Analytical optimal design of thermoelectric heat pumps

• An analytical method is proposed to design single thermoelectric heat pumps.
• Optimal design variables and electric current are related via simple ratios.
• It is recommended to minimize the leg length to reduce the material volume.
• Maximizing the leg section reduces the number of junctions needed.
• The compact classical design of thermoelectric module has to be reconsidered.

This paper proposes an analytical method to design thermoelectric heat pumps (THPs), in order to meet a given thermal power demand with a maximum coefficient of performance (COP). The method returns the optimal thermoelectric element (TE) design (leg length, leg section and number of legs) and optimal electric current, assuming that the hot and cold operating temperatures, the thermal power demand and the material properties are known. The optimal operating conditions are derived analytically from steady-state analytical models in the literature. Analytical development leads to defining an equivalent Seebeck coefficient when the Thomson effect is taken into account. Given that the optimal variables are closely related, many designs can meet the two performance criteria: (i) meeting thermal demand and (ii) maximizing the COP. To define a single optimal design, two additional manufacturing criteria are also considered: (iii) minimizing the material volume and (iv) minimizing the number of electrical junctions. This approach leads to the following recommendations:- identify the maximum THP area acceptable, depending on the application targeted, in order to decrease the thermal flux density and thus increase THP performance;- minimize the leg length in order to reduce the material volume and thus the THP cost;- maximize the leg section (leading to work with the maximal electric current achievable) in order to reduce the number of junctions, thus facilitating the manufacturing process.Finally, the optimal number of legs and electrical current can be calculated via simple ratios.