Modeling of anomalous thermal conduction in thermoelectric magnetohydrodynamics: Couette formulation with a multiphase pressure gradient

Abstract

A metal/liquid-metal junction is a practical thermoelectric cell causing heat absorption or release according to the direction of electric current and temperature gradient. During thermoelectric processes, the possibility of activating the anomalous heat transfer is considered in this work based on adopting a fractional version of Jeffreys equation with three fractional parameters. Because of the connection between the mean-squared displacement of diffusive hot particles and the thermal conductivity, the fractional Jeffreys law is employed to simulate the low thermal conductivity with crossovers; accelerated or retarded transition, and the transition from high (superconductivity—above the Fourier heat conduction) to low (subconductivity—below the Fourier heat conduction) thermal conductivity. The Couette formulation describing a pressure-driven flow of a viscous thick liquid-metal layer bounded by two similar metallic plates, in the presence of a constant transverse magnetic field, is investigated. A triple-phase pressure gradient, consisting of the phases: (i) ramp-up, (ii) dwell, and (iii) exponential decay, is applied as a real-life flow cause and compared with the classical constant pressure gradient and the impulsive pressure gradient case. The velocity and temperature are obtained in the Laplace domain, and then a suitable numerical technique based on the Fourier series approximation is used to recover the solutions in the real domain. It is found that the retarded crossover of low thermal conduction shows “ultraslow” temperature propagation within the thick layer, which indicates to a case of ultralow heat conduction. As well as the strong correlation between the pressure gradient type (constant, impulsive, or three-phase) and direction (favorable or adverse) and its induced velocity, the temperature gradient between the two plates plays a key role in the determination of the velocity direction and magnitude.