Estudio de los resultados

This section illustrates the theoretical analysis of proposed system for estimating the limiting heat flux of thermoelectric generators that are under test in this research. There is a need to determine the limiting heat flux of thermoelectric generators since the performance of these devices is poor under small heat flux and improves as the input heat flux increases. Thermoelectric generators can be used with different heat sources for power generation; however it is preferable to have a heat source that can supply high heat flux for better performance of these devices. Solar energy is one of the most easily accessible energy sources that can be used for power generation using thermoelectric generators. Average value for direct incident solar radiation heat flux over the flat surface in Melbourne, Australia is approximately 900W/m2. High heat flux can be achieved using various solar concentration techniques that can be used for better performance of thermoelectric power generators. Solar concentrators such as parabolic dish, parabolic trough, fresnel lens or reflective mirrors have been commonly used for solar concentration.

Figure 23 shows the proposed design for this research that uses solar concentrator for achieving heat flux at the target area. Thermoelectric generators are sandwiched between the target plate on one side and the heat sink on the other side. Conventional passive cooling methods are adopted to reduce the auxiliary power consumption of the system. This will reduce the net power output and increase the overall system efficiency.

Figure 23 Heat flow path with key components of system

Incoming solar radiations are transmitted from the larger aperture area towards the smaller target area to increase the solar concentration. Amount of energy reaching the target plate can be determined using the optical efficiency of the solar concentrator. Heat flow path is illustrated in Figure 24 with the help of equivalent thermal circuit using the thermal resistances and key temperatures.

Figure 24 a) Schematic of thermoelectric generator sandwiched between target plate and finned heat sink b) Thermal circuit showing the heat flow path through system

Some heat is lost to the surroundings from the target plate due to convection and radiation losses. Heat is further transferred to the thermoelectric generator by conduction from the target plate. Thermal resistance of the thermoelectric generator creates the temperature difference across the hot and cold side of thermoelectric generator. Cold side temperature is further reduced by using different types of heat sinks.

Indoor testing facility was set-up to experimentally determine the limiting heat flux of type A and B TEGs with conventional heat sinks while maintaining the respective hot side temperature within the allowable limit. Solar heat flux was simulated in the indoor test setup by embedding the resistive heating elements inside 100mm long, 100mm wide and 20mm thick aluminum block. Figure 25 shows the schematic of the energy flow in the indoor testing rig.

Figure 25 Schematic of energy flow in indoor testing rig

The amount of energy received by the heater plate is given as follows

̇ 3.9

Where, is the voltage supplied to the electric heating elements and is the current flowing through them. In case of an actual solar concentrator the total energy reaching the surface of the target plate is also expressed in equation 3.9. is the direct incident solar radiation flux on the inclined surface of aperture that uses the two axes solar tracking system and is the aperture area of the solar concentrator. Figure 26a and Figure 26b illustrates the schematic of Fresnel lens solar concentrator and the detailed heat distribution in the whole system.

Figure 26 a) Schematic of the Fresnel lens solar concentrator with bare plate as heat sinks

b) Detailed description of heat distribution at target plate, thermoelectric generator and heat sink

The solar concentration ratio can be calculated for indoor test setup and outdoor Fresnel setup as stated in equation 3.10.

3.10

Total energy supplied to the target plate will be equal to heat lost from target plate plus power extracted from thermoelectric generator plus heat dissipated from base plate in case of absence of fins as shown in Figure 27. Energy balance equation for the setup shown in Figure 27 is given as follows

Figure 27 Solid model of indoor testing rig without fins on the heat sink plate

In case of finned heat sink there will be an added component of heat dissipated through fins as shown in Figure 28. The energy balance equation for the setup in Figure 28 is given as follows

Figure 28 Solid model of the indoor testing rig with fins on the heat sink plate

Figure 29 Thermal circuit diagram of the indoor testing rig

̇ ̇ ̇ 3.13

Energy is lost at the target plate via convection and radiation heat transfer to the ambient air. Energy lossed due to convection is expressed as follows.

̇ 3.14

Convection heat transfer coefficient is calculated using the heat transfer correlations and termed as , target area is termed as and the target temperature and ambient temperature are and respectively.

Energy loss due to radiation heat transfer from the target plate to the ambient air is expressed as follows.

̇ ( ) 3.15

Here, is Stefan Boltzmann constant, is the surface emissivity. Thermoelectric generator offers some thermal resistance to the flow of heat. Energy flowing though the thermoelectric generator can be expressed as

̇

3.16 Thermal resistance offered by the thermoelectric generator is expressed as and is the base plate temperature in equation 3.16. Heat transfer gel with thermal conductivity of 3.5W/m.K is used in between the contact surfaces to reduce the contact thermal resistance. The contact surfaces have a good surface finish and are in contact with each other under pressure and there is thin film of thermal gel between the contact surfaces. So for this analysis the contact interface thermal resistance is neglected and hence it is assumed that the cold side temperature of the thermoelectric generator will be equal to the base plate temperature. Thermal resistance of the thermoelectric generator used in this research is experimentally verified against the manufactures specification.

Heat dissipated by the base plate through convection and radiation is stated in equation 3.17 where is the base area and is the convection heat transfer coefficient calculated using the heat transfer correlations for corresponding geometry temperatures and flow types (Incropera, 2007).

Similarly in case the fins are attached to the base plate, the heat will be dissipated from the fin surface as well. Since all the fins are very closely placed, the radiation heat transfer through fin surface is neglected in this analysis.

Figure 30 Theoretical estimation of limiting heat flux for Type A thermoelectric generators [Solar Flux (W/m2) vs. Velocity (m/sec), hot side temperature = 150°C and

250°C Ambient Temp: 18°C, Velocity of air range from 0m/sec - 5m/sec] (b) Theoretical estimation of limiting heat flux for Type B thermoelectric generators

[Solar Flux (W/m2) vs. Velocity (m/sec), hot side temperature = 150°C and 250°C Ambient Temp: 18°C, Velocity of air range from 0m/sec - 5m/sec]

Estimated limiting heat flux for type A and type B thermoelectric generator is illustrated in Figure 30 where the hot side temperature is maintained at 150°C and 250°C for type A and type B thermoelectric generators respectively. The ambient temperature is assumed to be 18°C and air velocity is varied between 0m/sec to 5m/sec. Limiting heat flux for type A and type B thermoelectric generators is predicted for various conventional heat sink configurations including bare plate and finned heat sink with different fin lengths. Fin lengths and fin gap are varied considering the heat sink optimization illustrated in earlier section. For both type A and type B thermoelectric generators it can be observed that there is a considerable improvement in the limiting heat flux when bare plate is replaced with a finned heat sink with 60mm fin. As seen in

the heat sink optimization section, the improvement in the thermal resistance of heat sink reduces as the length of the fin extends beyond 0.1m. Theoretical estimation of type A thermoelectric generator in Figure 30 show that the limiting heat flux would enhance by 12% when the fin length is increased from 60mm to 80mm but it increases only by 7% on increasing the fin length from 80mm to 100mm at lower velocities. At higher velocities the improvement is even lower and drops to 5% from 80mm to 100mm fin. This trend is similar for the type B thermoelectric generators. From the theoretical analysis of fin optimisation and the analytical modelling for estimating the limiting heat flux it can be concluded that, there is significantly small reduction in heat sink thermal resistance as the fin length approaches 100mm and hence any further increase in fin length can be considered to be uneconomical.