Analytical solutions of transient heat conduction in semi-infinite solid with time varying boundary conditions by means of similarity transformation

1995 ◽  
Vol 22 (1) ◽  
pp. 89-97 ◽  
Author(s):  
Ahmet Z. Şahin
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Analytical Solutions ◽  
Similarity Transformation ◽  
Transient Heat Conduction ◽  
Time Varying

Finite-Element Method Applied to Heat Conduction in Solids with Nonlinear Boundary Conditions

1973 ◽  
Vol 95 (1) ◽  
pp. 126-129 ◽  
Author(s):  
R. E. Beckett ◽  
S.-C. Chu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Transient Heat Conduction ◽  
Nonlinear Boundary Conditions ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Element Method

By use of an implicit iteration technique, the finite-element method applied to the heat-conduction problems of solids is no longer restricted to the linear heat-flux boundary conditions, but is extended to include nonlinear radiation–convection boundary conditions. The variation of surface temperatures within each time increment is taken into account; hence a rather large time-step size can be assigned to obtain transient heat-conduction solutions without introducing instability in the surface temperature of a body.

scholarly journals Semi-derivative integral method (SDIM) to transient heat conduction: Time-dependent (power-law) temperature boundary conditions

2021 ◽  
pp. 143-143
Author(s):  
Jordan Hristov
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Power Law ◽  
Integral Method ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Time Dependent ◽  
Conduction Time ◽  
Parabolic Profile ◽  
Temperature Boundary

Transient heat conduction in semi-infinite medium with a power-law time-dependent boundary conditions has been solved by an integral-balance integral method applying to a semi-derivative approach. Two versions of the integral-balance method have been applied: Goodman?s method with a generalized parabolic profile and Zien?s method with exponential (original and modified) profile.

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