Magnetic field control of three‐dimensional self‐driven multi‐physical thermoelectric system in metal energy storage

Abstract

Summary A thermoelectric generator system is an essential component in thermal energy storage. Through the interaction of magnetic field and thermoelectric current, the thermal energy of liquid metal can be converted into kinetic energy directly, which stirs up a flow without an external hydraulic pump. The effect of the magnetic field on the flow pattern, velocity, and heat transfer efficiency of the self‐driven thermoelectric system is investigated through three‐dimensional numerical simulation. The coupling effect of the magnetic field, temperature field, and velocity field are taken into consideration using the consistent conservative scheme and partitioned iteration algorithm for multi‐region. Hartmann number (Ha) and thermoelectric number (Te) are introduced to measure the relative strength of magnetic damping effect and Seebeck effect. When the magnetic field is small (Ha/Te1/4 ≤ 0.52), the Seebeck effect dominates the flow in the bulk flow region, the velocity of rotating flow increases with the magnetic field, the direction of the Lorentz force is consistent with the flow direction. The maximum velocity of the thermoelectric system occurs when Ha/Te1/4 ∼ 0.52. Hereafter, the flow is dominated by the magnetic damping effect, the velocity decays gradually. A rotating flow in a horizontal plane is resulted from the vertical magnetic field, while a rotating flow in a vertical plane results from a horizontal magnetic field. The latter flow structure gets a larger Nusselt number and lowers the decay rate of kinetic energy because it can transport heat downward more efficiently. The rate of working of the Lorentz force depends on the magnitudes of the Seebeck coefficient and temperature difference.

Heat Transfer Enhancement of Liquid Metal Thermal Convection Affected by the Seebeck Effect and Magnetic Field

“…Velocity at the walls is no-slip boundary condition. The partitioned iteration algorithm is used to ensure the continuity of electric potential and normal current flux at the interface between liquid lithium and stainless steel (Equation ( 9)), as summarized in previous paper [23], where subscripts f , s, and w denote fluid, solid, and wall, respectively. The formulation of electric potential boundary condition is derived using the Taylor series expansion of boundary value and internal value, with a two-dimensional schematic diagram shown in Figure 2, where Δ s = 1/δ s and Δ f = 1/δ f .…”

“…This flow can be explained by the model of thermoelectric magnetohydrodynamic (TEMHD) flow proposed by Shercliff [24]. The self-driven thermoelectric system [23] shows that the Seebeck effect and magnetic field convert the temperature difference into kinetic energy of liquid metal fluid. And the conversion efficiency does not change monotonically with increasing magnetic field.…”

“…Therefore, it is difficult to improve the heat transfer efficiency of liquid metal in strong magnetic field. When the Seebeck effect is considered, the magnetic field exhibits a dual effect and induces significant flow [22,23]. The Seebeck effect between conducting materials with different thermoelectric parameters will generate thermoelectric currents that circulate between the fluid-solid interfaces [24].…”