A FINITE ELEMENT METHOD FOR SOLUTION OF THE THREE-DIMENSIONAL TIME-DEPENDENT HEAT-CONDUCTION EQUATION WITH APPLICATION FOR HEATING OF STEELS IN REHEATING FURNACES

1999 ◽  
Vol 35 (2) ◽  
pp. 155-172 ◽  
Author(s):  
Dag Lindholm
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Conduction ◽  
Heat Conduction Equation ◽  
Three Dimensional ◽  
Time Dependent ◽  
Conduction Equation ◽  
Element Method

Analytical Solution for Three-Dimensional Hyperbolic Heat Conduction Equation with Time-Dependent and Distributed Heat Source

2016 ◽  
Vol 33 (1) ◽  
pp. 65-75 ◽  
Author(s):  
M. R. Talaee ◽  
V. Sarafrazi
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Time Dependent ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction

AbstractThis paper is devoted to the analytical solution of three-dimensional hyperbolic heat conduction equation in a finite solid medium with rectangular cross-section under time dependent and non-uniform internal heat source. The closed form solution of both Fourier and non-Fourier profiles are introduced with Eigen function expansion method. The solution is applied for simple simulation of absorption of a continues laser in biological tissue. The results show the depth of laser absorption in tissue and considerable difference between the Fourier and Non-Fourier temperature profiles. In addition the solution can be applied as a verification branch for other numerical solutions.

Sign in / Sign up

Export Citation Format

Share Document