Evaluation of Shrinking Direction of Movement Using Monte Carlo Simulation in A Rectangular Slab

Abstract

Heat transfer is frequently encountered in everyday life and in engineering practice. As such there is constant urge to explore new approach for its numerical estimation. Monte Carlo being relatively untapped tool is explored in this work. A model was developed using Shrinking Boundary Monte Carlo Method for analysis of steady state heat conduction in a rectangular slab. The model was used to obtain temperature distribution in a Zig-zag manner, Rectangular left to right, Rectangular right to left. The result of which was compared to ordinary Monte Carlo Method. The computational run time for each of the shrinking pattern was determined. The study established that the average of the run time for various sizes of the slab indicates that horizontal left to right is shorter. It is the best ways of calculating temperature distribution in a rectangular slab of fixed boundary temperature. Horizontal left to right is also good for larger network calculation as used in Shrinking Boundary Methods. Application of the shrinking boundary Monte Carlo Methods to study heat conduction in rectangular slabs yielded favourable results. The obtained results are close to those obtained by finite difference technique. The different shrinking directions of movement for a given size of a rectangular slab have the same surface graph and % deviation. The maximum deviation was not more than 11.5 with deviation of 2.9% for temperature distribution in a rectangular slab with boundary conditions.