Thermoelectric and Thermomagnetic Heat Pumps

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Abstract
The dynamical equations which govern the simultaneous flows of heat and electricity in crystals express the electric and heat current densities as linear combinations of the gradients of the electrochemical potential and the temperature. When a magnetic field is applied, the coefficients in these equations become functions of the applied field. Magnetic field effects are included by expanding the coefficients in powers of the magnetic field. For isotropic media, expansion of the electrical and thermal conductivities and the Seebeck coefficient to the first order in the magnetic field gives the Hall, Righi-Leduc, and Nernst coefficients, respectively. The resulting dynamical equations have been solved assuming (a) ρ,κ,S are not functions of position or temperature, H≠0, current density J is either parallel or perpendicular to the temperature gradient ▿T and to the heat current density Q; (b) ρ and κ not functions of position or temperature, H=0, J∥▿T.