Pal Debashis, Chakraborty Suman
Department of Aerospace Engineering and Applied Mechanics, Indian Institute of Engineering Science and Technology Shibpur, Howrah 711103, India.
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India.
Phys Rev E. 2020 Mar;101(3-1):033105. doi: 10.1103/PhysRevE.101.033105.
We demonstrate that considerable variation of mean Prandtl number (Pr_{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 (Pr_{0}≫1 and Pr_{0} ≪ 1) through detailed order-of-magnitude analysis. Our study reveals that the viscous penetration depth scales universally with Pr_{0} so long as such depth remains small compared to the wavelength of the applied thermal wave. While a high Pr_{0} is found to obstruct the mean flow, the converse is not necessarily true. Subsequent analysis clearly shows that a low-Pr_{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 Pr_{0} agrees well with the scaling estimates for both high-Pr_{0} and low-Pr_{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.
我们证明，平均普朗特数（Pr₀）与1的显著差异会在沿周期性加热固体壁的热粘性膨胀所引起的瞬时流以及时间平均（平均）流的动力学中引入一个额外的长度尺度（称为粘性渗透深度，δᵥ）。我们通过详细的量级分析研究了高普朗特数和低普朗特数（Pr₀≫1和Pr₀≪1）的极限情况。我们的研究表明，只要粘性渗透深度与所施加热波的波长相比仍然很小，粘性渗透深度就普遍与Pr₀成比例。虽然发现高Pr₀会阻碍平均流，但反之不一定成立。随后的分析清楚地表明，低Pr₀流可在热边界层内产生负热粘性力，从而阻碍平均运动，导致沿平板的净质量流显著减少。摩擦系数随Pr₀变化的数值预测与高Pr₀和低Pr₀流体的标度估计结果吻合良好。这些发现很可能作为工程设备的基本设计基础，这些设备可能会基于非稳态加热开发用于热分子捕获以及颗粒分选和聚集。
