CBE 3322 Heat Transfer Operations
Lab Manual COMBINED CONVECTION AND RADIATION
September 2008
CBE 3322 Heat Transfer Operations
HT 14C COMBINED CONVECTION AND RADIATION
The 'Combined Convection and Radiation' accessory comprises a centrifugal fan (15) with a vertical outlet duct (4 and 6) at the top of which is mounted a heated, horizontal cylinder (7). The mounting arrangement for the cylinder is designed to minimize loss of heat by conduction to the wall of the duct allowing the combined effects of convection (free or forced) and radiation to be measured. A thermocouple attached to the wall of the heated cylinder provides a measurement of the surface temperature from which heat transfer calculations can be performed. The accessory is mounted on a PVC base plate (1) which stands on the bench top alongside the HT10X. Technical details of the 'Combined Convection and Radiation' accessory are as follows: The heated cylinder (7) has an outside diameter of 10 mm, a heated length of 70 mm and is internally heated throughout its length by an electric heating element which is operated at low voltage for increased operator safety. The heating element is rated to produce 100 Watts nominally at 24 VDC into the cylinder. The power supplied to the heated cylinder can be varied and measured on the HT10X. The electrical connections to the cylinder incorporate temperature resistant insulation with plug connection (11) to the variable 24 Volt DC supply socket marked OUTPUT 3 on HT10X. The surface of the cylinder is coated with heat resistant paint which provides a consistent emissivity close to unity. Thermocouple T10 is attached to the wall of the heated cylinder to indicate the surface temperature of the cylinder mid way along the cylinder. This type K thermocouple is fitted with a
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CBE 3322 Heat Transfer Operations
standard plug (12) for direct connection to the HT10X service unit. The resolution of the temperature reading is 1°C. The heated cylinder is mounted in such a way that the body can be rotated to allow the position of the thermocouple to be varied and the temperature distribution around the surface of the cylinder to be determined. A lever (10) allows the hot cylinder to be rotated and a locking screw (9) allows any position to be retained. The maximum surface temperature of the cylinder is in excess of 600°C when operated in free convection at full heater power. However, to preserve the life of the heating element the maximum temperature should be limited to 500°C in normal use. The heated cylinder is mounted horizontally at the top of a cylindrical duct which is attached to the outlet of a centrifugal fan. The inside diameter of the duct is 70 mm. The cylindrical duct is fabricated in two parts (4 and 6) with a rotating vane type anemometer (5) mounted between the two sections to allow the velocity of the air approaching the heated cylinder to be measured. The lead from the anemometer (13) connects directly to the socket marked U a on the HT10X to provide readings of air velocity directly in units of meters/sec. The operating range of the anemometer is 0 - 10 meters/sec. In normal operation the maximum air velocity is approximately 8 meters/sec when the fan is operated from a 50 Hz electrical supply (-A version). A variable throttle plate (17) at the inlet to the fan allows the velocity of the air through the outlet duct to be varied by adjusting the screw (16) at the centre of the front of the plate. The centrifugal fan is mains operated and obtains its supply from a mains outlet (OUTPUT 1) at the rear of the service unit. The connecting lead (18) is connected to this socket on the HT10X. A thermal switch (2) protects the fan against over-current, in the event of a fault condition, and allows the fan to be switched off for free convection demonstrations. Thermocouple T9 is fitted in the wall of the duct, upstream of the anemometer to measure the temperature of the air upstream of the heated cylinder. This thermocouple is fitted with a miniature plug (14) for direct connection to the HT10X service unit. The resolution of the temperature reading is 0.1°C. A guard (8) covering the outlet from the vertical duct prevents inadvertent contact with the heated cylinder or the hot wall of the duct when the accessory is in use or cooling down following operation. Details of connections between the HT14 and the HT10X service unit are given in the section Connection to Services.
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CBE 3322 Heat Transfer Operations
Exercise C 1. Objective -To determine the effect of forced convection, on heat transfer from the surface of a cylinder at varying air velocities and surface temperatures. -To demonstrate the relationship between air velocity and surface temperature for a cylinder subjected to forced convection. 2. Method By measuring the temperature on the surface of a horizontal cylinder subjected to heat loss by radiation and forced convection in combination then comparing the results with those obtained from a theoretical analysis. 3. Equipment Required HT10X Heat Transfer Service Unit; HT14 Combined Convection and Radiation Accessory; IFD5 PC Interface Console; PC Equipment set-up Before proceeding with the exercise, ensure that the equipment has been prepared as follows: Locate the HT14 Combined Convection and Radiation Accessory alongside the HT10X Heat Transfer Service Unit on a suitable bench. • Set the VOLTAGE CONTROL potentiometer to minimum (anticlockwise) and the selector switch to REMOTE. • Ensure that the service unit is connected to an electrical supply. 4. Theory/Background In free/natural convection the heat transfer rate from a surface is limited by the small movements of air which are generated by changes in the density of the air as the air is heated by the surface. In forced convection the air movement can be greatly increased resulting in improved heat transfer rate from a surface. Therefore a surface subjected to forced convection will have a lower surface temperature than the same surface subjected to free convection, for the same power input. If a surface, at a temperature above that of its surroundings, is located in moving air at the same temperature as the surroundings then heat will be transferred from the surface to the air and the surroundings. This transfer of heat will be a combination of forced convection to the air (heat is transferred to the air passing the surface) and radiation to the surroundings. A horizontal cylinder is used in this exercise to provide a simple shape from which the heat transfer can be calculated. Note: Heat loss due to conduction is minimized by the design of the equipment and measurements mid way along the heated section of the cylinder can be assumed to be unaffected by conduction at the ends of the cylinder. Heat loss by conduction would normally be included in the analysis of a real application. Total heat loss from the cylinder Qtot = Q f + Qr
Heat loss due to forced convection Q f = H fm As (TS − Ta )
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CBE 3322 Heat Transfer Operations
Heat loss due to radiation Qr = H rm As (TS − Ta ) Heat transfer area AS = πDL The heat transfer coefficients H fm due to forced convection and H rm due to radiation can be calculated using the following relationships: T 4 − Ta4 H rm = σξF S W / m2 K (TS − Ta ) Where: σ : Stefan-Boltzmann constant, σ = 56.7 *10 −9 W / m 2 K 4 . ξ : Emissivity of surface. TS : Surface temperature of cylinder, (K ) . Ta : Ambient temperature, (K ) . F : Viewing factor, F = 1 . k H fm = Nu m W / m 2 K D Where: k : Conductivity of the air, (W / mK ) . D : Diameter of the cylinder (m ) . Nu m : Average Nusselt number (dimensionless) . Average Nusselt number could be calculated by using the following empirical correlation:
(
)(
)
(
(
Nu m
(0.62 Re = 0.3 +
)
)
)
0.5 Pr 0.33 ⎛⎜ ⎛ Re ⎞ ⎞⎟ 1+ ⎜ ⎟ 0.25 ⎛ ⎛ 0.4 ⎞ 0.66 ⎞ ⎜⎝ ⎝ 282000 ⎠ ⎟⎠ ⎜1 + ⎜ ⎟ ⎜ ⎝ Pr ⎟⎠ ⎟ ⎝ ⎠ 0.5
From SW Churchill and M Bernstein “A Correlating Equation for Forced Convection from Gases and Liquids to a Circular cylinder in cross flow". Journal of Heat Transfer, 99:300-306 (1977). Where Re : Reynolds number. Pr : Prandtl number for air. Re = U c D /ν ν : Kinematic viscosity. U c Corrected air velocity (m/s) Corrected air velocity U c = 1.22U a (m/s) (The cylinder causes a blockage in the duct resulting in a local increase in the air velocity.)
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CBE 3322 Heat Transfer Operations
Values for k, n and Pr depend on the temperature of the air and can be found using the table included in the HT14 teaching manual. The actual power supplied to the heated cylinder Qin = V I
(W)
5. Operating Procedure 1. Run the HT14–303 software selecting ‘Section C - Determining the effect of forced convection’ and read through any introductory screens needed to gain familiarity with the operation of the software. 2. Switch on the front Mains switch (if the panel meters do not illuminate check the RCD and circuit breakers at the rear of the service unit, all switches at the rear should be up). 3. Start the centrifugal fan by pressing the switch on the connection box. 4. Monitor the air velocity in the duct using the 'IFD Channel History' window or mimic diagram. 5. Set the heater voltage to 17 volts. (Adjust the voltage control on the mimic diagram to give a voltage of 17 volts.) 6. Open the throttle plate on the front of the fan by rotating the adjustment knob to give an air velocity reading of 0.5 m/s displayed on the mimic diagram. 7. When the temperatures are stable, click 'sample now' and the HT14 software will record the following: a. T9, T10, V, I, Qa. 8. Adjust the throttle plate to give a velocity of 1.0 m/s. 9. Watch the IFD Channel History and allow the HT14 to stabilize before taking the next set of experimental readings. 10. Repeat the above procedure changing the air velocity in steps of 1.0 m/s until the air velocity is set to 7.0 m/s. 11. Set the heater voltage to 20 volts. (Adjust the voltage control on the mimic diagram to give a voltage of 20 volts.) . 12. Repeat steps from 6-11.
6. Results and Calculations The HT14 software logs and calculates the following data: Heater Voltage Heater Current Heater Flow Qin Watts Temperature of air in duct Temperature of heated cylinder Air velocity in the duct
V I
Volts Amps
T9 T10 Ua
(°C) (°C) (m/s)
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CBE 3322 Heat Transfer Operations
For this exercise the following constants are applicable Diameter of cylinder Heated length of cylinder Air velocity correction factor
D = 0.01 L = 0.07 1.22
(m) (m)
For each set of readings the HT14 software calculates the following results: Note. To view all data columns questions will have to be answered in the Theory section of the walk through. (Watts) (m2) (m/s)
Heat flow (Power to heater) Heat transfer area (surface area) Corrected air velocity Heat transfer coefficient (forced convection)
Qin AS Uc H fm
Heat transfer coefficient (radiation) Heat transferred by forced convection
H rm Qf
(W)
Heat transferred by radiation Total heat transferred
Qr Qtot
(W) (W)
You should also estimate and record the experimental errors for these measurements and calculations using the note-taking feature. Compare the theoretical values for Qtot with the measured values for Qin and explain any differences in values. Compare the calculated heat transferred due to Convection Q f and radiation Qr . The graph of surface temperature T10 against corrected air velocity U c is produced in the 'View Data in Graph Format'. Observe that the surface temperature of the cylinder reduces as the air velocity increases for a fixed heat input Qin . Observe that the surface temperature reduces more rapidly at low air velocities and reduces more slowly at high air velocities.
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CBE 3322 Heat Transfer Operations
7. Conclusions You have demonstrated how the heat transfer from a heated surface to its surroundings is a combination of forced convection and radiation (the effect of conduction must also be included where relevant) when the surface is located in a moving air steam. For equilibrium, heat input to a surface must equal the heat transferred from the surface to its surroundings. Since heat transfer from a surface increases with the velocity of the air, increased air velocity past a surface results in a decrease in the temperature of the surface. The calculation of the heat transfer coefficient H fm for forced convection involves the use of empirical equations which are specifically related to heat transfer from a horizontal cylinder. Empirical equations are available for other classical shapes which will allow a theoretical analysis to be performed. The effect of air velocity forced convection on surface temperature.
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CBE 3322 Heat Transfer Operations
Nomenclature Name Voltage to heated cylinder Current to heated cylinder Power supplied to heated cylinder
Symbol V I Qin D L AS
SI unit V A W
Air velocity in duct (free stream velocity)
Ua
m/s
Corrected air velocity (due to blockage)
Uc
m/s
Heat transferred due to natural convection
Qc
W
Heat transferred due to forced convection
Qf
W
Heat transferred due to radiation Total heat transferred from cylinder
Qr Qtot
W W
Heat transfer coefficient for natural convection
Hc
W / m² K
Heat transfer coefficient for forced convection
H fm
W / m² K
Heat transfer coefficient for radiation
H rm σ ξ F
W / m² K
Diameter of heated cylinder Heated length of cylinder Heat transfer area
Stefan Boltzmann constant s Emissivity of cylinder View factor (geometric factor) Dynamic viscosity of air
ν
Thermal conductivity of air Reynolds number (local) Nusselt number (local) Prandtl number Angular position of thermocouple (measured from the stagnation point) Surface temperature of heated cylinder Surface temperature of heated cylinder Temperature of ambient air/surroundings Temperature of ambient air/surroundings Film temperature of air Subscripts D M
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W / m² K4 Dimensionless Dimensionless m² / s
k Re Nu Pr θ
W / mK Dimensionless Dimensionless Dimensionless Degrees
T10 Ts T9 Ta T film
°C K °C K K
Diameter mean (average) Film
F
m m m²
CBE 3322 Heat Transfer Operations
Physical Properties of Air
T film(K) 300 350 400 450 500 550 600
u(m²/s) 1.684 x 10-5 2.076 x 10-5 2.590 x 10-5 3.171 x 10-5 3.790 x 10-5 4.434 x 10-5 5.134 x 10-5
K(W/ m K) 0.02624 0.03003 0.03365 0.03707 0.04038 0.04360 0.04659
Pr 0.708 0.697 0.689 0.683 0.680 0.680 0.680
The HT14 software utilizes the following relationships in the spreadsheet analysis to calculate the physical properties of air:-
ν of air = (-2.4E-13*Tfilm³) + (4.319048E-10*Tfilm²) - (1.2252857E-7*Tfilm) + 2.11523809524E-5 Accuracy of relationship: @ 350K n = 1.679E-05 @ 600K n = 5.128E-05
99.70% 99.88%
κ Of air = (-2.9619E-8*Tfilm²) + (9.44571429E-5*Tfilm) + 5.826190476E-4 Accuracy of relationship: @ 350K k = 0.02625 99.96% @ 600K k = 0.04659 100%
Pr of air = If Tfilm >= 500 then 0.68 Else (5E-7*Tfilm²) - (5.41E-4*Tfilm) + 0.82525 Accuracy of relationship: @ 350K Pr = 0.708 100% @ 600K Pr = 0.680 100%
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