Air University (ML-235 Thermo fluids Lab II)

Experiment # 9

Objective

Measuring the temperature distribution along an extended surface and the result with a theoretical analysis.

Method

By heating one end of a solid cylindrical rod (a pin) and measuring the temperature distribution along the surface of the rod.

Equipment Required

• HT10XC Heat Transfer Service Unit

• HT15 Computer Compatible Extended Surface Heat Transfer Accessory

• WindowsTm-compatible PC running WindowsTM 98, 2000 or XP.

Equipment Set-up:

• Locate the HT15 Extended Surface Heat Transfer accessory alongside the HT10XC Heat Transfer Service Unit on a suitable bench. Since heat transfer from the extended surface relies on natural convection and radiation to the surroundings, the accessory must be located away from draughts or sources of radiation.

• Connect the nine thermocouples on the HT15 to the appropriate sockets on the front of the service unit. Ensure that the labels on the thermocouple leads (TI - T9) match the labels on the sockets.

• Set the VOLTAGE CONTROL potentiometer to minimum (anticlockwise) and the selector switch to MANUAL then connect the power lead from the HT15 to the socket marked OUTPUT 2 (HT10XC) at the rear of the service unit.

• Ensure that the service unit is connected to an electrical supply.

Theory /Background

Where it is required to cool a surface by convection, the rate of heat removal can be improved by increasing the area of the surface. This is usually achieved by adding extended surfaces called fins or pins.

A temperature gradient exists along each fin or pin due to the combination of the conductivity of the material and heat loss to the surroundings (greater at the root and less at the tip).

The temperature distribution along the fin or pin must be known to determine the heat transfer from the surface to its surroundings. Since radiation and natural convection from the surface occur simultaneously, both of these effects must also be included in the analysis.

By considering the steady-state energy balance for an extended surface of uniform material and cross sectional area the following equation can be derived:

Where

Since H, P, A and k Brass are constant for a given rod with fixed power input, m2 must be constant and therefore in must be constant.

Assuming that the diameter of the pin is small in comparison with its length then heat loss at the tip can be assumed to be negligible (at the tip x - L).

Therefore:

The purpose of this exercise is to observe the temperature gradient along the extended surface and to show that the term in is constant at all positions along the surface.

Procedure:

• Switch on the MAINS switch.

• Check that the software indicates IFD OK in the bottom right hand corner of the software window.

• Set the heater voltage to 20 Volts. If using the HT15 software to control the accessory remotely then the voltage can be controlled using the control box on the mimic diagram screen. If operating the accessory manually using the HT10X/HTI0XC console then adjust the VOLTAGE CONTROL potentiometer to give a reading of 20 Volts on the top panel meter with the selector switch set to position V.

• Monitor temperature T1 regularly using the software screen or the lower selector switch. When TI reaches 80ºC reduce the heater voltage to 9 Volts (the initial higher setting will reduce the time taken for the temperatures on the rod to stabilize).

• Allow the HT15 to stabilize. Monitor the temperatures using the software screen or the lower selector switch/meter.

• If using the software, select the GO icon to record the voltage and current supplied to the heater, the temperature at each position along the rod (T1 to T8 and the ambient air temperature T9.

• Set the heater voltage to 16 Volts then allow the HT15 to stabilize.

• If using the software then create a new results sheet using the icon.

• Record the readings as before.

• If time permits repeat the readings with the heater voltage set to 12 Volts the 14 Volts.

Results and Conclusions:

For this experiment, tabulate the following data:Temperature at heated end where x= 0 = T1 Temperature at x = 0.05m = T2Temperature at x = 0.10m= T3Temperature at x = 0.15m = T4Temperature at x= 0.20m = T5Temperature at x = 0.25m = T6Temperature at x = 0.30m = T7Temperature at tip where x= 0.35m = T8Temperature of ambient air = T9 Length of rod = L = 0.35m

Sr.No

VoltageV

CurrentA

PowerW

T1OC

T2OC

T3OC

T4OC

T5OC

T6OC

T7OC

T8OC

T9OC

1 23

You should also estimate and record the experimental errors for these measurements.

For each position along the rod (dimension x) use the corresponding measured temperatures to find the value elm which satisfies the relationship:

Note: The value for in can be found by iteration using a suggested starting value of 7.4.

Find the average value of m, then use this value to calculate the theoretical temperature Tx at each position x along the rod. Repeat this procedure for each set of temperature readings obtained and confirm that for each set of readings the value for re remains constant (within the experimental errors).

Estimate the cumulative influence of the experimental errors on your calculated values for m and measured values for TI to T9, x and L.

For each set of measurements. Plot a graph of measured surface temperature Tx against position x along the extended surface and draw a smooth curve through the points. Your graphs should look similar to the following diagram:

Plot the theoretical temperature profile which you have calculated using the average value for in and compare the curve with your measured values.

What was the effect of varying the heater power (heat flow along the rod)?

Observe the change in surface temperature of the rod falls with increasing distance? Observe that the temperature gradient at the heated end of the rod and at the cool end of the rod.

You have demonstrated how the temperature prodle varies along the length of an extended surface having constant cross sectional and constant thermal conductivity.

The theoretical profile can be determined if the constant in is known (Exercise C uses the theoretical relationship to determine the thermal conductivity of the rod).