Lorentz Force and Joule Heat Induced in an Electrically Conducting Plate Moving With Time-Dependent Velocity Under the Influence of a Homogeneous Magnetic Field

Abstract

This paper investigates the interaction of an initially uniform magnetic field with an electrically conducting slab that moves perpendicularly to the magnetic field with arbitrary time-dependent velocity. It is demonstrated that the problem of determining the time-dependent Lorentz force and the time-dependent Joule heat in the slab is mathematically equivalent to solving a 1-D heat diffusion problem with time-dependent boundary conditions and to submitting the solution to a nonstandard postprocessing procedure. For the particular case of an impulsively driven slab we exploit the mathematical analogy between magnetic diffusion and heat diffusion by translating a textbook solution of the corresponding heat-transfer problem into exact and previously unknown relations for Lorentz force and Joule heat. Moreover, we use a 1-D finite-difference code to investigate more general time dependencies of the velocity including smooth accelerations and random velocity changes. Our numerical determination of reaction times (T 98) of the Lorentz force in the case of smooth accelerations provides a useful design tool for the development of Lorentz force flowmeters with short reaction times.

Experimental investigation of the transient phase of the Lorentz force response to the time-dependent velocity at finite magnetic Reynolds number

“…an increase in τ Re m makes the system 'conductor-magnetic field' more stiff, and as a consequence the non-dimensional saturation time * T 98 becomes less. Concluding this section, we would like to note that there is an excellent agreement between the measured Lorentz force and the force that was obtained analytically in [12] (figure 7). The theory is based on a 1D-model of a conducting plate moving through a homogeneous magnetic field with a timedependent velocity.…”

“…This should be taken into consideration when evaluating the measurement error. The studied effects in solid conductors are similar to some extent to the effects in Comparison between the experimental and theoretical Lorentz force response [12]. A discrepancy between the curves after the end of the acceleration phase is explained by the charge leakage in the piezoelectric force sensor that leads to a signal decay.…”

Investigation on a flow transducer using modified force sensing technique

“…Here the platinum elements act as the Joule heaters and temperature detectors under the constant temperature difference mode. Weidermann et al [9] have studied the timedependent Lorentz force and Joule heat of a conducting slab moving perpendicularly to an initially uniform magnetic field and have shown that the conductor with uniform acceleration in a magnetic field is a useful design tool for developing a Lorentz force flowmeter with short reaction time. The effect of external magnetic field on the electric potential probe of a liquid metal magneto-hydrodynamic flow through a rectangular duct has been analysed by Mistrangelo et al [10] to support the physical interpretation of the potential measurement of a potential probe in the conductance anemometry for the measurement of the flow velocity.…”

“…Weidermann et al . [9] have studied the time‐dependent Lorentz force and Joule heat of a conducting slab moving perpendicularly to an initially uniform magnetic field and have shown that the conductor with uniform acceleration in a magnetic field is a useful design tool for developing a Lorentz force flowmeter with short reaction time. The effect of external magnetic field on the electric potential probe of a liquid metal magneto‐hydrodynamic flow through a rectangular duct has been analysed by Mistrangelo et al .…”

No-Slip Motion of a Spherical Magnet on the Top of a Conductive Plate

“…Most coupled mechanical-electromagnetic problems concern devices which have only one mechanical degree of freedom [1]- [2]- [3], notable exceptions are magnetohydrodynamical flows. Most cases describe either the field-circuit coupling [4] or the mechanical coupling [5].…”