Thermophoresis is a significant deposition mechanism for the fouling of exhaust gas recirculation (EGR) coolers. The present paper is motivated by the need to understand and predict the rates of deposition of soot particles in heat exchanger fins used in EGR coolers. This preliminary study considers flat plate channels in the laminar and transitional turbulent regimes. Because of the nano-meter range of the particles, an Eulerian approach is used to determine the particle concentration. Full consideration is given to property variations due to changes in temperature. The inlet gas is at a fixed temperature and the effects of wall temperature are studied for several Reynolds numbers in laminar and transitional turbulent regimes. A finite difference method is used to march downstream in both laminar and transitional turbulent flows. The Launder-Sharma two-equation low-Reynolds-number k-ε model is employed in the numerical simulations to obtain data about flow friction, heat transfer and mass transfer.