One-way flow over uniformly heated U-shaped bodies driven by thermal edge effects

Satoshi Taguchi,Tetsuro Tsuji

doi:10.1038/s41598-022-05534-y

Abstract

The thermal edge flow is a gas flow typically induced near a sharp edge (or a tip) of a uniformly heated (or cooled) flat plate. This flow has potential applicability as a nonmechanical pump or flow controller in microelectromechanical systems (MEMS). However, it has a shortcoming: the thermal edge flows from each edge cancel out, resulting in no net flow. In this study, to circumvent this difficulty, the use of a U-shaped body is proposed and is examined numerically. More specifically, a rarefied gas flow over an array of U-shaped bodies, periodically arranged in a straight channel, is investigated using the direct simulation Monte-Carlo (DSMC) method. The U-shaped bodies are kept at a uniform temperature different from that of the channel wall. Two types of U-shaped bodies are considered, namely, a square-U shape and a round-U shape. It is demonstrated that a steady one-way flow is induced in the channel for both types. The mass flow rate is obtained for a wide range of the Knudsen numbers, i.e., the ratio of the molecular mean free path to the characteristic size of the U-shape body. For the square-U type, the direction of the overall mass flow is in the same direction for the entire range of the Knudsen numbers investigated. For the round-U type, the direction of the total mass flux is reversed when the Knudsen number is moderate or larger. This reversal of the mass flow rate is attributed to a kind of thermal edge flow induced over the curved part of the round-U-shaped body, which overwhelms the thermal edge flow induced near the tip. The force acting on each of the bodies is also investigated.

Highlights

The thermal edge flow is a gas flow typically induced near a sharp edge of a uniformly heated flat plate
In this study, we investigate a rarefied gas flow over periodically arranged U-shaped bodies using the direct simulation Monte-Carlo (DSMC) method
We investigate the steady behavior of the gas induced in the vessel under the same assumptions as expressed in “Formulation,” that is, the molecules make diffuse reflections on the sidewalls of the vessel as well as on the upper and lower walls. This situation is appropriate for investigating the qualitative behavior of the gas flow induced by the uniformly heated U-shaped body because there is no interaction between neighboring bodies inherent in the original problem

Summary

Introduction

The thermal edge flow is a gas flow typically induced near a sharp edge (or a tip) of a uniformly heated (or cooled) flat plate This flow has potential applicability as a nonmechanical pump or flow controller in microelectromechanical systems (MEMS). For the round-U type, the direction of the total mass flux is reversed when the Knudsen number is moderate or larger This reversal of the mass flow rate is attributed to a kind of thermal edge flow induced over the curved part of the round-U-shaped body, which overwhelms the thermal edge flow induced near the tip. The nonlinear thermal stress flow is induced when the distance between neighboring isothermal lines varies along the lines in the interior of the gas, provided the temperature variation is considerable These properties have been clarified by a systematic asymptotic analysis of the Boltzmann equation with small Knudsen numbers[12,13]. It is known that the magnitude of the flow velocity is proportional to Kn1/2 when the Knudsen number is small[5,6,13]

Methods

Results

Conclusion