An analytical study on fluid flow characteristics for flow within a microchannel of rectangular cross section

Abstract

The present work considers fluid flow analysis within a microchannel of rectangular cross section with different exact and approximate analytical techniques. Thus, velocity slip at the solid wall of the channel is considered. The slip flow is transformed to a no-slip flow with some minor modifications by applying an average slip velocity. The flow is represented by the Navier-Stokes equation exposed to slip boundary conditions. The governing equation is solved considering separation of variables method (SOV) as an exact method and, Integral and Variational methods as approximate methods. The Poiseuille number and slip coefficient are also determined for each method. The present prediction agrees well with available literature. To predict accuracy level of all the techniques, the results are presented in a comparative scale along with numerical prediction. It is observed that the accuracy level for the velocity profile obtained in each technique depends on the aspect ratio where as for the prediction of Poiseuille number and slip coefficient, all the technique show less dependency on the aspect ratio.