Constructal design of thermoelectric power packages Adrian Bejan a,⇑ , Sylvie Lorente b , Deok-Hong Kang c a Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300, USA b Université de Toulouse, INSA, 135 Avenue de Rangueil, 31077 Toulouse, France c Research Institute of Industrial Science and Technology, Energy & Resources Research Department, Pohang, Republic of Korea article info Article history: Received 11 July 2014 Received in revised form 4 August 2014 Accepted 5 August 2014 Keywords: Thermoelectric Constructal Vascular Serpentine abstract In this paper we consider the complete thermofluid design and performance of a thermoelectric module. We increase the temperature difference that must be maintained across the module, and at the same time we reduce the pumping power required by the streams that bathe the hot and cold plates of the module. We find that for greater power output the two streams must be configured in parallel, not in counterflow, and not between two well mixed plenums. We also find that the loss of thermoelectric power due to the temperature nonuniformity of the two plates competes with the power lost during the pumping of the two streams, and that from this competition results the optimal mass flow rates of the two streams. At the optimum, the maximized power output of the module is proportional to a group of geometric parameters (Eq. (39)), which can be maximized further by designing vascular flow architec- tures for the two plates. The vascular designs reveal an optimal ratio of channel diameters, optimal plate aspect ratio, and a channel flow volume fraction that is of the same order as the ratio of the fluid thermal conductivity divided by the solid thermal conductivity. The flow architectures are further illustrated with numerical examples of vascular and serpentine configuration and performance. Ó 2014 Elsevier Ltd. All rights reserved. 1. Thermoelectric power generation Thermoelectric power generation (TE) is attracting interest from across the spectrum of technology because it offers a path to clean, renewable energy. In addition, TE devices offer compact- ness and simplicity because they do not have moving parts. The efficiency of TE designs is limited by the transport properties of the thermoelectric materials accounted for in the property group Z discussed in Eq. (1). Progress toward greater efficiencies can be made by optimizing the geometry—the relative shapes and sizes—of the legs of the module [1–3]. This and other aspects of the optimization of thermoelectric modules (TEM) has generated a growing body of literature [1–19]. In the present study we consider the whole picture—the ther- mofluid design and performance of the TEM. We consider not only the temperature difference that must be maintained across the TEM, but also the fluid mechanics of the vascular hot and cold plates that sandwich the TEM. We show that important tradeoffs exist in the thermofluid design such that the overall performance of the TEM is increased. The thermoelectric module (TEM) is defined in Fig. 1. The hot plate is heated by a stream of hot oil. The cold plate is cooled by a stream of water. Heat flows by conduction perpendicular to the plates, from the hot plate to the cold plate. Larger stacks are obtained by sandwiching several TEMs as shown in Fig. 2. All the TEMs are identical. Each is a sandwich of three parts: hot plate (H), thermoelectric converter (T), and cold plate (C), in other words, HTC, or CTH. There are two ways to assemble such elements in a stack: (a) Alternating orientations, i.e., plates of the same temperature touching each other: HTC CTH HTC ... (b) Elements oriented in the same way: HTC I HTC I HTC ... The simplest design is (a). In design (b), a layer of insulation (I) must be placed between the C and H plates of adjacent elements. Fig. 2 shows the (a) rule of assembly. If the TEM is small enough and the hot and cold fluid flow rates are large enough, then the hot and cold plates are essentially iso- thermal, at T H and T L , respectively. The thermodynamics of the TEM is detailed in Ref. [1], and it shows that the maximum thermo- dynamic efficiency of a module with isothermal ends is http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.08.008 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: abejan@duke.edu (A. Bejan). International Journal of Heat and Mass Transfer 79 (2014) 291–299 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt