The Application of Random Vortex Method in the Analysis of Heat Conduction in a Slab

Thermal conduction problems have traditionally been solved using analytical or numerical tools. Deterministic numerical tools such as Finite Element and Finite Difference Methods have been common. However these methods require many mathematical and computational skills. In the light of this, random vortex method which is probabilistic in nature was applied to study heat conduction in a rectangular slab. Two cases were considered: one with the slab boundary held at constant temperature and the other with part of the boundary isothermal and part adiabatic. The generated results were then validated using Taylor's series approximation test. From the results, the maximum deviation from the Taylor's series tests was 0.10 for the purely isothermal boundary slab and 0.07 for slab with partly isothermal and partly adiabatic boundary.