Numerical solutions to some common heat transfer scenarios
Monte Carlo based solution to a Dirichlet problem -- Laplace's equation with constant boundary conditions. A paper by E. M. Sparrow and A. Haji-Sheikh titled, "The Solution of Heat Conduction Problems by Probability Methods" (Journal of Heat Transfer, Volume 89, Issue 2, May 1967) describes a methodology for applying probabilistic methods to a host of heat transfer scenarios. This first example will demonstrate using numerous random walks to calculate the temperature distribution across a 2D plate with constant temperature boundary conditions.