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DOI: 10.1615/HeatTransRes.2014007120
pages 621-641

AN ANALYTICAL SOLUTION OF NON-FOURIER HEAT CONDUCTION IN A SLAB WITH NONHOMOGENEOUS BOUNDARY CONDITIONS USING THE SUPERPOSITION TECHNIQUE AND SOLUTION STRUCTURE THEOREM

M. Akbari
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
Farshad Kowsary
Department of Mechanical Engineering, University College of Engineering, University of Tehran, Tehran 515-14395, Iran

ABSTRACT

Non-Fourier heat conduction in a slab with nonhomogeneous boundary conditions is investigated analytically. In this research, the solution structure theorems, along with the superposition technique, are applied to obtain a closed-form solution of the hyperbolic heat conduction (HHC) equation using fundamental mathematics. In this solution, a complicated problem is split into multiple simpler problems which 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, initial conditions, and the boundary conditions to different values in each subproblem. The methodology provides a convenient and accurate solution to the HHC equation, which is applicable to a variety of HHC analyses for various engineering applications. The results obtained show that the temperature will start retreating at approximately t = 1.05 and at t > 1.04 the temperature at the left boundary decreases leading to a decrease in the temperature in the domain. Also, the shape of profiles remains nearly the same after t = 1.5.