Modeling of Non-Uniform Thermoelement Devices Subject to Lateral Heat Convection

Abstract

In this paper, we draw attention to the importance of the lateral convection heat transfer effect on the operation of thermoelements with variable cross-sectional area. The significance of lateral heat convection arises from a new application, in which thermoelements form the walls of a MEMS-based convergent-divergent micronozzle in order to pump heat from the divergent part of the micronozzle to the convergent part to enhance overall performance. To assess the effect of thermoelement, we develop a quasi-one-dimensional model for thermoelements, in which, the physical phenomena of Peltier effect, Joule heating, Seebeck effect, longitudinal heat conduction, and lateral heat convection are considered. The general energy equation of the thermoelement with variable material properties is formulated with heat convection modeled as a lateral heat source. We used the model to study thermoelements with rectangular cross section and uniform thickness, but variable width. The width of the element is maximum at the location forming the micronozzle throat. Several geometries have been investigated; a piece-wise linear, parabolic and piece-wise sine wave. Two parameters which play important role in the thermal performance of thermoelement are identified. These are the thermal resistance ratio; ratio of longitudinal conduction resistance to lateral convection resistance, and heating ratio; ratio of Joule heating to Fourier conducted heat. The effects of varying these two parameters as well as thermoelement geometry have been investigated thoroughly and the results are presented in the form of charts to assist the design and material selection of the thermoelement.