A boundary integral equation formulation for the thermal creep gas flow at finite Peclet numbers

Abstract The integral equation formulation developed previously by the authors to study isothermal micro flows under shear slip boundary condition is extended in this work to consider the case of non-isothermal micro gas flows with thermal creep effects at finite Peclet numbers. The effect of thermal creep over the flow patterns with and without considering the effect of shear slip is investigated in detail using a boundary element method. In this work the boundary integral approaches for both fluid velocity and temperatures fields are used to solve the problem of shear-driven cavity flow at finite Peclet number. This is obtained by considering the diffusive-convective heat equation using the Dual Reciprocity Method to transform the corresponding volume integral of the convective terms into equivalent surface integrals.