Objective

        Measurement of the average convective heat transfer coefficient for the forced convection of air past a flat disc thermistor heat transfer model, and the development of an appropriate empirical correlation for the Nusselt number.

Back to the top
 

Theoretical Background

        The average convective heat transfer coefficient, , can be defined indirectly 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 - T_f). Thus

= A (T - T_f)                                                (1)

Solving for the convective heat transfer coefficient, h, yields

                                            (2)

        Therefore, the experimental measurement of the convective heat transfer coefficient, , requires the measurement of each of the four quantities on the right-hand side of Equation 2; , A, T, and T_f. In general, the two experimental measurements which present the least difficulty are the heat transfer surface area, A, and the bulk fluid temperature, T_f. The area is usually obtained indirectly by knowing the geometry involved, and the fluid temperature can usually be measured indirectly using a standard temperature measuring device such as a thermocouple. The two most difficult measurements to obtain are the surface temperature of the solid, T, and the rate of convective heat transfer through the surface, . Direct surface temperature measurements are susceptible to large errors. Mounting a thermocouple on the surface can actually influence the convective heat transfer process being measured, thus biasing the experimental results.

        Measurement of the actual convective heat transfer rate must be 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, temperature gradients, etc. The main difficulty with this measurement is that one of the above indirect measurement techniques is used to represent the actual rate of heat transfer through the particular surface area in question. Such an approximation may introduce significant errors, especially if the geometry is small.
 

Utilization of Thermistor Heat Transfer Models

        The convective heat transfer apparatus utilizes thermistors of different geometry's 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 a temperature sensitive resistor, the surface temperature, T, of the thermistor is the temperature of the thermistor itself, and it can be measured indirectly by measuring the resistance of the thermistor. The rate of heat transfer, , from the thermistor is generated within the thermistor model itself by joule heating. Thus,  can be measured indirectly by measuring the current flow through and the voltage drop across the thermistor.
 

Thermistor Resistance-Temperature Characteristics

        The resistance-temperature characteristics of the various thermistor heat transfer models can be measured by inserting the Heater Section into the apparatus as discussed later, and using a Test Section Module containing a particular heat transfer model. It is possible to measure the resistance-temperature characteristics of the thermistor by simply varying the temperature of the air flow by varying the power supplied to the Heater Section. By measuring the thermistor resistance with an ohmmeter, and the fluid temperature with a thermocouple, the thermistor resistance can be measured over a wide range of temperatures.

        By utilizing the resistance-temperature characteristics of the thermistor, the problem of measuring the heat transfer model surface temperatures, T, is resolved. The thermistor temperature is determined from the measured thermistor resistance and the resistance-temperature calibration curve.
 

Thermistor Measurement Circuitry

Referring to the schematic of Test Section Module shown in Figure 1, a disc type thermistor heat transfer model is utilized to demonstrate how the average convective heat transfer coefficient, , can be experimentally measured. The schematics of the Thermistor Measurement.  Circuitry utilized in measuring the average forced convective heat transfer coefficient, , is shown in Figure 2.

        At a given fluid velocity, as measured by the pitot tube, electrical power is delivered to the thermistor from the D.C. power supply which in turn 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 inside, the thermistor temperature will increase causing the resistance to decrease, thus causing a still higher level of joule heating, a runaway situation which causes the thermistor to burn out. However, by employing a standard resistance of a known value, and a particular circuit configuration (see Fig2 ), this problem can be overcome.

Back to the top

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,

Referring to the Thermistor Measurement Circuit shown in Figure 6, the voltage across the thermistor and the standard resistor can be expressed as:

Dividing Equation 7 by Equation 6 yields,

Therefore, by substituting Equations 8 and 9 into Equation 5, an expression for the heat transfer

rate, , is obtained. Thus:

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, the only direct measurements required to indirectly determine the average convective heat transfer coefficient, , are the voltages, V_S and V_T.
 

Dimensionless Correlations

        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:

where 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:

where C, and n are values obtained from the experimental data by statistical means.

Back to the top
 

Apparatus

The following apparatus is used in this experiment.

        1. A convective heat transfer measurement system, detailed below.
        2. Test section modules.
        3. Heating element.
        4. Two digital multimeters.
        5. Pitot-static tube and digital manometer.
        6. Thermocouple and digital temperature indicator.

Click here to see apparatus

Back to the top

Convective Heat Transfer Measurement System

      The Convective Heat Transfer Measurement System is an experimental apparatus for measuring forced and natural convection heat transfer for external flows over surfaces of various geometries. A sketch of the basic apparatus for forced convection measurement is shown in Figure 3, and a cut-away section is shown in Figure 4.

        Starting at the far right of the sketch, a Diffuser Section allows air to enter into the apparatus from the air supply with the intent of shaping a uniform velocity profile further downstream in the long tubular section referred to as the Velocity Developing Region. A Heater Section may be inserted in between the Diffuser Section and the Velocity Developing Region Section so that a variable A.C. power supply connected to the Heater causes the temperature of the flowing air to be varied over a wide range.

        By using the Heater Section in conjunction with a given Test Section Module, housing a particular thermistor heat transfer model, the resistance-temperature characteristics of the thermistor may be experimentally measured. In determining the resistance-temperature characteristics of the thermistor, the wall temperature is assumed to be equal to the temperature of the flowing air. The air exits the apparatus through a Noise Suppression Section. Near the end of the Velocity Developing Region Section, a pitot-static tube and a thermocouple probe are inserted to measure the air velocity and temperature, respectively. The pitot-static tube is connected to a digital manometer where the dynamic pressure can be measured. From the dynamic pressure measurement, the air velocity flowing past the heat transfer model may be indirectly measured.

Test Section Modules

        Note the modular design of the individual thermistor heat transfer models. These modules can be interchanged easily. The Noise Suppression Section is connected to the apparatus by means of a long metal rod. By simply pulling the muffler away from the apparatus slightly, the Test Section Module can be removed and another inserted with ease. This compact feature makes provisions for various heat transfer surface geometries, and also for various fin configurations. A sketch of a typical test section is shown in Figure 1, where the particular heat transfer model is a disc type thermistor. Mounted on the side of each Test Section Module is a standard resistor which is "matched" to the particular thermistor heat transfer model inside. The Test Section Module fits into the apparatus as shown in the cutaway view of the apparatus in Figure 4.

Click here to see apparatus

Thermocouple and fluid temperature measurement

        Referring to Figures 3 and 4, the temperature of the fluid is monitored by a thermocouple probe located downstream from the pitot tube. It protrudes approximately one-half inch into the fluid field. Locating the thermocouple downstream from the pitot tube prevents the thermocouple probe from distorting the fluid velocity profile which could be the case if it were located upstream from the pitot tube.

Pitot-static tube and velocity measurement

        The combination of the diffuser section and velocity developing section of the apparatus is designed in such a way that the air flow entering the Test Section Module possesses a uniform velocity profile as it approaches the thermistor heat transfer module. The mean velocity of the air flowing through the Test Section Module is measured with a pitot tube set at the centerline of the Velocity Developing Section, it is found that the pitot tube is a reasonable means of measuring the mean air velocity over a wide range of air flow rates. It should be noted that when the fluid velocities are being monitored, the Heater Section should be removed. This is done to prevent the Heater from distorting the mean velocity profile of the flowing air.

Back to the top

Experimental Procedure:

1.   Guidelines for Experiments

1. When operating the DC power supply, the current knob is always at the maximum setting.

Only the voltage is varied.
2. When conducting heat transfer tests, adjust V_T/V_S as close to 1 as possible for low velocities

without tripping the thermistor protection circuit, and then vary the velocity.
3. 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

1. Assemble the Test Section stand as follows:

1. Loosen thumb screw on the top of the down-stream velocity development section support block.
2. Insert desired thermistor test module into support block so that it seats snugly against the velocity development section tube. When inserting the thermistor test module, make certain that the thermistor is in the upstream direction (towards the velocity development section) and the standard resistor faces the front of the unit.
3. Tighten thumb screw securely. (DO NOT OVER TIGHTEN!)
4. Loosen thumb screw on the front side of the downstream support block.
5. Slide muffler section support rod into hole in the support block, making certain that flat on the support rod faces forward (toward the thumb screw).
6. Slide muffler section on to the thermistor test module, seating snugly.
7. Tighten thumb screw to secure assembly.
8. Loosen thumb screw on heater adapter section and slide heater module into adapter section fully. Tighten thumb screw.
9. Loosen thumb screw on heater module and slide air nozzle module into heater module. Tighten thumb screw.

NOTE: The heater module is used only for resistance - temperature calibration of the thermistor test
               module, and should be removed when conducting experiments. The air supply nozzle module
               may be connected directly to the heater adapter section.

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

     c.  Connect heater module cable to heater supply receptacle on control panel.

     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.

     e.   Plug into 110 VAC 60 Hz supply.

Back to the top

THE UNIT IS NOW READY TO OPERATE.

NOTE: The heater module will not operate until a minimum of 5 psi air is supplied across the heater element. This insures against heater element burn-out and also against damage to the thermistor test module due to over-heated air.

3.   Thermistor calibration

       A calibration curve of thermistor resistance versus temperature for the given disks will be provided. However, you are required to confirm the calibration for at least two points.

1. Connect the heater section in the setup.
2. Connect the thermistor plugs to a digital multimeter, and configure the multimeter to read the resistance of the thermistor.
3. Open the air supply regulator valve until a pressure of approximately 40 psi is registering on the pressure gauge.
4. Switch on the heater.
5. Pick two temperatures between 100 ⁰F and 180 ⁰F.
6. Increase the heater current. This will increase the temperature of the heater coil, causing the air  temperature to rise.
7. When the first temperature selected is reached, measure the resistance of the thermistor.
8. Record the temperature and the resistance of the thermistor.
9. Go on to the next temperature, and repeat Steps 3f -- 3h.
10. Turn down the heater current, and allow the unit to cool down.
11. After room temperature is attained by the apparatus, switch off the heater, and close the air supply  regulator valve.
12. Remove the heater section from the setup.

4.     Measurement of Forced Convective Heat Transfer Coefficient

      In performing the experiment, the Heater Section is not used (it must be removed) as it interferes with the velocity profile of the air flowing in the apparatus.

1. Setup the thermistor circuitry as shown in Figure 2. Consult the laboratory TA for setting up this circuit.
2. Connect the DC power supply to the setup. The DC power supply is the variable power supply referred to in Figure 2.
3. Connect the plugs of the standard resistor and the thermistor to the two digital multimeters, as shown in Figure 2.
4. Configure the multimeters to read voltage.
5. Open the air pressure regulator valve.
6. You will take ten different readings for each unit.
7. The lab TA will give you the dynamic pressure range over which the ten readings will betaken. The interval between the readings will be left to your discretion.
8. Record the freestream air temperature.
9. Record the resistance of the standard resistor.
10. Increase the air pressure till the first dynamic pressure setting is reached.
11. Maintaining the current at its maximum, slowly increase the voltage.
12.  Reset the thermistor protection circuit.
13.  As the power supplied is increased, the following will occur:

                n.    Record the voltage.
                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.
                q.    Repeat Steps 4k – 4p 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 test module, and replace it with the second test module.
                t.     For the same pressure range, carry out Steps 4a – 4r for the second test module.

Click here to see apparatus

Back to the top

Report Specifications

1. Compare the calibration data obtained by you to the calibration data provided by the instructor by plotting them on the same graph. Discuss the probable reasons for the difference between your results and the data provided.
2. Perform the necessary calculations to find the influence of free stream velocity, vf , on the heat transfer coefficient, , over the entire range of velocities measured.
3. Convert the above experimental data to a dimensionless form, and plot the Nusselt # as a function of the Reynolds #,  Re, on log-log scale, where:

                    and d is the diameter of the disk.

            4.  Estimate the uncertainty of the experimental data and plot appropriate uncertainty bands on the
                 above log-log plot.

            5.  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.

            7.  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 his 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 the this temperature? If yes, explain, how?

Back to the top

Note: Please note the units of the quantities which are being measured, when recording data. For example, when measuring voltage, if the voltmeter reads 16 mV, then write down 16 mV instead of just 16.

               I.         Checking temperature-resistance calibration for the thermistors:

                II.           Determining the influence of free stream velocity on heat transfer coefficient:

YOU NEED TO GET THE LAB INSTRUCTOR'S SIGNATURE BEFORE LEAVING.

The student has performed the experiment satisfactorily and has cleaned the work area.
 

___________________________ _______________

(Lab assistant's signature)                          Date

Back to the top

Back