## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2015, Special Issue (2015), Article ID 203404, 9 pages.

### Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient

#### Abstract

An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.

#### Article information

**Source**

J. Appl. Math., Volume 2015, Special Issue (2015), Article ID 203404, 9 pages.

**Dates**

First available in Project Euclid: 13 October 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1444742688

**Digital Object Identifier**

doi:10.1155/2015/203404

**Mathematical Reviews number (MathSciNet)**

MR3407075

**Zentralblatt MATH identifier**

1354.80004

#### Citation

Tu, Te-Wen; Lee, Sen-Yung. Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient. J. Appl. Math. 2015, Special Issue (2015), Article ID 203404, 9 pages. doi:10.1155/2015/203404. https://projecteuclid.org/euclid.jam/1444742688