Chapter 4: Thermalhydraulic Characterization of
4.6. Heat Transfer Aspects
The situation is, however, noticeably different from heat transfer point of view. Effect of source and sink temperatures on average heat transfer coefficient at source with all the three fluids at 8 MPa pressure level is presented in Figure 4-12. Local Nusselt number values are calculated using the dimensionless temperature gradient prevailing at the tube surface and that is employed in estimating the concerned heat transfer coefficient. Water is single-phase liquid and hence exhibit very high heat transfer coefficient.
R134a is in supercritical condition, but the considered temperature range is well below the pseudocritical temperature (about 411.4 K at 8 MPa). So it also behaves nearly like a single-phase medium with poor thermal conductivity, resulting in very low heat transfer coefficient. Under identical conditions, heat transfer coefficient for water can be as much as 6 times that of R134a. With
increase in source-to-sink temperature differential, heat transfer coefficient moderately increases with R134a, while it remains nearly the same for water.
When the sink temperature is higher than pseudocritical temperature for CO2
(about 307.8 K at 8 MPa), its heat transfer performance is very poor compared (a)
(b)
Figure 4-12. Variation of heat transfer coefficient at source with (a) source temperature for 𝑇𝑐 = 315 K and (b) sink temperature for 𝑇ℎ = 331 K with
three different working fluids at 𝑝 = 8 MPa
to water and can even be inferior to R134a, due to poor thermal conductivity.
However, when CO2 crosses the pseudocritical point within the heater, it experiences a sharp drop in thermal conductivity, along with a small intermediate peak (Figure 1-7). The consequence is evident from Figure 4-12b, as heat transfer coefficient is comparable with water for low sink temperatures and drops sharply with any increase thereof. It emphasizes the role of local
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Heat transfer coefficient (W/m²K)
Source temperature (K)
CO₂ R134a Water
0 2000 4000 6000 8000
270 280 290 300 310 320
Heat transfer coefficient (W/m²K)
Sink temperature (K)
CO₂ R134a Water
buoyancy in enhancing both mass and heat transfer rate. Such behavior is, however, found only for supercritical pressure levels close to the critical value.
Heat transfer coefficient generally increases with system pressure (Figure 4-13). When the sink condition is higher than pseudocritical, heat transfer coefficient monotonically decreases with larger source-to-sink temperature differential and the concerned gradient is much steeper at higher pressure levels. Rapid deterioration in heat transfer coefficient can be found when the working fluid is made to cross the pseudocritical temperature, as is explained earlier.
(a)
(b)
Figure 4-13. Variation of heat transfer coefficient of CO2 at source with (a) source temperature for 𝑇𝑐 = 315 K and (b) sink temperature for 𝑇ℎ = 331 K at
three different pressure levels 0
1000 2000 3000
330 340 350 360 370 380
Heat transfer coefficient (W/m²K)
Source temperature (K) 6 MPa 8 MPa 10 MPa
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270 280 290 300 310 320
Heat transfer coefficient (W/m²K)
Sink temperature (K)
6 MPa 8 MPa 10 MPa
NCL under consideration has temperature-coupled boundary condition and hence the rate of heat transfer from source-to-sink depends on both mass flow rate and heat transfer coefficient. Figure 4-14 presents the variation of the rate of heat transfer with source and sink temperature for all the three fluids at two different pressure levels. Large heat transfer coefficient for water and high mass flow rate for R134a help achieving large power transmission
(a)
(b)
Figure 4-14. Variation of rate of heat transfer at source with (a) source temperature for 𝑇𝑐 = 315 K and (b) sink temperature for 𝑇ℎ = 331 K with
three different working fluids
with either of the working fluids. The same increases continuously with enhanced source-to-sink temperature differential, without any significant influences of system pressure. Till a certain limit of source temperature, R134a provides greater rate of heat transport. However the steeper profile for
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330 340 350 360 370 380
Rate of heat transfer (W)
Source temperature (K)
CO₂8 MPa CO₂10 MPa R134a 8 MPa R134a 10 MPa Water 8 MPa Water 10 MPa
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270 280 290 300 310 320
Rate of heat transfer (W)
Sink temperature (K)
CO₂8 MPa CO₂10 MPa R134a 8 MPa R134a 10 MPa Water 8 MPa Water 10 MPa
water owing to the substantially higher heat transfer coefficient, results in larger power transport with water at higher level of source temperatures. Rate of heat transfer for the CO2-based loop is dependent on the working temperature limits. When the sink temperature is higher than the pseudocritical value, both heat transfer coefficient and mass flow rate being low, CO2 at 8 MPa can transfer energy at a very low rate. At 10 MPa, however, CO2 exhibits the largest flow rate till a certain source temperature limit.
Corresponding heat transfer coefficient values are also much higher than 8 MPa (Figure 4-13). Therefore CO2 loop at 10 MPa is able to provide the largest heat transfer rate for almost the entire range of source temperature considered here. On the other hand, when the sink temperature is well below pseudocritical, extremely high rates of heat transport can be obtained with CO2 loop, which can be as high as 8 times that of water at 8 MPa. But the rapid deterioration in heat transfer coefficient, as the sink temperature approaches the pseudocritical point, is also reflected in the heat transfer rate, which shows a sharp decline with increase in sink temperature. Still the amount of power transmitted by the CO2-loop is higher than other two fluids for the conditions considered in present study. Therefore supercritical CO2 as a working fluid is able to provide favourable heat transmission characteristics for majority of the conditions. The use of CO2-based loops can specifically be suggested at higher system pressures and large source-to-sink temperature differential, with the sink temperature being well below the pseudocritical limit and the source temperature being well above the same. However it demonstrates inferior performance for system pressure close to the critical point and with sink temperature higher than pseudocritical at corresponding pressure.