Numerical simulation of steady state heat conduction in a slab with non-isothermal boundaries using Markov Chain Technique

Abstract

Numerical techniques such as finite difference and finite element have played a major role in analysis of heat transfer in solid medium. The probability methods later developed have been hampered by their slow execution time. This has however been improved upon using Markov chain technique; however analysis has been limited to isothermal boundary cases. In this study Markov chain technique was applied to analyse steady state heat transfer in non-isothermal boundaries. The conventional Markov chain equations were modified in order to handle adiabatic and convective boundaries as well as domain with internal heat generation. The developed procedure was used to determine temperature distribution inside solid domain with non-isothermal boundaries. The results obtained were compared with finite difference solutions. The execution time for the developed procedure was also compared with that using finite difference technique.

The results using the Markov chain technique were very close to the finite difference solutions. The execution time using Markov chain technique was shorter than that obtained using the finite difference technique.

It is thus concluded that the developed Markov Chain technique could be used for analysis of steady state heat conduction in solid domain with non-isothermal boundaries.

Keywords: Heat Conduction, Probability method, Non-Isothermal, Markov Chain