EAS 327

EAS327: LABORATORY 3, Nusselt number of a Cylinder

A metal cylinder (brass, aluminum) is heated to a temperature (T) considerably above room temperature (T_a), then mounted in a wind tunnel. Its rate of cooling is measured with a chromel-constantin thermocouple, which measures the cylinder-air temperature difference (T - T_a), where we will assume T_a is constant. The thermocouple signal, 60 mV for each degree (K) of temperature difference, is received by a data-logger set to a Full Scale Range of +/- 5 millivolts. From the time variation of (T - T_a) and other data, the heat transfer coefficient is to be determined.

THEORY: We will neglect radiation heat transfer and assume the energy balance to be (verbally):

Volume of cylinder x volumetric heat capacity of cylinder x rate of change of temperature = cylinder surface area x convective heat flux density from air to cylinder; ie.

(l p r²) r c dT/dt = (2 p rl) Q_H

where the convective heat flux density is

Q_H = r_a c_pa (T_a-T)/r_H

Rearranging,

r_H = { 2 r_a c_pa} / { r r c } * (T_a - T) / (dT/dt)

DATA:

		Aluminum	Brass
density	kg m-3	2700	8400-8700
specific heat	J kg-1 K-1	900	370-400
conductivity	W m-1 K-1	201	109
thermal diffusivity	m2 s-1	8.3 E-5	3.4 E-5

Notes:

(1) brass is an alloy of copper and zinc, typically in the ratio of 70% / 30%, but very often containing a fraction of other metals, such as aluminum. There is a huge range of brass alloys, fabricated for a range of purposes; properties given here are generic and do not accurately represent any particular alloy.

(2) For the calculations of this exercise you will NOT need to use the conductivity and thermal diffusivity of the metals, for these affect only the internal transfer of heat.

PROCEDURE:

1. Measure the local pressure according to the mercury barometer in Tory 2-108 and calculate the air density in the lab.
2. Check the calibration of the data-logger using the Analogic D.C. voltage standard.
3. Program the logger to receive the thermocouple signal and convert to give a direct readout of the temperature difference T-T_a. Also set up an analog output from the logger to drive a chart recorder.
4. Insert the hot (and cold) thermocouple junctions in the cylinder (tunnel airstream). Heat the cylinder in the hot-air gun, to a temperature of about T_a+40^oC. Replace the hot cylinder it in the wind tunnel (but NOT if it is hotter than T_a+40^oC).
5. Tabulate a cooling curve at intervals Dt=20 sec, until T-T_a is reduced to 5^oC.
6. Use the heated-sphere anemometer to determine the wind velocity U in the wind tunnel
7. Repeat for other cylinder

ANALYSIS:

1. For each cylinder, present a graph of (T-T_a) versus t, and a graph of the rate of change of the temperature difference, ie. D(T-T_a)/Dt, versus (T-T_a). According to our theory, the latter graph should show a linear relationship whose slope we require to determine r_H.
2. In each case, determine the slope, including an estimate of your range of uncertainty (in %). From your slope, determine r_H and the Nusselt number N_u.
3. For each cylinder, compare your experimental values of r_H, N_u with theoretical values based on your tables.
4. We neglected in our energy balance a term due to radiation heat transfer. Assess the possible importance of this term (relative to Q_H) in our experiment. Assume only long-wave radiation is important, and approximate the net long wave radiative flux density as

   Q* = s (T⁴ - T_a⁴)

   where s = 5.67 E-8 [W m^-2 K^-4] is the Stefan-Boltzmann constant.

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Last Modified: 12 Feb. 2005