Theory of the Longitudinally Isothermal Ettingshausen Cooler

Abstract

The temperature distribution T(x), maximum temperature difference ΔTmax, and coefficient of performance ε are determined for an Ettingshausen cooler of rectangular cross section when the temperature is constant in the direction of current flow (longitudinal isothermal condition). The calculation is carried out for the two cases (1) temperature-independent transport coefficients and (2) the Nernst and resistivity coefficients proportional to T−1. In both cases the expressions for ΔTmax and ε correspond closely to those for the transversely isothermal Peltier cooler while the temperature distribution differs considerably. In the longitudinally isothermal Ettingshausen cooler the electric field is constant, in the contrast to the transversely isothermal Peltier cooler, in which the current density is constant. Recognition of this fact allows the validity of the results to be established for all possible values of the figure of merit. A value of ΔTmax measured on a Bi(97)Sb(3) cooler is compared with the value determined by substitution of independently measured values of the transport coefficients into the theoretical expression for ΔTmax. Although the temperature dependence of the transport coefficients is not taken into account exactly, the agreement is good. The effect of shaping the cooler (in effect, cascading) is discussed and experimental evidence for enhancement of cooler performance due to shaping is presented.

Robust longitudinal spin-Seebeck effect in Bi-YIG thin films

“…Recently, Huang et al15 claimed that, in a similar structure (YIG/Pt), the platinum film itself becomes ferromagnetic, as magnetic proximity effects induce magnetic behavior in platinum. If this claim stands true, then the observed voltages originally attributed to SSE are not only due to the spin-Seebeck effect, but also possess a contribution resulting from the anomalous Nernst effect in platinum16. Thus, before the origins of the SSE are investigated, this claim must be addressed.…”

Driving Perpendicular Heat Flow: (p×n)-Type Transverse Thermoelectrics for Microscale and Cryogenic Peltier Cooling

“…Provided the thermal gradient is orthogonal to the current density ∇T = dT dyŷ , the longitudinal electric field component E x is constant everywhere, 5 and the heat flux component Q y will depend only on y. The longitudinal current and transverse heat flow are…”

“…4 However practical application of the N-E effect is limited since a high 1.5 T magnetic field is required. 5 Stacked synthetic transverse thermoelectrics have also been demonstrated which have structural asymmetry by alternately stacking macroscopic millimeter-thick slabs of semiconductor with large Seebeck coefficient upon (semi)metal slabs with large electrical and thermal conductivity.…”

Thermomagnetic Mechanism for Self-Cooling Cables

“…The cable is much longer than wide, so that besides some effects at the ends of it, all quantities are constant by respect to z and θ and the heat flows radially. Following Kooi et al [7] the relevant equations in the present case, written in cylindrical coordinates, are:…”

“…The two figures of merit are related by Z a = Z 1−ZT . It can be shown [5][6][7] that in a parallalelepiped setup like the one depicted in the upper panel of Fig.1 the expected temperature drop ∆T is roughly (exactly, if N , ρ, K and thus Z are independent of temperature):whereT = (T h + T l )/2 is the middle temperature between the hot and cold side. ∆T is then for example of the order of 30K for a material with ZT=0.2 in a device with a heat sink at the ambient temperature of 300K.…”