Constructing a heat exchanger model

(4.24)

As the thermal balance between the thermal flows entering the hot junction and leaving from the cold junction of the TE module, Equations 4.19 and 4.20 are equal to Equations 4.22 and 4.23 by ignoring the Thomason effect . By combination these equations, the heat balance equations at two junctions of the TE module are illustrated as:

As the energy conversion efficiency of even the best TE modules available is very low, a proper heat exchanger system design is essential for a good TEG system design.

A larger temperature difference between the two sides of the TE module means that more electrical energy can be generated by the TE module. Hence, it is very important to maintain a large temperature difference between the two sides of TE module. When the internal thermal resistance of the TE module is equal to the sum of all external thermal resistance, the maximum output power occurs (Chen et al., 2005). As shown in Figure 4.3, the external thermal resistance is determined by contact resistance between parts and between the surroundings, and the thermal resistance of the exchangers themselves. In order to maximize the efficiency of the heat exchanger system and to predict the performance of the generator, a numerical model of the heat exchangers subsystem should be designed and associated with the TE module model.

A heat exchanger subsystem is composed of two heat exchangers, one is attached to a heat source to harvest heat from the heat source and another is exposed to thermal interface (air) to evacuate the heat from the cold side of the module. Because metals

are good thermal conductor materials, a piece of metal is considered as an ideal hot side heat exchanger. Moreover, as a large temperature difference between the heat source and the TE module can be obtained to compensate an inefficient hot side heat exchanger, a 1.7mm thickness and square cross-section aluminium plate has been employed as the hot side heat exchanger in this chapter. The diagram of Figure 4.7 is being used to determine the thermal resistance of the hot-side heat exchanger. In Figure 4.7, T1 and T2 are the temperature of the hot side and cold side of the hot side heat exchanger, dT=T1-T2 is the temperature difference between the two sides of the heat exchanger, and Q is heat being absorbed by the hot side heat exchanger. The total thermal resistance of the hot side exchanger is the sum of the thermal resistance of the hot side heat exchanger and the contact resistance of between the heat source and the hot side heat exchanger, as expressed:

will be described in the later section. For the thermal resistance of the hot side heat exchanger, it can be expressed in Equation 4.27.

(4.27) where is thermal conductivity of the aluminium plate and the value is according to datasheet of aluminium material (Aluminium, 2010), and A and h1 is the surface area and the thickness of the aluminium plate, respectively.

Figure ‎4.7 Circuit analysis of the hot side heat exchanger

Because the system energy conversion efficiency is dependent on the temperature difference between two sides of the TE module, the cold side heat exchanger is another critical design parameter which should be determined. A solid to air interface is normally used in a lot of TEG systems. But unfortunately, this interface represents the largest barrier for the heat dissipation. Hence, a high efficient heat sink should be used to dissipate the tremendous amount of heat from the cold side of the TE module.

The cold side heat exchanger is shown in Figure 4.8 and the overall thermal resistance of the heat sink, , can further be decomposed into three classical components:

thermal resistance of heat sink , thermal contact resistance , and thermal resistance of ambient .

(4.28)

Figure ‎4.8 Analysis circuit of a heat sink Based on Equation 4.13, the thermal resistance of the heat sink is

(4.29)

where is the thickness of the heat sink used in a TEG system, is the thermal conductivity of the heat sink, is the effective surface area of the heat sink.

The thermal resistance between the heat sink and ambient, , is normally type of media (gas or liquid) and the flow properties such as flow velocity. Generally, the convective heat transfer coefficient for ambient air is within the ranges of surfaces being brought together into intimate contact. Unfortunately, no matter how well-prepared, solid surfaces are never really flat or smooth enough to permit intimate contact because all surfaces have a certain roughness. When two rough surfaces are pressed together, they actually touch only at a limited number of discrete parts of the interface, leaving the untouched area filled with air, as shown in Figure 4.9 (a).

Therefore, the real heat transfer area of the joints only occurs at several points of the apparent contact area and the thermal contact resistance is relatively high when the two rough surfaces are placed together. Because two ceramic plates are used as the two surfaces of the TE module to isolate electrical contact of the P- and N- type semiconductor, the surfaces of the TE module is very rough. The thermal contact resistance between the TE module and the hot side heat exchanger, as well as the thermal contact resistance between the TE module and the heat sink are considered in this chapter. As air is poor conductor of heat, it should be replaced by a more conductive material to increase the joints conductivity and to enhance the heat flow across the thermal junctions. Thermal joint compounds, typically bulk properties material, are usually used to enhance the contact area of the junction. Then the surface contact area can be redrawing as illustrated in Figure 4.9 (b).

Figure ‎4.9 (a) Junction with no thermal interface and (b) Junction with thermal interface

Based on the simplified assumption of homogeneous properties of the materials, the joint thermal resistance to the heat flow that incorporates the thermal joint compounds of the interstitial layer can be schematically shown in Figure 4.10.

Figure ‎4.10 Equivalent thermal resistance circuit for two plates with thermal interface material

The joint thermal resistance, Kj, at the interface can be defined as (Marotta et al., 2002)

(4.34)

where Kb is the thermal resistance of thermal interface material, which is determined by the thermal grease used in the system and the thermal contact resistances and

can be calculated by using Equation 4.35 (Wang et al., 2010).

√ (4.35) where and are the thermal conductivity of the two contacting surfaces, respectively, P is the contact pressure (MPa), H is the surface micro-hardness (MPa) of the softer of the two contacting surface, and and are the surface roughness (m) of the two adjoining surfaces, respectively. The effective absolute mean asperity slope m can be obtained from the approximate correlation equation from (Antonetti et al., 1993)

√ (4.36)

and from Equation 4. 34 are the thermal gap resistances at each interface.

They can be calculated by using Equation 4.37 (Antonetti et al., 1993).

(4.37) where , which is the thermal conductivity of air, and is gas parameter, which is assumed to be zero for the two plates with thermal interface material and Y is the mean plane separation, estimated to be 0.05mm (Antonetti et al., 1993). The model of the heat exchanger subsystem is constructed by integrating the hot side heat exchanger and the heat sink together.