RT Journal Article
ID 65350d084e201114
A1 Akbari, Mohammad
A1 Saedodin, Seyfolah
A1 Toghraie, Davood Semiromi
A1 Kowsary, Farshad
T1 ANALYTICAL SOLUTION OF THE PROBLEM OF NON-FOURIER HEAT CONDUCTION IN A SLAB USING THE SOLUTION STRUCTURE THEOREMS
JF Heat Transfer Research
JO HTR
YR 2015
FD 2015-04-07
VO 46
IS 5
SP 447
OP 464
K1 structure theorem
K1 non-Fourier
K1 analytical solution
K1 temperature components
AB This paper studies an analytical method which combines the superposition technique along with the solution structure theorem such that a closed-form solution of the hyperbolic heat conduction equation can be obtained by using the fundamental mathematics. In this paper, the non-Fourier heat conduction in a slab at whose a left boundary there is a constant heat flux and at the right boundary, a constant temperature T_{s} = 15, has been investigated. The complicated problem is split into multiple simpler problems that in turn can be combined to obtain a solution to the original problem. The original problem is divided into five subproblems by setting the heat generation term, the initial conditions, and the boundary conditions for different values in each subproblem. All the solutions given in this paper can be easily proven by substituting them into the governing equation. The results show that the temperature will start retreating at approximately t = 2 and for t = 2 the temperature at the left boundary decreases leading to a decrease in the temperature in the domain. Also, the shape of the profiles remains nearly the same after t = 4. The solution presented in this study can be used as benchmark problems for validation of future numerical methods.
PB Begell House
LK http://dl.begellhouse.com/journals/46784ef93dddff27,3386fabe739c4ff9,65350d084e201114.html