case is analyzed. Additionally, the effects of different parameters on the temperature distribution are studied.