Objectives

        To examine the heat transfer in a single cylindrical extended surface (a fin or a pin) in free or forced convection. To develop an understanding of fin effectiveness and the parameters which influence it.

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Theoretical Background

        An extended surface is commonly used in reference to a solid that experiences energy transfer by conduction within its boundaries, as well as energy transfer by convection between its boundaries and its surroundings. The extended surface is most often utilized in the removal of heat from a body. In this case, the extended surface is often referred to as a ``fin''. A fin with a cylindrical shape and a high aspect ratio (length/diameter) is called a pin. Fins are often seen in electrical appliance cooling such as in a computer power supply or substation transformers. Fins are also used for engine cooling. Figure 1 illustrates different fin shapes. The analysis of fin heat
 
 

transfer assuming steady state, one-dimensional heat conduction (temperature varies only axially and not radially), uniform convective heat transfer coefficient, h, and constant thermal conductivity, k, results in the differential heat equation in the following form,
 
 

where A_c is the cross-sectional area, A_s is the surface area, T is the temperature, and T¥ is the freestream temperature. If the fin has a uniform cross-sectional area, A_c, and a base temperature of T_b, Equation 1 reduces to

where P is the perimeter. Defining
 
 

we can rewrite Equation 2 as
 
 

where m² = h P/(k A_c). Equation 4 is a linear, homogeneous, 2nd order, constant coefficient ordinary differential equation, whose solutions depend on the boundary conditions.  A summary of various boundary conditions and the resulting solutions are given in Table 1. The effectiveness of an infinite fin is given by
 
 

The fin effectiveness is defined as the ratio of the fin heat transfer rate to the heat transfer rate that would exist without the fin. It is often desired to maximize the fin effectiveness. There are various ways to achieve this.

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Apparatus

The following apparatus will be used in this experiment:

1. A constant temperature bath.
2. An extended surface constructed from aluminium, and shown in Figure 2.
3. Thermocouples.
4. Digital temperature indicator.
5. Switchbox.
6. Wind tunnel

Case	Tip Condition (x = L)	Temperature Distribution	Fin Heat Transfer Rate
A     B           C         D	Convection     Adiabatic     Prescribed Temp.     Infinite fin

Click here to see apparatus

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Experimental Procedure

1. The constant temperature bath is adjusted to 80 ° C and started up at least an hour before the start of the lab session.
2. Measure the free convection temperature profile, i.e. with the wind tunnel switched off.
3. Record this temperature profile.
4. Start the wind tunnel with the counter set at 100.
5. Allow the fin to reach steady state.
6. Record the temperature profile.
7. Repeat Steps 5- 6 for the wind tunnel counter settings of 200 - 500, in increments of 100.

Report Specifications

        1.      Calculate the non-dimensional temperature profile
 
 

               for each flow situation and compare it to the theoretical temperature profile.

        2.    Plot the nondimensional experimental and theoretical temperature profiles on the same graph for
               each flow situation.

        3.    Discuss the results in detail. Compare the experimental and theoretical values. What boundary
               conditions did you assume? Why? What may cause the experimental profile to differ from the
               theoretical profile?

        4.    Calculate the fin effectiveness. Which case has the highest effectiveness and why? Discuss ways
               to improve fin effectiveness.

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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.

       1. Maintain constant temperature bath at approximately 80 oC.

        2. For each measurement allow fin to reach steady state then record the temperature profile. For
            steady state, wait 15 minutes after raising speed in windtunnel.

        3. Velocity (m/s)= 0.06424 (counter reading) - 4.65215
 
 
 

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

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