Numerical assessment of the thermodynamic performance of thermoelectric cells via two-dimensional modelling q Klaudio S.M. Oliveira, Rodrigo P. Cardoso, Christian J.L. Hermes ⇑ Laboratory of Thermodynamics and Thermophysics, Federal University of Paraná, 81531990 Curitiba, PR, Brazil highlights  A 2-D model for thermoelectric cells is advanced based on the finite-volume method.  The model accounts for the Fourier, the Thomson, and the Joule effects.  The model predictions were validated against experimental data.  The effects of the thermoelectric properties and the cell geometry were assessed. article info Article history: Received 12 March 2014 Received in revised form 20 May 2014 Accepted 21 May 2014 Keywords: Thermoelectric cooling Two-dimensional model Sensitivity analysis Finite-volume method abstract The present paper is aimed at putting forward a two-dimensional model for thermoelectric cells. The energy conservation equation was formulated in order to account for the Fourier (heat) conduction, the Thomson (thermoelectric) effect, and the Joule heating on the temperature distribution. The electric field was also modelled in order to come out with the current and voltage distributions. The governing equations were discretized by means of the finite-volume method, whereas the TDMA algorithm was adopted for solving the sets of linear equations. An explicit solution scheme was employed to address the temperature influence on the thermoelectric effect. The model results have been compared with experimental data, when a satisfactory agreement was achieved for both cooling capacity and COP, with errors within a 10% band. In addition, the model was employed to assess the effects of the thermophysical properties and the couple geometry on the thermodynamic performance of the thermoelectric cell. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction In the past decades, solid-state cooling technologies have come onto some particular market niches, especially the applications related to portable cooling [1]. The most significant advances have been achieved in the realm of thermoelectric cooling [2], in which an electric current produces a temperature difference in a couple of dissimilar semiconductor materials. A typical thermoelectric module is manufactured with two thin ceramic wafers and an array of p- and n-type blocks of doped semiconductor material sandwiched between them. A pair of p- and n-type blocks connected electrically in series and thermally in parallel make up a thermoelectric couple [3]. Several studies have been conducted both theoretically and numerically to assess the thermodynamic performance of thermoelectric cells. Samples of the most influencing works are summarised in Table 1. The literature review points out that most models are one-dimensional, being not able to evaluate the influence of the cell geometry on its performance. In addition, the literature analysis also reveals that the few available multidi- mensional approaches are often developed aided by commercial packages, which provide restricted access to the mathematical formulation and the numeric algorithm. At last, most models do not account for the heat transfer in the air cavity, which may also affect the system performance. The present paper is therefore aimed at advancing a tailor-made two-dimensional model, in the realm of the irreversible thermodynamics, which is suitable to evaluate the sensitivity of the thermophysical properties and the cell geometry on its thermodynamic performance. http://dx.doi.org/10.1016/j.apenergy.2014.05.050 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved. q An abridged version of this manuscript has been accepted to be presented at the 15th International Refrigeration and Air Conditioning Conference at Purdue, July 14–17, 2014. ⇑ Corresponding author. Tel./fax: +55 41 3361 3239. E-mail address: chermes@ufpr.br (C.J.L. Hermes). Applied Energy 130 (2014) 280–288 Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy