Chapter 3 Theoretical analysis of conventional passive heat sink
3.2 Optimization of finned heat sink
Prerequisite to determine the limiting heat flux for two TEG’s with finned heat sink is to estimate the optimum finned heat sink configuration that will be best suited for the proposed system. An extensive research has already been done on optimization of the heat sinks fin length and fin spacing under natural cooling and forced cooling conditions. This section focuses on estimating the optimum fin length and fin gap or in other words optimum number of fins that will provide the least thermal resistance for the proposed configuration of the concentrated solar thermal system with thermoelectric power generation.
Figure 20 Schematic of the finned heat sink illustrating the nomenclature used for various dimensions
To determine the thermal resistance of the heat sink under consideration, it is necessary to know the base temperature of the heat sink. Heat sink base temperature can be determined by using the information about the TEG’s hot side limiting temperature, the thermal resistance of TEG and the heat flux applied across the TEG.
( )
3.1 The thermal resistance of the heat sink depends on the convection heat transfer coefficient and fin arrangement. Heat sink optimization involves choosing the optimum number of fins and fin gap for certain air speed along the length of the fins.
3.2 Fin gap is illustrated in equation 3.2 where is the width of the heat sink and is the fin thickness as shown in Figure 20. The exposed surface area of the base plate is defined in equation 3.3
( ) 3.3
Total surface area of one fin including both the sides is defined in equation 3.4
3.4
Velocity of air flowing over the fins can be calculated from equation 3.5 by knowing the volume flow rate ̇.
̇
( ) 3.5
Teertstra’s equation (Teertstra et al., 1999) to estimate the Nusselt number for determination of convection heat transfer coefficient is being used here and mentioned below.
[ * + * √ √ √ + ] 3.6
Equation 3.7 is used to calculate the fin efficiency that affects the performance of the heat sink
3.7
While is as defined in equation 3.8
√
3.8
Thermal conductivity of the fin material is stated as . In this case fin material is considered to be aluminum with thermal conductivity of 180W/m.K. Optimization of the heat sink to be used for cooling of thermoelectric generator under concentrated solar thermal heat source is discussed in further section by using the above mentioned equations. The maximum surface area available for attaching the heat sink on the cold side of thermoelectric generator is equal to the target area of the solar thermal concentrator.
Figure 21 Effect of number of fins on the thermal resistance of the fin heat sink at various air speeds
It can be observed from Figure 21 that, increasing the number of fins on the heat sink will reduce its thermal resistance. This is due the increase in the surface area for heat transfer from the heat sink. Figure 21 also illustrates the relationship between the variation of heat sink thermal resistance and the change in number of fins at different ambient wind velocities. The range of air velocity considered for optimization of the heat sink is selected by referring to the local average ambient air speed throughout the year (data acquired from the Bureau of Meteorology, Australia (Meteorology, 2013)). It is observed that the thermal resistance reduces steeply as the number of fins increases from 0-4 irrespective of ambient wind velocity. The thermal resistance undergoes less steep reduction between 4-8 numbers of fins for all the ambient velocities. Beyond 8 fins the thermal resistance for velocities 3-5 m/sec does not change much. This can be attributed to the increased pressure drop due to the reduction in the fin gap at high ambient wind velocity. Pressure drop increases due to higher numbers of fins being fitted over the same surface area and fin gap is decreases. It can be concluded from above observation that
increasing the number of fins beyond 8 fins will have very little advantage on reduction of thermal resistance of heat sink for ambient wind velocities in the range of 3-5m/sec. Thus the optimum number of fins is fixed as 8 to be used for the further optimisation analysis in the next section.
Figure 22 Effect of fin length on the thermal resistance of the heat sink for 8 numbers of fins at various air speeds
Fin length plays an important role as well in having an optimum design for the heat sink. Figure 22 illustrates the effect of increase in the fin length on the thermal resistance of the heat sink at various ambient wind velocities. It is observed that the thermal resistance of heat sink significantly reduces for 1-3m/sec of ambient wind velocity with increase in the fin length; however for ambient wind velocity of 4m/sec and 5m/sec the drop in thermal resistance is insignificant with increasing in the fin length. For higher ambient wind velocities the convection heat transfer coefficient is large and results in low thermal resistance even for the smaller fin length and does not reduce significantly even with the increase in the fin length. But for the smaller ambient wind velocities, the
thermal resistance is large for smaller fin length and significantly reduces as the fin length increases. It can be observed from Figure 22 that the effect of fin length on the heat sink thermal resistance at low ambient wind velocities has a dominant effect on choosing the optimum fin length of the heat sink. The thermal resistance does not reduce drastically beyond the fin length of 0.1m for any ambient wind velocity. Hence the fin length of the finned heat sink is selected to be varied from 0.06m to 0.1m for the purpose of this research.