A - A Cross-section View
CHAPTER 3 DATA REDUCTION
The single-phase liquid convection and two-phase flow boiling heat transfer coefficients of the coolant FC-72 flowing over the small heated copper plate flush mounted on the bottom of a horizontal rectangular-channel will be deduced from the measured raw data. The space-average heated surface temperature is calculated from the measured average temperature from the thermocouples located near the upper surface of the copper plate according to the one-dimensional steady state conduction heat transfer.
Specifically,
W Cu Cu
T = T - (q l )
×k
(3.1) where is the average measured temperature from the thermocouples and and l are individually the thermal conductivity of copper and the vertical distance between the thermocouple tips and the upper surface of the copper plate.
TCu kCu
3.1 Single-phase Heat Transfer
Before the two-phase experiments, the net power input to the coolant flowing over the copper plate is evaluated from the difference between the total power input to the copper plate and the total heat loss from the test section . The total power input can be calculated from the measured voltage drop across the electric-heater V and the electric current passing through it I.
Qn
Qloss
Q t
The total power input and the effective power input are hence evaluated respectively from the equations:
Qt Qn
Q = V It ⋅ (3.2)
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and
n t lo
Q = Q - Q ss (3.3) Here the total heat loss from the copper plate is approximately estimated by accounting for the radial conduction heat transfer from the copper plate to the cylindrical Teflon block and downward heat conduction from the electric heater to bottom Teflon plate as
T w T,s e T,b
loss T,s w T,b M
T T,b M M
2 Lk (T -T ) (T -T )
Q = +
L L
ln(r /r )
k A +k A
π (3.4)
In the above equation and are the thermal conductivities of the Teflon and the mica, respectively; AT,b and are respectively the bottom surface areas of the Teflon and mica plates;L, LT,b and LM are individually the thickness of the copper, Teflon and mica plates; and are respectively the space-average temperature of the copper plate and the temperature at the bottom surface of the electric-heater; TT,b is the temperature of the bottom Teflon plate, as schematically shown in Fig. 2.7.
kT
Te
kM
AM
Tw
The net imposed heat flux at the copper plate surface is defined as
cp (3.5) q = Q / An
where is the surface area of the copper plate. The relative heat loss from the heated copper plate is defined as
Acp
loss t
ε = Q 100%
Q × (3.6) The results from this estimation show that the relative heat losses for all cases investigated here for the single-phase flow are about 20% at q=1W/cm2. The average single-phase liquid convection heat transfer coefficient over the copper plate is defined as
n 1
cp w in
h = Q
A (T - T )
φ ⋅ (3.7)
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where is the coolant temperature at the inlet of the test section and is the space-average temperature of the upper surface of the copper plate.
Tin Tw
3.2 Flow Boiling Heat Transfer
In the flow boiling experiment the state of coolant FC-72 at the inlet of the rectangular flow-channel is evaluated from the energy balance for the pre-heater. The total heat transfer rate in the pre-heater is calculated from the temperature drop on the water side as
w,p w,p p,w w,p,i w,p,o
Q = m c (T ⋅ ⋅ - T ) (3.8)
Where is the mass flow rate of the hot water at the inlet of the pre-heater, cp, is the specific heat of water, and Tw,p,i and Tw,p,o are respectively the temperatures of the water at the pre-heater inlet and outlet. Note that in the pre-heater the coolant FC-72 is still in liquid state. Hence on the coolant side in the pre-heater
mw,p w
,o ,
,o
w,p r p,r r,p,o r,p,i
Q = m c (T ⋅ ⋅ - T ) (3.9) where is the mass flow rate of the coolant in the pre-heater, cp,r is the specific heat of coolant, and Tr,p and Tr,p i are respectively the temperatures of the coolant at the outlet and inlet of the coiled pipe immersed in the container in the pre-heater. Combining the above two equations allows us to calculate Tr,p , which is considered as the temperature of FC-72 at the test section inlet. On the other hand, the average two-phase boiling heat transfer coefficient for the coolant flow over the copper plate is defined as
mr
2 ,sat n
cp w sat
h = Q for saturated and subcooled flow boiling, A (T - T )
φ ⋅ (3.10)
Where Tsat is the time-average saturated temperature of the coolant FC-72.
Note that the above definitions for single-phase convection and two-phase boiling heat transfer coefficients are usually adopted in steady heat transfer. They are also
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employed here for the transient oscillatory boiling heat transfer investigated in the present study with and also evaluated by Equations (3.1)-(3.3) through using the measured instantaneous values for V and I and the measured instantaneous temperature data at selected locations.
Qt Qn
3.3 Uncertainty Analysis
Uncertainties of the single-phase liquid convection and flow boiling heat transfer coefficients and other parameters are estimated by the procedures proposed by Kline and McClintock [51]. The detailed results from this uncertainty analysis are summarized in Table 3.1.
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Table 3.1 Summary of the uncertainty analysis
Parameter Uncertainty
Rectangular channel geometry
Length, width and thickness (%) ±0.5%
Area (%) ±1.0%
Parameter measurement
Temperature, T (℃) ±0.2
Temperature difference, ΔT (℃) ±0.3
Mean system pressure, P (kPa) ±2
Mean mass flux of coolant,G (%)
Amplitude of mass flux oscillation,+G G/ (%) Period of mass flux oscillation, (sec) tp
Mean imposed heat flux, q
Amplitude of heat flux oscillation,+q q/ (%) Period of heat flux oscillation, (sec) tp
±3
±4.8
±0.25
±2.1
±0.2
±0.25 Single-phase heat transfer in rectangular channel
Heat transfer coefficient, h1φ (%) ±12.3
Two-phase heat transfer in Rectangular channel
Heat transfer coefficient, h2φ (%) ±12.3
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CHAPTER 4
TIME PERIODIC SATURATED FLOW BOILING OF FC-72 OVER A SMALL