Analytical and numerical solution for steady-state differential conduction equation in a right triangular plate with constant-temperature boundary condition

Authors

1 university of tabriz

2 university of tanriz

Abstract

This article presents, in general, means to acquire analytical and exact solutions for steady-state partial differential conduction equation, and consequently finding the exact distribution of temperature in irregular geometries with one or more edges unparalleled with Cartesian axes(with various boundary conditions) . To get to this goal and to clarify, one specific problem, a steady-state right triangular plate with the right angle on the origin and with constant-temperature boundary conditions has been considered. In the analytical technique used, the importance and strength of complex variables and their applications, such as complex transformations, especially the Schwarz–Christoffel transformation is clearly visible. Finally, to validate the analytical solution acquired, the problem has been solved using the finite element method in COMSOL Multiphysics 5.0. The results has been compared, and the correspondence has confirmed the analytical solution.
Keywords: conduction equation ; Cartesian coordinate system ; analytical solution ; irregular geometry ; right triangle ; Schwarz–Christoffel transformation

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References

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Journal of Solid and Fluid Mechanics
Volume 5, Issue 3 - Serial Number 3
September and October 2015
Pages 289-302

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