Suscripción a Biblioteca: Guest
Factor de Impacto: 0.404 Factor de Impacto de 5 años: 0.8 SJR: 0.264 SNIP: 0.504 CiteScore™: 0.88

ISSN Imprimir: 1064-2285
ISSN En Línea: 2162-6561

# Heat Transfer Research

DOI: 10.1615/HeatTransRes.2014006434
pages 447-464

## ANALYTICAL SOLUTION OF THE PROBLEM OF NON-FOURIER HEAT CONDUCTION IN A SLAB USING THE SOLUTION STRUCTURE THEOREMS

Department of Mechanical Engineering, Semnan University, Semnan, Iran
Seyfolah Saedodin
Department of Mechanical Engineering, Semnan University, Semnan, Iran
Davood Semiromi Toghraie
Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran
Department of Mechanical Engineering, University College of Engineering, University of Tehran, Tehran 515-14395, Iran

### SINOPSIS

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 Ts = 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.

### Articles with similar content:

AN ANALYTICAL SOLUTION OF NON-FOURIER HEAT CONDUCTION IN A SLAB WITH NONHOMOGENEOUS BOUNDARY CONDITIONS USING THE SUPERPOSITION TECHNIQUE AND SOLUTION STRUCTURE THEOREM
Heat Transfer Research, Vol.45, 2014, issue 7
Davood Semiromi Toghraie, M. Akbari, Farshad Kowsary, Seyfolah Saedodin
SOLUTION OF THE INVERSE RADIATIVE LOAD PROBLEMS BY THE SINGULAR VALUE DECOMPOSITION
ICHMT DIGITAL LIBRARY ONLINE, Vol.7, 1995, issue
Akiyoshi Kuroda, Takahiko Saito, Kazuhiko Kudo, Amr Eid, Masahito Oguma
A GENERALIZED COORDINATES APPROACH FOR THE SOLUTION OF INVERSE HEAT CONDUCTION PROBLEMS
International Heat Transfer Conference 11, Vol.19, 1998, issue
M. N. Ozisik, HELCIO ORLANDE, Jose P. Alencar Jr.
Simulation of Melting of Ice under a Constant Temperature Heat Source Using a Combined Transfinite Interpolation and Partial Differential Equation Methods
Journal of Porous Media, Vol.10, 2007, issue 7