Conversion of Heat into Electricity Through Natural Convection of a Single-Phase Liquid Metal in a Closed Loop with a Magnetic Field

Abstract

Conventional waste heat recovery systems usually require water (e.g. to supply steam for a turbine) and imply the wearing of moving parts, to the detriment of usability in case of drought and/or in the long term. Unconventional approaches (thermoacoustic and thermoelectric conversion of heat into electricity) overcome these obstacles, but their utilization for multi Kilowatt (KW) electric power in an industrial environment is jeopardized either by large working pressure, excessive noise, the need for cooling systems or huge magnetic fields. Welander and Erhard et al. discuss the existence and the stability of steady-state convection driven by an applied temperature gradient of a fluid circulating in a tube that forms a vertical, closed loop. Convection ensures the spontaneous conversion of heat into mechanical energy through competing buoyancy, drag and heat conduction between the fluid and the walls of the tube. Crucially, their results do not depend on the nature of the drag. If the working is an electrical conductor and a magnetic field is applied, the impact of the resulting Lorenz force acts as a drag on the motion of the fluid just like viscosity; the viscous and the magnetic drag are dealt with on an equal basis. The magnetic drag transforms the mechanical energy of the convective motion of the fluid into electric energy. Since convection is driven by a temperature gradient, spontaneous, water-free conversion of heat into electricity occurs with no moving part at atmospheric pressure. Such conversion is suitable for the purposes of waste heat recovery. As an example, let a 1-cm-radius tube filled GalinstanTM (a commercially available, atoxic liquid metal alloy) be rolled up in a double helix wrapped around a 30-m-tall, 3-m-radius chimney located above a furnace. If there is a 350 K temperature difference between the bottom of the tube (near the furnace) and the top, and if permanent magnets located on the tube provide a 0.017 T magnetic field, then conservative estimates show that we obtain 2 KW DC electric power with efficiency > 2.1%. This lower bound suggests that our system is competitive with thermoacoustic and thermoelectric conversion.