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GVSU EGR 468 - EGR468 Heat Transfer from a Cylinder in Crossflow

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Heat Transfer from a Cylinder in Cross FlowbyDan SchwarzSchool of EngineeringGrand Valley State UniversityEGR 468 – Heat TransferSection 02Instructor: Dr. M. SozenApril 3, 20081OutlineI. Introduction/Purposea. The purpose of the experiment is to experimentally determine the heat transfercoefficient of an aluminum circular cylinder in cross flow.II. Theorya. Describe the purpose of calculating the Biot number.b. Describe lumped heat capacitance method of calculating the heat transfercoefficient.c. Describe the Reynolds number dependant empirical method of calculating theheat transfer coefficient.III. Procedurea. Provide details about setting up the experimentb. Figure 1: Illustration of systemIV. Lab-equipmentV. Resultsa. Table 1: Comparison of experimental and theoretical heat transfer coefficients.b. Interpret the data.c. Suggest reasons for discrepancy.VI. Discussion/Conclusiona. Summary.VII. Appendix A: Determine the Wind Tunnel Speed Required for Turbulent flow.VIII. Appendix B: Calculate Biot Number for the Maximum Wind Tunnel Speed.IX. Appendix C: Determine the Governing Convection Heat Transfer Equation.X. Appendix D: Determine Heat Transfer Coefficients from Experimental Data.XI. Appendix E: Calculate the Theoretical Heat Transfer Coefficients for Each Condition.2Introduction/PurposeThe heat transfer coefficient for a circular cylinder in cross flow was determinedexperimentally using an aluminum bar. Since the internal thermal resistance of the aluminumbar was relatively small compared to the convection thermal resistance, lumped heat capacitancewas used to model the system.In order to verify the experimental results, the heat transfer coefficient was alsocalculated using empirical relationships that are based on Reynolds number. The results showedthat the experimental heat transfer coefficients were generally larger than the theoretical heattransfer coefficients.TheoryThe experimental heat transfer system can be accurately modeled using lumped heatcapacitance since the Biot number is less than 0.1. A small Biot number indicates that theinternal thermal resistance is relatively small compared to the convection thermal resistance.Details in Appendix B.1.0kAhVBi(1)Lumped heat capacitance was used to determine the convection heat transfer coefficientsfor the experimental systems. Details in Appendix C.tVchATTTToln(2)The convection heat transfer coefficient was also determined using an empiricalrelationship that is based on Reynolds number. Details in Appendix E.dkChn 3/1PrRe(3)ProcedureThe aluminum cylinder was placed in an oven until it reached a temperature ofapproximately 100°C. While the cylinder was heating, the wind tunnel was brought up to speedand the manometer reading was recorded. The heated cylinder was then removed from the ovenand placed into a wooden holder within the wind tunnel. The data acquisition cycle was initiatedonce the test section of the wind tunnel was sealed. Temperature measurements were taken fromthe surface of the cylinder as well as the ambient temperature. Figure 1 shows the experimentalsystem.3Figure 1: The experimental cylinder was contained in the test section of a wind tunnel.Lab Equipment- National Instruments DAQ (CA-1000)- National Instruments Voltage Meter (NI-4350)- Computer with Labview Data Acquisition Software- Two K-type Thermocouples- Wind Tunnel- Aluminum Cylinder with Wooden RampResultsThe experimental heat transfer coefficients are compared to the theoretical heat transfercoefficients in Table 1. See Appendix D and E for details.Table 1: Comparison of experimental and theoretical heat transfer coefficients.Manometer(in)Experimental h(W/ m2·°C)Theoretical h(W/m2·°C)% Discrepancy0.9 146.8 133.2 9%1.7 175.5 162.4 7%4.0 224.2 211.5 6%6.0 163.1 239.8 47%The results seem to make sense because the heat transfer coefficient increased as the flowvelocity and Reynolds number for the system increased. The experimental heat transfercoefficients were slightly larger than the theoretical heat transfer coefficient because the bottomof the aluminum bar was not considered. If we had considered the bottom section of thealuminum bar, the theoretical heat transfer coefficients would be larger and the % discrepancywould be smaller.4 V0.04m0.26m0.01275mThe experimental data set for 6 inches of water does not agree with the theoretical heattransfer coefficient at all. This was most likely due to a poorly connected thermocouple. Thelow this would produce an incorrect natural log temperature curve. Consequently, the slope ofthe curve would not lead to a correct estimate of the heat transfer coefficient.ConclusionSeveral heat transfer coefficients were determined using experimental data from a coolingcircular cylinder in cross flow. These estimate were confirmed using empirical relationships forcircular cylinders with respect to Reynolds number. All of the empirical results, except for thelast data set, seem to verify the experimental results with a % discrepancy of less than 10 %.The two most probable sources of error in the heat transfer coefficient calculations arepoor thermocouple measurements and the neglect of the bottom of the cyclinder.Appendix A: Determine the Wind Tunnel Speed Required for Turbulent flow.Find the wind tunnel velocity as a function of the water manometer height reading. Begin withBernoulli’s equation.222212112121zVPzVPEliminate non-applicable terms and solve for the pressure differential. The pressure differentialwill be measured using a water manometer.ghVPPwaterair222121Solve for the air velocity at the beginning of the test section.airwaterghV22Use the velocity equation to calculate the manometer reading which corresponds to the transitionto turbulence.dV2Re     smmmkgsmkgdV /2.61601275.0/1774.1/0000185.0000,500Re32      ininmsmmkgmkgsmgVhwaterair900/0254.0/81.9/9972/1774.1/2.61622332225Appendix B: Calculate Biot Number for the Maximum Wind Tunnel Speed.Determine the film temperature for the aluminum rod if it is heated to 100°C. Find theproperties of air at this


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GVSU EGR 468 - EGR468 Heat Transfer from a Cylinder in Crossflow

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