A Simplified Method for Solving Transient Heat-Conduction Problems With Nonlinear Boundary Conditions

1968 ◽  
Vol 90 (3) ◽  
pp. 358-359 ◽  
Author(s):  
A. L. Crosbie ◽  
R. Viskanta
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Transient Heat Conduction ◽  
Nonlinear Boundary Conditions ◽  
Simplified Method

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.

The Solution of Heat Conduction Problems by Probability Methods

1967 ◽  
Vol 89 (2) ◽  
pp. 121-130 ◽  
Author(s):  
A. Haji-Sheikh ◽  
E. M. Sparrow
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Moving Boundaries ◽  
Heat Sources ◽  
Arbitrary Boundary ◽  
Physical Problems ◽  
Wide Range ◽  
Probability Methods

Fundamental concepts pertaining to the solution of heat conduction problems by probability methods (Monte Carlo methods) are devised and techniques of application are developed. It is demonstrated that probability methods can be applied over the entire range of heat conduction problems. These include both steady state and transient situations in bodies of arbitrary shape with arbitrary boundary conditions (including derivative conditions) and with volume heat sources. Problems involving nonlinear boundary conditions (e.g., combined convection and radiation) and moving boundaries (change of phase) are also accommodated by probability methods. All of these various situations are treated in the paper. Numerous computational experiments are carried out, many of which provide results for physical problems not heretofore solved in the literature. A new concept, the floating random walk, is introduced and this provides the flexibility needed to accommodate such a wide range of problems.

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