Scaling laws for external fluid flow induced by controlled periodic heating of a solid boundary

Abstract

We demonstrate that considerable variation of mean Prandtl number ( P r 0 ) from unity brings in an additional length scale (called the viscous penetration depth, δ v ) into the dynamics of instantaneous as well as time-averaged (mean) flow induced by thermoviscous expansion along a periodically heated solid wall. We investigate the limiting cases of high and low Prandtl numbers ( P r 0 ≫ 1 and P r 0 ≪ 1) through detailed order-of-magnitude analysis. Our study reveals that the viscous penetration depth scales universally with P r 0 so long as such depth remains small compared to the wavelength of the applied thermal wave. While a high P r 0 is found to obstruct the mean flow, the converse is not necessarily true. Subsequent analysis clearly shows that a low- P r 0 flow can induce negative thermoviscous force within the thermal boundary layer and thus retard the mean motion, leading to a nontrivial reduction of net mass flow along the plate. Numerical prediction of friction factor variation with P r 0 agrees well with the scaling estimates for both high- P r 0 and low- P r 0 fluids. The findings may very well act as fundamental design basis for engineering devices that may potentially be developed for thermal molecular trapping and particle sorting and accumulation based on unsteady heating.