Non-Newtonian rivulet flows on an inclined planar surface applying the 2nd Stokes problem

Spectral variational approach to the non-Newtonian stokes problem in a spherical shell

Several recent papers have examined the transport of heat between a hot and cold fluid reservoir when the two reservoirs are connected to each other by an array of open-ended pipes and when the fluid within these pipes is set into sinusoidal axial oscillations. This new heat transfer mode involves the periodic interaction of axial convection with radial heat conduction between the fluid core and Stokes boundary layer formed by the oscillations and can lead to effective axial conductivities orders of magnitude larger than achievable by axial conduction in the absence of oscillations. An interesting property of this heat transfer method is that there is no convective mass exchange between the fluid displacement within the tubes is less than the tube length and the flow remains laminar. In the above studies the oscillations responsible for the enhanced heat transfer are due to a periodic pressure gradient produced by moving pistons or membrances located within the fluid reservoirs. It is the purpose of the present note to show that the same enhanced heat transfer process can occur along rigid walls bounded by a viscous fluid-solid interface, and a longitudinal temperature gradient is present. In particular, the authors examine the problem ofmore » thermal pumping existing in the classical Stokes problem of a sinusoidally oscillating flat plate immersed within a viscous fluid of infinite extent. A constant-temperature gradient is superimposed on the fluid parallel to the plate surface and in the direction of the plate motion. As will be seen, this leads to a large longitudinal heat flux within a relatively narrow boundary layer region next to the plate. The thickness of this layer, containing 99 percent of the time-averaged thermal flux, is found to be no more than 3.754 of the Stokes viscous boundary layer thickness and for low Prandtl number fluids, such as liquid metals, can become considerably less than one Stokes layer thickness.« less