Experimental research of block algorithm for the difference solution of heat conduction equation. Implicit Difference Scheme Case

2021 ◽  
Author(s):  
Dimitry Golovashkin ◽  
Liudmila Yablokova
Keyword(s):  
Heat Conduction ◽  
Difference Scheme ◽  
Experimental Research ◽  
Heat Conduction Equation ◽  
Conduction Equation ◽  
Implicit Difference Scheme ◽  
Block Algorithm ◽  
The Difference ◽  
Difference Solution

scholarly journals METHOD OF LINES AND FINITE DIFFERENCE SCHEMES WITH THE EXACT SPECTRUM FOR SOLUTION THE HYPERBOLIC HEAT CONDUCTION EQUATION

2011 ◽  
Vol 16 (1) ◽  
pp. 220-232 ◽  
Author(s):  
Harijs Kalis ◽  
Andris Buikis
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Difference Scheme ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Method Of Lines ◽  
Numerical Results ◽  
Conduction Equation ◽  
Finite Difference Schemes ◽  
Hyperbolic Heat Conduction

This paper is concerning with the 1-D initial–boundary value problem for the hyperbolic heat conduction equation. Numerical solutions are obtained using two discretizations methods – the finite difference scheme (FDS) and the difference scheme with the exact spectrum (FDSES). Hyperbolic heat conduction problem with boundary conditions of the third kind is solved by the spectral method. Method of lines and the Fourier method are considered for the time discretization. Finite difference schemes with central difference and exact spectrum are analyzed. A novel method for solving the discrete spectral problem is used. Special matrix with orthonormal eigenvectors is formed. Numerical results are obtained for steel quenching problem in the plate and in the sphere with holes. The hyperbolic heat conduction problem in the sphere with holes is reduced to the problem in the plate. Some examples and numerical results for two typical problems related to hyperbolic heat conduction equation are presented.

On Hyperbolic Heat Conduction and the Second Law of Thermodynamics

1995 ◽  
Vol 117 (2) ◽  
pp. 256-263 ◽  
Author(s):  
C. Bai ◽  
A. S. Lavine
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Model Problem ◽  
Second Law Of Thermodynamics ◽  
Hyperbolic Type ◽  
Conduction Equation ◽  
Second Law ◽  
Hyperbolic Heat Conduction ◽  
The Difference ◽  
Modified Equation

For situations in which the speed of thermal propagation cannot be considered infinite, a hyperbolic heat conduction equation is typically used to analyze the heat transfer. The conventional hyperbolic heat conduction equation is not consistent with the second law of thermodynamics, in the context of nonequilibrium rational thermodynamics. A modified hyperbolic type heat conduction equation, which is consistent with the second law of thermodynamics, is investigated in this paper. To solve this equation, we introduce a numerical scheme from the field of computational compressible flow. This scheme uses the characteristic properties of a hyperbolic equation and has no oscillation. By solving a model problem, we show that the conventional hyperbolic heat conduction equation can give physically wrong solutions (temperature less than absolute zero) under some conditions. The modified equation does not display these erroneous results. However, the difference between results of these two models is negligible except under extreme conditions.

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