Temporal Differential Transform and Spatial Finite Difference Methods for Unsteady Heat Conduction Equations with Anisotropic Diffusivity

Sungu I. C., Demir H.

GAZI UNIVERSITY JOURNAL OF SCIENCE, vol.27, no.4, pp.1063-1076, 2014 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 27 Issue: 4
  • Publication Date: 2014
  • Journal Name: GAZI UNIVERSITY JOURNAL OF SCIENCE
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.1063-1076
  • Keywords: Differential Transform Method, Finite-difference approximation, Heat conduction, anisotropic diffusivity, time-dependent heating
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Three unsteady heat conduction problems with anisotropic diffusivity and time-dependent heating or heat flux and/or heat source are considered in showing the utility of a hybrid method involving a combination of temporal differential transform and spatial finite difference methods. The segregation of time from the spatial component is the greatest advantage of the hybrid method that exhibits no instability of finite difference methods generally seen with parabolic equations. The easy-to-implement algorithm that is essentially a Poisson solver works with both linear and non-linear heat transport problems without any difficulty of sorts. To gain confidence in the results some simulation results are also presented of problems that have an Adomian solution. The method can be used in practical heat transfer problems concerning non-uniform materials like composites, alloys, heterogeneous porous media with thermal equilibrium or non-equilibrium, multi-layered media and such other problems.