1. Application of solution structure theorems to Cattaneo-Vernotte heat conduction equation with non-homogeneous boundary conditions.
- Author
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Lam, Tung and Fong, Ed
- Subjects
- *
MATHEMATICS theorems , *HEAT conduction , *DIFFERENTIAL equations , *LAPLACE transformation , *INTEGRAL equations , *HEAT flux , *BOUNDARY value problems - Abstract
In this study, a non-Fourier heat conduction problem formulated using the Cattaneo-Vernotte (C-V) model with non-homogeneous boundary conditions is solved with the superposition principle in conjunction with solution structure theorems. It is well known that the aforementioned analytical method is not suitable for such a class of thermal problems. However, by performing a functional transformation, the original non-homogeneous partial differential equation governing the physical problem can be cast into a new form such that it consists of a homogeneous part and an additional auxiliary function. As a result, the modified homogeneous governing equation can then be solved with solution structure theorems for temperatures inside a finite planar medium. The methodology provides a convenient, accurate, and efficient solution to the C-V heat conduction equation with non-homogeneous boundary conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2013
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