An Exact Analytical Solution for Heat Conduction in a ‎Functionally Graded Conical Shell

Abstract

In this study, an exact analytical solution for the heat conduction problem in a truncated conical shell is presented. The cone is made of functionally graded materials and it is considered that the material properties vary according to power-law functions. The general thermal boundary conditions are applied to cover a wide variety of actual applications. The results are successfully validated. Two examples, which are tried to mimic practical conditions, are studied using the derived solution, and a parametric study is done to shed light on the problem. The outcomes of this research provide useful information for understanding the nature of heat transfer behavior in the specific geometry of a cone. Regarding the specific applications of conical shells, the results can be used in the prefabrication process of these shells and tailoring the design parameter of functionally graded materials.

Keywords

• exact analytical study
• conical shell
• functionally graded material
• heat conduction
• general thermal boundary conditions