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

• Non-isothermal micro gas flows under thermal creep effect is analysed including shear slip.
• Boundary integral approaches for both velocity and temperatures fields are used.
• Thermal creep is accounted by imposing the Maxwell boundary condition.
• It relates tangential gas velocity to the tangential shear stress and heat flux.
• Velocity and temperature fields were evaluated under Peclet number variations.

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.