Experiment 8

Forced Convection on a Flat Disk

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Theoretical Background
Apparatus
 Experimental Procedure
Questions to be Answered
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Objective

The goal of this experiment is to measure the average convective heat transfer coefficient for forced convection of air past a flat disc thermistor, which is used as a heat transfer model. The measured heat transfer coefficient will also be used to determine the appropriate empirical Nusselt number correlation for this geometry.
Theoretical Background
The average convective heat transfer coefficient,   , can be indirectly defined by Equation 1, in terms of the rate of convective heat transfer between the solid and the fluid,   , the surface area through which the energy is being transferred, A, and the difference between the solid surface and the bulk fluid temperature, (T  -  Tf).
  =   A (T  -  Tf)                        (1)

Solving for the convective heat transfer coefficient, , yields

                                      (2)










Therefore, the experimental measurement of   , requires the measurement of each of the four quantities on the right-hand side of Equation 2, namely:   , A, T, and Tf. In general, the two experimental measurements which present the least difficulty are the heat transfer surface area, A, and the bulk fluid temperature, Tf. The area is obtained from the geometry involved and the fluid temperature can usually be measured using a standard temperature measuring device such as a thermocouple. In contrast, reliable measurements of the surface temperature of the solid, T, and the rate of convective heat transfer from the surface,   , are generally more difficult to obtain. Direct surface temperature measurements are susceptible to large errors because mounting a thermocouple on the surface can actually influence the convective heat transfer process being examined, thus biasing the experimental results.

Measurement of the actual convective heat transfer rate is usually an indirect measurement which represents the cause or effect of the heat transfer such as, electrical joule heating, vaporization rate, condensation rate, transient temperature changes or temperature gradients, etc. The use of such an indirect measurement to obtain the actual rate of heat transfer through a particular surface area is an approximation which may introduce significant errors, especially if the geometry is small.

Thermistor Heat Transfer Models

 
The convective heat transfer apparatus used in this experiment utilizes thermistors of different geometries as heat transfer models. Thus the instrumentation for measuring both the surface temperature, T, and the heat transfer rate,   , is the heat transfer model itself. Since the thermistor is the heat transfer model, the surface temperature, T, of the thermistor is a good representation of the bulk temperature of the thermistor; and, as we learned in experiment 4 ,  the temperature of a thermistor can be obtained by measuring its resistance. The rate of heat transfer,   , from the thermistor is equal to the energy generated within the thermistor model due to joule heating. Hence  can be measured by measuring the current flowing through and the voltage drop across the thermistor.
The resistance-temperature characteristics of the various thermistor heat transfer models used in this experiment have been measured and can be obtained from the lab instructors. Using the measured resistance-temperature characteristics, the surface temperature, T, of any model is easily obtained.

 

Thermistor Measurement Circuitry

The thermistor models used in this experiment are disks of various thickness and diameters. At a given fluid velocity, which is measured using a pitot-static tube, electrical power is delivered to the thermistor from a D.C. power supply, which causes the thermistor temperature to increase due to joule heating. Now, if a fixed voltage is applied across the thermistor, and the convective heat transfer from the thermistor is less than the joule heating, the thermistor temperature will increase causing the resistance to decrease, thus causing a still higher level of joule heating, a runaway situation can occur which causes the thermistor to burn out. However, by employing a standard resistance of a known value, and a particular circuit configuration (see Figure 1), thermal runaway can be prevented. Details of this approach are discussed in the next section.

Figure 1. Schematic of the thermistor measurement circuitry

 

Experimental Determination of 

An empirical expression for measuring the heat transfer rate,   , from the thermistor to the flowing fluid may be found in terms of the electrical power, P, delivered to the thermistor. Therefore,
  = P = i VT                                                             (3)


however, since

                                                                               i = VT/RT                                                             (4)
substituting Equation 4 into Equation 3 yields
  = VT2 / RT                                                        (5)
Referring to the Thermistor Measurement Circuit shown in Figure 1, the voltage across the thermistor and the standard resistor can be expressed as:
                                                                                 VT = i RT                                                          (6)
                                                                             Vs = i Rs                                                    (7)
 Dividing Equation 7 by Equation 6 yields,
                                                                       VT/VS = RS/RT                                                             (8)
 or,

                                                                        RT = RSVT / VS                                                           (9)

 Therefore, by substituting Equations 8 and 9 into Equation 5, an expression for the heat transfer  rate,   , is obtained.:

  = VTVS / RS                                                             (10)

Substitution of Equation 10 into Equation 2 yields an experimental expression for the indirect measurement of the average forced convective heat transfer coefficient,   , for a given fluid velocity.

Therefore, since the geometry and the resistance-temperature characteristics of the thermistor heat transfer model are known, along with the standard resistance, RS, the only direct measurements required to determine the average convective heat transfer coefficient,   , are the voltages, VS and VT.

 

Dimensionless Correlations for Convective Heat Transfer Coefficient

For the case of fluid flow past a disc-type thermistor, the Nusselt number, Nu, is a function of the Prandtl number, Pr, and the Reynolds number, Re. Experimental evidence suggests that for many situations involving forced convection heat transfer, the Nusselt number can be expressed in the following generalized form:
                                                                 Nu = cPrmRen                                                  (11)
 where,         and 
In Equation 11, C, m, and n are empirical parameters which must be determined from the experimental data by statistical methods. Note that the parameters k, m, r, Cp, and  u ¦  represent the thermal conductivity, the viscosity, the density, the specific heat, and the free-stream velocity of the fluid, respectively. A wide range of average forced convective heat transfer data is found to be of the form:
                                                             Nud = CPr1/3 Red n                                                           (12)
where C, and n are values obtained from the experimental data.

 

Apparatus


 

The following hardware is used in this experiment.

 1. A convective heat transfer measurement system, described later.
 2. Thermistor heat transfer models.
 3. Two digital multimeters.
 4. Pitot-static tube and digital manometer.
 5. Thermocouple and digital temperature indicator.

 

Convective Heat Transfer Measurement System

The Convective Heat Transfer Measurement System consists of a small subsonic wind tunnel, a thermistor model and associated electrical circuitry and electrical components required to heat the thermistor and measure the various voltages (see Equation 10). A picture of the wind tunnel placed on a test bench is shown in the Figure 2 . Also shown in the figure is the test model thermistor, which is placed inside the wind tunnel test section using a ‘C-shaped’mount.The test bench houses the various electrical components needed for this experiment.A pitot-static tube and a thermocouple probe are placed in the test section to measure the air velocity and temperature, respectively. The pitot-static tube is connected to a digital manometer which measures the flow dynamic pressure from which, the flow velocity can the determined.

 
 

Experimental Procedure

1. General Guidelines
 (a) When operating the DC power supply, the current knob is always at the maximum setting.  Only the voltage is varied.
 (b) When conducting heat transfer tests, adjust the voltage slowly to obtain the ratio, VT/VS as close to 1, as possible without tripping the thermistor protection circuit.
 (c) When the thermistor protection circuit is tripped, lower the voltage from the DC power supply before pressing the reset button. However, a small voltage is necessary for the reset to work.

 

 2. Assembling the Hardware

 (a) Mount the thermistor in the C-mount, and hand-tighten the set screws used to hold the thermistor in place inside the mount.

 (b) Place the C-mount inside the wind tunnel, as shown in Figure 2. Hand-tighten the screws to ensure that the C-mount is securely fastened in the tunnel.

 (c) Insert the red and black plugs of the thermocouple probe into their respective jacks on the control panel (jacks marked air temperature).

 (d)  Connect jumper cables from thermistor circuit diagram on control panel to corresponding  jacks on control panel to corresponding jacks on control panel, (power supply to power  supply, multi-meter etc.) in accordance with circuit diagram in Figure 1.

 (e) Plug into 110 VAC 60 Hz supply.

THE UNIT IS NOW READY TO OPERATE.
 
 

 3 . Measurement of Forced Convective Heat Transfer Coefficient

 Setup the thermistor circuitry as shown in Figure 1

 (a) Connect the DC power supply to the setup. The DC power supply is the variable power supply referred to in Figure 2.

 (b) Connect the plugs of the standard resistor and the thermistor to the two digital multimeters, as  shown in Figure 2.

 (c) Configure the multimeters to read voltage.

 (d) STOP.Please ask the laboratory instructor to verify that the circuit has been connected properly, before proceeding any further.

 (e) Turn on the Wind Tunnel.

 (f) You will obtain measurements at ten different air velocities for each model.

 (g) The lab TA will give you the dynamic pressure range over which the ten readings will be taken. The interval between the readings should be approximately constant.

 (h) Record the freestream air temperature.

 (i) Record the resistance of the standard resistor.

 (j) Increase the wind tunnel velocity until the first dynamic pressure setting is reached.

 (k) Maintaining the current at its maximum, slowly increase the voltage.

 (l) As the power supplied is increased, the following will occur:

 i. Initially, the voltage across the thermistor rises rapidly with the voltage across the standard resistor lagging behind.

 ii. As more power is delivered, a point is reached where the thermistor voltage drops steadily and the standard resistor voltage rises.

 iii. Eventually, the two voltages equal one another.

 (m) Record the voltage when VT/VS » 1.

 (o) Record the dynamic pressure from the digital manometer

 (p) If, however, the thermistor temperature exceeds the safety limit before the voltages become equal, the thermistor protection circuit will come into action, and break the circuit, resetting everything to zero. Hence, the voltage should be increased slowly. If the circuit is tripped, start at step k again.

 (q) Repeat Steps k – 4 for the remaining nine readings for the test module.

 (r) After the ten readings are taken, close the air pressure regulator valve.

 (s) Remove the first thermistor model, and replace it with the second test model.

 (t) Repeat steps a – r for the second test model over a similar pressure (i.e. velocity) range.
 

Questions to be Answered

 
 1. Perform the necessary calculations to find the influence of free stream velocity, V ¦ , on the
 heat transfer coefficient,   , over the entire range of velocities measured.
 2. Convert the above experimental data to a dimensionless form, and plot the Nusselt # as a function of the Reynolds #, Re , on a linearlized plot, where:   and d is the diameter of the disk.
 3. Estimate the uncertainty of the experimental data and plot appropriate uncertainty bands on the above plot.
4. Considering the functional relationship between the Nusselt # and Reynolds'# to be of the form:
                                            (13)

Determine the constants ``c'' and ``n''. Also estimate the ranges of ``c'' and ``n'' within the limits of the experimental uncertainty bands.

 5. What are the similarities and differences between the emperical correlation and the analytical  model developed for flow over a flat plate? How does the emperical correlation compare to those given in the text for turbulent flow over a flat plate? (Note: You need to compare numerical values)

 6. Due to the resistance-temperature characteristics of the thermistor, it is very easy to overheat the thermistor and destroy it. The thermistor overheat protective circuit used in this experiment guards the thermistor, against overheating, by switching off the system when a certain temperature is exceeded. Explain how it determines this temperature.  Also, is it possible to adjust this temperature? If yes, explain, how?