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Transcript
HEATED TRANFER IN A FIN The heated bar method is based on the theory of extended surfaces (fins). This apparatus can be used to calculate either the thermal conductivity of a material given the convection coefficient, h; or, h can be calculated given the thermal conductivity, k. The apparatus consists of a sample with rectangular cross-section clamped on one end by means of two aluminum blocks. Four flexible heaters are attached to the aluminum blocks that supply heat to the base of the sample. Heat is transferred by the sample via two pathways: 1. conduction through the solid sample 2. convection from the surface to the surroundings The temperature profile of the sample is measured by attaching eight thermocouples on the top surface at regular intervals. Two thermocouples are also attached to the aluminum blocks to measure the base temperature. This experiment can be conducted under four different tip conditions. 1. convection heat transfer 2. adiabatic 3. tip is at prescribed temperature 4. the fin is infinitely long However, for this particular design, only two conditions can be maintained, namely: conduction heat transfer, and maintaining the tip at a prescribed temperature. The corresponding temperature profiles for these two conditions are as follows. 1. Convection heat transfer: h( ) k d dx xL the temperature distribution h cosh m( L x) sinh m( L x) mk h b cosh mL sinh mL mk 2. Prescribed temperature ( L) L : where the temperature distribution L b b sinh mx sinh m( L x) sinh mL In all equations listed above, the following is true: ( x) T ( x) T m2 hP kAc M hPkAc b h – convection coefficient k- thermal conductivity P- perimeter of sample (2w+2l) Ac- cross-sectional area of sample Once is known at different ‘x’ values, a best fit curve can be interpolated at the various data points to get a value of ‘m’ and ‘M’, or in other words, h/k. Thus, knowing one of the two, the other can be calculated. where As steady state is reached, the temperatures stabilize and data acquisition can begin. Using Fourier’s law of heat conduction and the convection heat transfer equation, the thermal conductivity of the sample can be determined, given the convection coefficient, h; or, the convection coefficient for the setup can be determined, given the sample’s thermal conductivity, k. Sample Size: 1” x 3” x 9” Power Supply: Acopian DC Power supply, 100V, 1.5A Heaters: Watlow flexible heaters: 125V, 25W Dimensions: 1” x 5” (4) Data Acquisition: National Instruments SCXI-1322 DIAGRAM OF APPARATUS base tip Direction of Heat Flow Heaters GENERAL OPERATING PROCEDURES Obtain sample conforming to dimensions above. Measure and record the cross sectional area and perimeter of bar. Attach eight thermocouples along the centerline of the bar in order to obtain a temperature profile. Install sample between the two aluminum heater blocks. Install surrounding insulation and close off holding box. Set power supply to desired output. Once steady state has been reached, data acquisition can begin. The temperature of the heated bars is determined by the average of all recorded readings. The temperature at each point of the temperature profile along the bar is determined by the average of all readings. Recorded data should include the voltage supplied to heaters, resistance of each heater, temperature of each thermocouple placed along the surface of the bar, and the surrounding, or ambient, temperature. QUESTIONS 1. What are the assumptions when dealing with heat transfer through an extended surface? 2. What possible sources of error are associated with this experiment? 3. Why are the thermocouples placed along the centerline of the sample? Would the results be the same if they where not placed along the centerline. 4. Suggest ways to improve this module.