New exact solutions for microscale gas flows

TL;DR

This paper derives exact solutions to linearised Grad equations for microscale gas flows, including flow, pressure, and temperature fields near boundaries, as well as unsteady and rotational solutions, advancing theoretical understanding of rarefied gas dynamics.

Contribution

It introduces new exact solutions to the Grad equations for various microscale gas flow scenarios, including steady, unsteady, and rotational cases, which were not previously available.

Findings

Exact solutions for flow and pressure near boundaries

Temperature field solutions for heat sources near jumps

Unsteady and rotational solutions for Grad equations

Abstract

We present a number of exact solutions to the linearised Grad equations for non-equilibrium rarefied gas flows and heat flows. The solutions include the flow and pressure fields associated to a point force placed in a rarefied gas flow close to a no-slip boundary and the temperature field for a point heat source placed in a heat flow close to a temperature jump boundary. We also derive the solution of the unsteady Grad equations in one dimension with a time-dependent point heat source term and the Grad analogue of the rotlet, a well-known singularity of Stokes flow which corresponds to a point torque.