Abstract: Lattice Monte Carlo methods are an excellent
choice for the simulation of non-linear thermal diffusion
problems. In this paper, and for the first time, Lattice Monte
Carlo analysis is performed on thermal diffusion combined
with convective heat transfer. Laminar flow of water modeled
as an incompressible fluid inside a copper pipe with a constant
surface temperature is considered. For the simulation of
thermal conduction, the temperature dependence of the
thermal conductivity of the water is accounted for. Using the
novel Lattice Monte Carlo approach, temperature distributions
and energy fluxes are obtained.