HTC SingleFin in Water 031506

7/29/2019 HTC SingleFin in Water 031506

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HEATTRANSFER EXPERIMENTNATURAL CONVECTION ON A FIN SURFACE

INTRODUCTION

The removal of heat from the surface of a body can be accomplished by conduction,

convection, and radiation. Convective heat transfer refers to the removal of heat by either

forcing a fluid over the surface (forced convection) or by the natural fluid motion due to

density gradients near the surface (free convection). The efficiency of a bodys ability totransfer heat by convection to the surrounding environment is defined by the convective

heat transfer coefficient (h).

In this experiment, a cylindrical fin, made of a metal, having a diameter d and a length L,

is placed inside a water tank. The base of the fin is attached to metal block that houses theelectrical heater and the heated base is well insulated from the surrounding air. As the

result, the supplied electrical energy is conducted through the base into the fin stem anddissipates into the water from the fin skin surface area via natural convection. In thissetup radiation heat transfer is negligible.

The heat transfer coefficient, h, can be determined by measuring the fin temperature

along its length (distance x). The heat transfer coefficient, h, can further be verified by

measuring the supplied electrical power and comparing the measured value with theresults from heat transfer analysis.

TECHNICAL OBJECTIVE

Study free convection heat transfer over a cylindrical fin and evaluate the convective heat

transfer coefficient, h. To achieve this, measure the fin temperature along its length usingtype E thermocouples. Convert the thermoelectric potential produced by thermocouples

to temperatures values using the appropriate National Bureau of Standards (NBS)

polynomial. Compensate all temperature measurements for undesired thermoelectric

potentials (e.g., ice junction). Obtain heat transfer coefficient from measured temperaturegradient. Use the obtained heat transfer coefficient to determine the fin heat transfer rate

and compare the result with the value found by measuring the input electric power.

PRE-LABASSIGNMENT

1.

Read section 9.2. 1, pp 274-281 of the text, Wheeler and Ganji, Introduction toEngineering Experimentation.

2. Review the appropriate heat transfer course material (22.341 Conduction &Radiation) --heat transfer from fins and extended surfaces.

3. Given that the copper fin diameter is 6.35 mm, what condition(s) must be met to usean infinite length fin model?


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4. Explain two ways of compensating for the thermoelectric potential that is generatedby connecting thermocouples to dissimilar metallic junctions at the interface of a

digital multimeter, oscilloscope, or PC based digital data acquisition system.

BACKGROUND

The heat transfer characteristics of fins are known as conduction-convection systems.Consider a cylindrical fin with a heat source located at its base and its surface is exposed

to a surrounding. The thermal energy is conducted away from the heat source into the

base and along the cylinder length. This energy will then be taken away by thesurrounding fluid if the environment is at lower temperature than the base temperature,

(free convection). Convective heat transfer rate can be calculated by:

Where:Q = heat transfer rate

h = averaged heat transfer coefficient

As = surface areaTw = local temperature of the cylinder surface

T = temperature of the fluid surrounding the cylinder

In case of fins, Tw, varies along the fin length and therefore, Equation 1 is not useful. Anenergy balance on a differential element of thickness dx yields the following equation:

Where:

Tx = temperature at position x

P = perimeter of the cylinder (d)K = thermal conductivity of the fin material

A = cross sectional area of the cylinder ( d2/4)

Applying the proper boundary conditions and assuming the fin can be modeled as aninfinitely long fin, the solution to Equation 2 is:


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Here, To, is the base temperature (at x = 0) and the parameter m is the slope of the natural

logarithm of the non-dimensional temperature ratio, x versus position x. Performing aregression analysis on the natural logarithm of the non-dimensional temperature ratio

versus position and using the definition of parameter m can determine the heat transfer

coefficient h. That is:

For the case of long cylindrical fin, the fin heat transfer rate is evaluated from:

Where, the value for h comes from the previous analysis, Equation 4.

THEEXPERIMENTALSETUP

The experimental setup is shown in Figure 1. It is consisted of a cylindrical fin with a

total of 15 type E thermocouples embedded along its length, 4 thermocouples before

and 11 after exposure to water; (thermocouple number 5 is the fin base temperature, To).Other components are: an electrical heat source, a DC power supply, a digital multi-

meter, an ice bath, and a multi-channel thermocouple switch. The fin stem is placed

inside a water tank holding about 3 gallons of water as shown in Figure 1.

Figure 2 shows a schematic diagram of the fin and the locations of the thermocouples.

The outputs of the four thermocouples before thread -- (these four are surrounded by


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insulation) -- are used to estimate the amount of heat being conducted from the electricheater to the water exposed section, (after thread).

Figure 2 - Schematic Diagrams of the Fin and the Locations of the Thermocouples

0.625 0.25

10.5 1 1 1 1.75 1.75 1.750.5 0.5 0.5 1.75

0.05 0.5 0.5 0.5 0.45

Thread

Thread

Thread


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PROCEDURE

The following experimental procedure is intended only as a guide. This procedure doesnot include all relevant information, which is required to successfully perform the

experiment.

1.

Measure and record the thermocouple resistances and make sure they are in goodworking condition and check the ice/water bath.

2. Record all pertinent atmospheric properties, initialize all instrumentation (record allinitial outputs).

3. Turn on the power supply, set the power level to produce the desired input powergiven by the lab instructor and record the time.

4. Record all thermocouple output voltages, the power supply voltage and current, andwater temperature every 10 minutes. When the system has reached steady state,

perform the final recording of the data.

5. Notify the lab instructor when the thermal part of experiment has been completed.6. Turn off the power supply and the multimeter.POST-LABANALYSIS

1. Correct all thermocouples (TCs) outputs for ice-junction compensation.2. Convert the corrected TCs outputs to temperature values using the appropriate NBS

polynomial and/or tables.

3. Determine whether or not the cylinder can be modeled as an infinite fin -- (useexperimental observations to support conclusions made).

4. Find the temperature slope (T/x) for the first 4 TCs and compute heat conductionthrough the fin stem [q = - k A (T/x)].

5. Compare the q result obtained in Step 4 with the heat supplied by the power supply.Is there a difference? Explain the reason.

6. Plot the natural logarithm of dimensionless temperature ratio versus position x.7. Calculate the convective heat transfer coefficient h.8. Based on the computed h value, evaluate the fin heat transfer rate from Equation 5.9. Compare this value with the data obtained in Step 4 and that of the power supply;

explain the differences.

10.How would you alter the design of the experiment to allow for the evaluation of thefin heat transfer using the expression given by:

fin

x 0

dTq k A

dx =

=

HTC SingleFin in Water 031506

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