Onsager Coefficients for Liquid Metal Flow in a Conduit under a Magnetic Field

TL;DR

This paper derives explicit Onsager coefficients for liquid metal flow in a conduit under a magnetic field, providing a framework for analyzing and optimizing magnetohydrodynamic devices in various applications.

Contribution

It introduces simplified explicit expressions for Onsager coefficients in liquid metal MHD flow, satisfying reciprocity, aiding device analysis and control.

Findings

Derived explicit Onsager coefficients for flow and electric current.

Demonstrated Onsager-Casimir reciprocity in the coefficients.

Provided a framework for optimizing MHD liquid metal devices.

Abstract

We analyze the flow of room and near room-temperature liquid metals in shallow, long rectangular conduits with two insulating and two perfectly conducting walls under a uniform magnetic field perpendicular to the flow direction and the insulating surfaces, focusing on moderate Hartmann numbers. A pressure gradient and Lorentz body forces may drive or oppose the flow. We derive explicit expressions for the Onsager coefficients that relate the flow rate and electric current on the one hand to the potential difference across electrodes and the pressure gradient on the other hand. We further demonstrate that these coefficients satisfy Onsager-Casimir reciprocity. These simplified expressions provide a convenient framework for analyzing, optimizing, and controlling magnetohydrodynamic (MHD) machines operating with liquid metals in applications such as power conversion, energy harvesting, pumping, actuation, valving, breaking, and sensing without moving components.