Experiment 3Extended Surface Heat TransferObjectivesTheoretical BackgroundFigure 1. Various extended surfacesApparatusExperimental ProcedureQuestion to be answeredExperiment 3 Extended Surface Heat Transfer Objectives • To examine heat transfer in a single cylindrical extended surface (a fin) in free and forced convection. • To develop an understanding of fin effectiveness and the parameters which influence it. Theoretical Background Fins are used to enhance convective heat transfer in a wide range of engineering applications. The fin material generally has a high thermal conductivity which is exposed to a flowing fluid. The high thermal conductivity of the fin allows for enhanced heat conduction from the wall to the fin. The design of cooling fins is encountered in many practical applications. An examination of the physical mechanism governing heat transfer through (or the perfomance of) fins is useful from a practical perspective. 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 appliances and electronics such as on computer processors and power supplies. They are also part of industrial applications such as heat exchangers and substation transformers. Fins are also used for engine cooling. Figure 1 illustrates different fin shapes. The analysis of fin heat Figure 1. Various extended surfacestransfer 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: ()01122=∞−⎟⎟⎠⎞⎜⎜⎝⎛−⎟⎟⎠⎞⎜⎜⎝⎛+TTdxdAskhAcdxdTdxdAcAcdxTd (1) where Ac is the cross-sectional area, As is the surface area, T is the temperature, and T∞ is the freestream temperature. If the fin has a uniform cross-sectional area, Ac, and a base temperature of Tb, Equation 1 reduces to ()022=∞−⎟⎟⎠⎞⎜⎜⎝⎛−TTAckhPdxTd (2) where P is the perimeter. Defining θ = T(x) -T∞ (3) we can rewrite Equation 2 as 0222=−θθmdxd (4) where m2 = h P/(k Ac). Equation 4 is a linear, homogeneous, 2nd order, constant coefficient ordinary differential equation, whose solutions depend on the boundary conditions. A summary of various, commonly encountered, boundary conditions and the resulting solutions are given in Table 1. The effectiveness of an infinite fin is given by AcfhkP=ε (5) 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 which can be achieved in are various ways. For example, based on equation 5, the fin geometry can be modified to increase its effectiveness. Similarly, using effectiveness can also be changed by using different fluids and/or fin material (QUESTION: How do you think the geometry needs to be modified; should the fin become thicker or thinner?).Apparatus The following apparatus will be used in this experiment: 1. A constant temperature bath. 2. An extended surface constructed from aluminum, and shown in Figure 2. 3. Thermocouples. 4. Digital temperature indicator. 5. Switchbox. 6. Wind tunnel Figure 2 Figure 2: Cylindrical extended surface, including thermocouple locations 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 frequency set at 5.0 Hz. 5. Allow the fin to reach steady state. 6. Record the temperature profile. 7. Repeat Steps 5- 6 for the wind tunnel frequency settings of 10 - 40, in increments of 5. 8. If the air velocity in the tunnel is ‘Y’ and the operating frequency is ‘X’ then the relation is Y = 1.062X + 0.056Table 1. Solutions to fin equation Question to be answered 1. Calculate the non-dimensional temperature profile ()()TTTTbb∞∞−−=θθ 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