A theoretical, numerical and experimental verification of the Reynolds thermal transpiration law

Abstract

Purpose

The purpose of this paper is the theoretical presentation of tensorial formulation with surface mobility forces and numerical verification of Reynolds thermal transpiration law in a contemporary experiment with nanoflow.

Design/methodology/approach

The velocity profiles in a single microchannel are calculated by solving the momentum equations and using thermal transpiration force as the boundary conditions. The mass flow rate and pressure of unstationary thermal transpiration modeling of the benchmark experiment has been achieved by the implementation of the thermal transpiration mobility force closure for the thermal momentum accommodation coefficient.

Findings

An original and easy-to-implement method has been developed to numerically prove that at the final equilibrium, i.e. zero-flow state, there is a connection between the Poiseuille flow in the center of channel and counter thermal transpiration flow on the surface. The numerical implementation of the Reynolds model of thermal transpiration has been performed, and its usefulness for the description of the benchmark experiment has been verified.

Research limitations/implications

The simplified procedure requires the measurement or assumption of the helium-glass slip length.

Practical implications

The procedure can be very useful in the design of micro-electro-mechanical systems and nano-electro-mechanical systems, especially for accommodation pumping.

Originality/value

The paper discussed possible constitutive equations in the transpiration shell-like layer. The new approach can be helpful for modeling phenomena occurring at a fluid–solid phase interface at the micro- and nanoscales.

Citation

Ziółkowski, P. and Badur, J. (2018), "A theoretical, numerical and experimental verification of the Reynolds thermal transpiration law", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 1, pp. 64-80. https://doi.org/10.1108/HFF-10-2016-0412