Full Solutions to Flow and Heat Transfer from Slip-Induced Microtube Shapes

Abstract

The main concern of this paper is to introduce some new tubular shapes whose cross-sections result from the imposition of Navier’s velocity slip at the surface. A new family of pipes induced by the slip mechanism is thus discovered. The family is shown to modify the traditional pipes with elliptical cross-sections in the absence of slip, and they partly resemble collapsible tubes. The velocity field through the new pipes is then analytically determined. Afterwards, the corresponding temperature field with a constant heat flux boundary is shown to be perturbed around the slip parameter, whose leading order is well known from the literature. The correction to this order is next evaluated analytically. The velocity and temperature fields are further discussed regarding such new shapes. More physical features, such as the wall shear stress, the centerline velocity, the slip velocity and the convective heat transfer are also studied in detail. From the solutions, it is observed that a circular pipe under the effect of a slip mechanism has the largest temperature and the lowest Nusselt number at the center of the modified pipe. The new pipes are thought to have engineering and practical value in the micromachining industry, besides offering new analytical solutions for the considered flow geometry.