Research Article Open Access

Analytical Solution Based on a New Series along with the Numeric Solution of the Non-Homogeneous Transient Heat Conduction Equation, in Hollow Cylinder under General Mixed Boundary Conditions

Mehdi Zare1 and F. Kardan2
  • 1 Iran University of Science and Technology, Iran
  • 2 Islamic Azad University, Iran
American Journal of Engineering and Applied Sciences
Volume 11 No. 2, 2018, 538-547

DOI: https://doi.org/10.3844/ajeassp.2018.538.547

Submitted On: 30 November 2017 Published On: 20 April 2018

How to Cite: Zare, M. & Kardan, F. (2018). Analytical Solution Based on a New Series along with the Numeric Solution of the Non-Homogeneous Transient Heat Conduction Equation, in Hollow Cylinder under General Mixed Boundary Conditions. American Journal of Engineering and Applied Sciences, 11(2), 538-547. https://doi.org/10.3844/ajeassp.2018.538.547

Abstract

In this study, the problem of transient conduction heat transfer for an infinite hollow cylinder under non-homogeneous mixed boundary conditions at the both surfaces simultaneously in radial direction with general heat source depend on time and radius, also general initial condition by the method of superposition and separation variables, is solved and temperature distribution is obtained analytically. A new series based on the Bessel functions is obtained for the problem of transient heat conduction without heat source by using separation of variables. Any function that has expanded conditions by the Fourier series can be expanded by this new series. Then, by expanding the heat source function according to this new series, the problem of transient heat transfer involving the thermal source has been solved and the radial temperature distribution is obtained. Due to the limited case studies, numerical solution of heat conduction equation with implicit finite difference method also is presented. Finally, a numerical example is given to compare between analytical and numerical solutions.

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Keywords

  • Hollow Cylinder
  • Mixed Boundary Condition
  • Heat Conduction
  • Fourier Series
  • Finite Difference Method
  • Heat Source