The approximation of boundary conditions of the third kind in certain problems of steady-state heat conduction

1969 ◽  
Vol 17 (1) ◽  
pp. 886-889
Author(s):  
E. A. Sidorov
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Boundary Conditions ◽  
The Third ◽  
State Heat ◽  
Steady State Heat

Steady State Heat Conduction Modeling by the Generalized Finite Element Method

2018 ◽  
Author(s):  
Humberto Alves da Silveira Monteiro ◽  
Guilherme Garcia Botelho ◽  
Roque Luiz da Silva Pitangueira ◽  
Rodrigo Peixoto ◽  
FELICIO BARROS
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Steady State ◽  
Generalized Finite Element Method ◽  
State Heat ◽  
Steady State Heat ◽  
Generalized Finite Element ◽  
Element Method

Analytical Solution to Steady-State Heat-Conduction Problems With Irregularly Shaped Boundaries

1971 ◽  
Vol 93 (4) ◽  
pp. 449-454 ◽  
Author(s):  
D. M. France
Keyword(s):  
Heat Conduction ◽  
Steady State ◽  
Analytical Solution ◽  
Least Squares ◽  
Series Solution ◽  
Point Matching ◽  
State Heat ◽  
Temperature Heat ◽  
Steady State Heat ◽  
Least Squares Approach

A method of obtaining an analytical solution to two-dimensional steady-state heat-conduction problems with irregularly shaped boundaries is presented. The technique of obtaining the coefficients to the series solution via a direct least-squares approach is compared to the “point-matching” scheme. The two methods were applied to problems with known solutions involving the three heat-transfer boundary conditions, temperature, heat flux, and convection coefficient specified. Increased accuracy with substantially fewer terms in the series solution was obtained via the least-squares technique.

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