Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 53 Issue 1 (Special Issue) 2021 03 21 Analytical Solution of Heat Transfer in a Cone Made of Functionally Graded Material Analytical Solution of Heat Transfer in a Cone Made of Functionally Graded Material 539 552 3674 10.22060/mej.2019.16288.6320 FA Amin Emamian Shahrood University of Technology 0000-0002-7568-0691 Amin Amiri Delouei Sajjad Karimnejad Shahrood University of Technology Hasan Sajadi بجنورد-فنی و مهندسی- گروه مهندسی مکانیک 0000-0002-0681-7682 Journal Article 2019 05 06 In the current study, the problem of two-dimensional steady-state heat conduction in a truncated hollow cone made of functionally graded materials is referred and an exact analytical solution is presented. In the present study, the properties of a material are modified in accordance with a power function. The thermal boundary conditions are also assumed to be non-homogeneous. The separation of variable method is implemented to acquire the exact steady-state temperature distribution. The obtained solution is adequately verified using numerical data. To further demonstrate the ability of the solution, an illustrative case that is exposed to a combination of boundary conditions is studied. In particular, the influences of effective parameters on the temperature distribution are investigated for the current geometry. The outcome of this study would be helpful to shed light on the process of designing and optimizing relatively complex geometries. Also, considering the analyticity of the present solution, the results of this study can be useful for a better understanding of the heat transfer mechanisms of functionally graded materials. In the present case, increasing the amount of <em>m</em> and <em>κ</em>, the thermal conductivity increased by about 8 and 2 percent respectively, which would increase the distribution of cone temperature. In the current study, the problem of two-dimensional steady-state heat conduction in a truncated hollow cone made of functionally graded materials is referred and an exact analytical solution is presented. In the present study, the properties of a material are modified in accordance with a power function. The thermal boundary conditions are also assumed to be non-homogeneous. The separation of variable method is implemented to acquire the exact steady-state temperature distribution. The obtained solution is adequately verified using numerical data. To further demonstrate the ability of the solution, an illustrative case that is exposed to a combination of boundary conditions is studied. In particular, the influences of effective parameters on the temperature distribution are investigated for the current geometry. The outcome of this study would be helpful to shed light on the process of designing and optimizing relatively complex geometries. Also, considering the analyticity of the present solution, the results of this study can be useful for a better understanding of the heat transfer mechanisms of functionally graded materials. In the present case, increasing the amount of <em>m</em> and <em>κ</em>, the thermal conductivity increased by about 8 and 2 percent respectively, which would increase the distribution of cone temperature. https://mej.aut.ac.ir/article_3674_f35fd567065af297ae65b621e0a21ae9.pdf