**Analytical Solution of Heat Conduction in a Symmetrical Cylinder Using the Solution Structure Theorem and Superposition Technique**

#### **Rasool Kalbasi 1, Seyed Mohammadhadi Alaeddin 2, Mohammad Akbari 1 and Masoud Afrand 3,4,\***


Received: 13 November 2019; Accepted: 9 December 2019; Published: 16 December 2019

**Abstract:** In this paper, non-Fourier heat conduction in a cylinder with non-homogeneous boundary conditions is analytically studied. A superposition approach combining with the solution structure theorems is used to ge<sup>t</sup> a solution for equation of hyperbolic heat conduction. In this solution, a complex origin problem is divided into, di fferent, easier subproblems which can actually be integrated to take the solution of the first problem. The first problem is split into three sub-problems by setting the term of heat generation, the initial conditions, and the boundary condition with specified value in each sub-problem. This method provides a precise and convenient solution to the equation of non-Fourier heat conduction. The results show that at low times (*t* = 0.1) up to about *r* = 0.4, the contribution of *T*1 and *T*3 dominate compared to *T*2 contributing little to the overall temperature. But at *r* > 0.4, all three temperature components will have the same role and less impact on the overall temperature ( *T*).

**Keywords:** heat conduction; non-fourier; solution structure theorems; superposition approach
