Von Karman’s problem of a rotating disk in an infinite viscous fluid is extended to the case where the disk surface admits partial slip. The nonlinear similarity equations are integrated accurately for the full range of slip coefficients. The effects of slip are discussed. An existence proof is also given.

The flow due to a rough rotating disk

The steady, laminar, axisymmetric flow of a Newtonian fluid due to a stretching sheet when there is a partial slip of the fluid past the sheet has been investigated. The flow is governed by a third-order non-linear boundary value problem whose exact numerical solution has been obtained non-iteratively in terms of the non-dimensional slip parameter @l. A perturbation solution valid for small @l and an asymptotic solution valid for large @l have been derived. Finally a solution based upon He's homotopy perturbation method has been developed. The latter, being analytical, is elegant but is sufficiently accurate for all values of @l.

Axisymmetric flow due to a stretching sheet with partial slip

In this article, a theoretical study is presented for peristaltic flow of a MHD fluid in an asymmetric channel. Effects of viscosity variation, velocity-slip as well as thermal-slip have been duly taken care of in the present study. The energy equation is formulated by including a heat source term which simulates either absorption or generation. The governing equations of motion and energy are simplified using long wave length and low Reynolds number approximation. The coupled non-linear differential equations are solved analytically by means of the perturbation method for small values of Reynolds model viscosity parameter. The salient features of pumping and trapping are discussed with particular focus on the effects of velocity-slip parameter, Grashof number and magnetic parameter. The study reveals that the velocity at the central region diminishes with increasing values of the velocity-slip parameter. The size of trapped bolus decreases and finally vanishes for large values of magnetic parameter.

Peristaltic transport of MHD flow and heat transfer in an asymmetric channel: Effects of variable viscosity, velocity-slip and temperature jump

Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition

Heat and mass transfer of the flow due to a rotating rough and porous disk

Flow about a porous-surfaced rotating disk

An analysis of internal flows with surface mass transfer is performed in which account is taken of velocity slip at the surface of the porous bounding wall. The solutions for channel and tube flows reveal a variety of interesting effects of velocity slip, which depend upon whether fluid is injected or withdrawn at the bounding wall and upon the sign of the streamwise pressure gradient. For example, relative to the situation in which there is no slip, the streamwise pressure gradient may either increase or decrease in the presence of slip and may even undergo a change of sign.

L. Y. Hung

Papers

Flow about a porous-surfaced rotating disk

Channel and Tube Flows with Surface Mass Transfer and Velocity Slip

Reply to comments of B. S. Bhatt and N. C. Sacheti