An inverse Laplace transformation for solving heat-conduction problems with discontinuous boundary conditions of the second kind

1986 ◽  
Vol 50 (5) ◽  
pp. 604-609
Author(s):  
V. P. Kozlov ◽  
V. S. Adamchik
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Laplace Transformation ◽  
Inverse Laplace Transformation ◽  
Discontinuous Boundary

Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions

2015 ◽  
Vol 137 (10) ◽  
Author(s):  
A. Amiri Delouei ◽  
M. Norouzi
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Laplace Transformation ◽  
Exact Analytical Solution ◽  
Function Technique ◽  
Conductive Heat ◽  
Fiber Reinforced ◽  
Legendre Series

The current study presents an exact analytical solution for unsteady conductive heat transfer in multilayer spherical fiber-reinforced composite laminates. The orthotropic heat conduction equation in spherical coordinate is introduced. The most generalized linear boundary conditions consisting of the conduction, convection, and radiation heat transfer is considered both inside and outside of spherical laminate. The fibers' angle and composite material in each lamina can be changed. Laplace transformation is employed to change the domain of the solutions from time into the frequency. In the frequency domain, the separation of variable method is used and the set of equations related to the coefficients of Fourier–Legendre series is solved. Meromorphic function technique is utilized to determine the complex inverse Laplace transformation. Two functional cases are presented to investigate the capability of current solution for solving the industrial unsteady problems in different arrangements of multilayer spherical laminates.

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