Modeling and trade-off analysis of a condenser with thermoelectric generation

Abstract

A transverse thermoelectric generator turns a heat exchanger tube into an electrical source without discrete junctions, ceramic substrates or interface layers, because the tube wall itself is the active medium. Existing work on such devices treats their thermal problem locally, with constant heat-transfer coefficients and a fixed tube length. That treatment is adequate for the single-phase device in which the architecture was demonstrated, and it is not adequate for a condenser, where the local heat flux collapses by close to an order of magnitude at the completion of condensation. This thesis develops a one-dimensional, segment-resolved model of a two-phase condenser whose wall is a transverse thermoelectric laminate, with bidirectional coupling between the thermal and the electrical problems. The tube is divided into segments in which the refrigerant state, the wall temperatures and the local thermoelectric quantities are solved together. The tilted metal and semiconductor laminate is reduced to effective transport properties by rotation of the transport tensors, condensation is closed by a three-regime correlation, and the segments are coupled by a single current. That current makes the electrical problem global while the thermal driving remains local, which is the structural feature the analysis exploits. Because the Seebeck and Peltier coefficients are one material property, the current returns into the wall boundary condition rather than following from it. Verification rests on conservation balances, grid convergence and limiting cases whose answer is known in advance. The two halves of the model are validated against independent measurements: the thermoelectric half against a manufactured tubular device, through a single fitted parameter representing the interfacial electrical contact resistance, and the condensation closure against measured quasi-local coefficients, which it reproduces to about 1 % in the shear-dominated regime without any adjusted parameter. Applied to a reference condenser, the model shows that the thermoelectric wall first imposes a thermal penalty, the effective conductivity falling from 20 W/(m K) to 13.9 W/(m K) . Closing the circuit delivers 42.1 mW against a duty of about 315 W, a system efficiency of 1.3 × 10−4. Roughly half the segments deliver negative power, occupying the subcooled region where the driving temperature difference is too small to sustain the common current, and 28.7 % of the gross production is destroyed internally before reaching the terminals. The sensitivity analysis ranks the parameters that remain once the laminate is taken as manufactured: power falls with tube length beyond the condensation zone, wall thickness is the strongest exchanger lever, the shell diameter is inert, and the conditions under which the device is installed outweigh the geometry around it. The conversion efficiency is negligible and the device is not an energy-recovery technology at this operating point. Its interest lies in the local coupling, which only a segment-resolved approach reveals: half the tube works against the other half, and that loss carries its own remedy in the form of an electrical partition at the phase boundary. The absolute levels rest on a fitted electrical parameter, omit an interfacial thermal resistance and use a condensation closure extrapolated below its validated domain, so they are reported as a preliminary mapping of an immature architecture rather than as a performance figure.