Boundary element solution of thermal creep flow in microfluidic devices

Flow in rarefied gases can be caused by a tangential temperature gradient along the contour boundaries (tangential heat flux), without the presence of any other external driven force, inducing a fluid motion from colder to hotter regions. This phenomenon is known as thermal creep and has gained importance in recent years in connection with micro-scale gas flow systems. Prediction of the flow field in micro-systems can be obtained by using continuum based models under appropriate boundary conditions accounting for the slip velocity due to tangential shear rate and heat flux. In this work a boundary integral equation formulation for Stokes slip flow, based on the normal and tangential projection of the Green's integral representational formulae for the velocity field is presented. The tangential heat flux is evaluated in terms of the tangential gradient of the temperature integral representational formulae presenting singularities of the Cauchy type, which are removed by the use of an auxiliary potential field. These formulations are used to evaluate the performance of different microfluidic devices.