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EGR coolers are widely used in reciprocating engines to reduce NOx emission. Thermophoresis-an important transport mechanism for submicron particles such as soot-drives gas-suspended particles from hot regions towards cool surfaces and is responsible for soot deposition and build-up in EGR coolers and related devices. Although much is known about thermophoresis in steady flow, little is known about soot deposition in flows with oscillatory heat and mass transfer. In this paper we present new results for the model problem of thermophoretic particle transport in a thin pulsatile shear layer above a flat, cold wall. The transport equations for this sublayer flow with oscillating shear have been solved numerically and, in the case of steady flow, are in excellent agreement with the exact solution for the steady wall shear.