EXPERIMENT 104. LINEAR HEAT CONDUCTION: COMPOSITE WALL REFERENCES Incropera, Heat and mass Transfer., Chap- ters 1 and 2, section 1.2 and 2.1 Section 70 of this lab manual OBJECTIVES In this experiment you will 1. measure the temperature distribution for steady- state conduction of energy through a composite plane wall and determine the overall heat trans- fer coefficient for the flow of heat through a com- bination of different materials in series. 2. understand the application of poor conductors (insulators) and determine the thermal conduc- tivity of an insulator T T ム A 4 A c 111 Th Fig. 1 Series composite wall d²TA dz2 VTA- -0 TA(a) a+b V2To dTa = =0 Ta(z) ap+bg. da (2) V2Tc dB Te dzB -0 Tc(2) ac + box APPARATUS Heat Transfer Service Unit (HTSU: section 70) Linear Heat Conduction Unit (LHCU: section 70) Stopwatch. Beaker or container THEORY Consider three plane walls in contact (composite wall) as shown fig.1. The individual walls are labeled A, B and C and each of thermal conductivity k, and thick- ness L, where ie (1,3). Assume the wall boundaries convect heat to the environment on both sides. Each side may have different convection coefficients h and environmental temperature T. Each layer must sat- isfy the heat conduction equation eq.1 whose solution is a linear function in 2. Consequently, we have the following solution for layers A through C. = FT V2T= მკ-2 =0. (1) To evaluate the constants a, b,, where i E (A,C) the boundary conditions at the different interfaces must be satisfied. particularly TA(0) T Te(LA+LB+Lc)=T TA(LA) =TB(LA) TB(LA+LB) Tc(LA + LB) kaba =kBbB kaba-kebc The above system of six equations can be solved for a, b, where ie {A,C) and the result substituted to obtain TA(z), TB(z), and Tc(z). The heat flux in the z direction is given by q=kabд=kBbB = kcbc. (4) 55 rection (in this case, the r direction). Consequently, in For A-D slab heat flow, heat can flow only in one di- the absence of heat sinks/sources in a layer, the heat flux must remain a constant as it passes through the convective air layer on the left, through each slab and finally through the convective air layer on the right. To simplify the solution for a composite wall (with no internal heat source), a simplified relation between the overall heat flux through the composite wall and the given temperature gradient from one side of the com- posite wall to the other is found to be Q=U (T.-T..). where U is the overall heat transfer coefficient 1 U = LB Le + + kp kc PROCEDURE Part A: The Overall Heat Transfer Coefficient (5) 1. Clamp the intermediate Stainless Steel section (not instrumented) between the heated and cooled section of the linear heat conduction unit (LHCU) having lightly coated the mating faces: with thermal paste. Connect the thermocouples to the appropriate sockets on the front of the service unit. 2. Start the computer. Start the heat transfer service unit (HTSU) using the power switch MAINS. Set the selector switch to "Automatic", then start the ArmSoft software and select "Ex- ercise C". 3. The Mimic Diagram is the most commonly used display of the software, it gives a pictorial rep- resentation of the equipment, with continuously updated display boxes for all the various sensor readings, calculated variables etc. To view the Mimic Diagram, click Diagram from the View drop down menu. 4. In order to establish communication between the software and HTSU, click on the "Power On" switch on the software diagram window 5. Open the water supply valve on the main sup- ply hose, then adjust the flow control valve (not the pressure regulator) to give approximately 1.5 litres/min. The actual flow can be checked using a stopwatch and a measuring cylinder. 6. Use the heater control box on the mimic diagram screen to adjust the percentage of full scale until the voltage display box reads 9 volts 7. Allow the LHCU to stabilise (at least 15 mins). Monitor the temperatures on the software mimic diagram screen to determine when the tem- peratures reach steady state (use "VIEW" and "SHOW HISTORY" buttons, as well as "VIEW" and "SHOW GAUGE" buttons). 8. When the temperatures have reached steady state, select the icon "GO" to record one set of data, which includes the following: Ti, Ta Ta. To. T. Ts. V, I. Use button "VIEW" and "PLOT RESULTS" to plot results and check if the measured points form a straight line. You can check results by looking at the "VIEW" and "TABLE" buttons. 9. Set the heater to 12 volts using the same method as before. Allow the LHCU to stabilise then re- peat the above readings. Use buttons "SAM- PLE" and "NEXT RESULTS" to enable the "GO" button. 10. Save the results of measurements using the com- mand "save as" from the file menu. Make sure that you specify excel format (filename.xls). 11. After completion of all measurements turn off the "Power On" button on the software screen, power button MAINS on the HTSU and turn off the water supply valve on the supply hose. Notes: The distance between each thermocouple is 0.015 m. The distance between thermocou- ple Ts, or Te and the end face is 0.0075 m. The thermal conductivity of the Brass sec- tions is approximately 121 W/m°C, and that of Stainless steel is approximately 25 W/m°C For this experiment the following constants are applicable: Distance between thermocouples Ty and the bot face Distance between hot face and cold face Distance between the cold face and thermocouple T Thot 0.0375 m int=0.030 m cold 0.0375 m Diameter of the bar D=0.025 m 56 APPLICATION OF THEORY Measurement errors: Temperature is measured with accuracy of ±0.1°C. Voltage is measure with ac- curacy of ±0.1V. Current is measured with accuracy of ±0.1A. Linear dimensions are known with accuracy of ±0.2mm. Position of thermocouples is known with accuracy of +0.3mm. Part A: The Overall Heat Transfer Coefficient 1. Estimate the cumulative influence of the exper- imental errors on your calculated values for Q. ATIs, khot, R and U. 2. Compare the two values obtained for the overall heat transfer coefficient. Um and U, and comment on any difference in the values obtained. 3. Plot a graph of temperature versus position along the bar and draw the best straight line through the points for the heated section and the cooled section. Extrapolate each line to the joint with the intermediate section then join these these two points to give the gradient through the intermediate section. Your results should give values of approximately 25 W/m°C for the thermal conductivity of Stainless Steel, assum- ing no heat loss from the equipment. As a small amount of heat loss is inevitable as the tempera- ture of the bar increases, the calculated value for the conductivity will increase at higher operating temperatures. 4. What was the effect of varying the heater power (heat flow through teh composite bar). EXPERIMENT 104. LINEAR HEAT CONDUCTION: COMPOSITE WALL-PRELAB 1. Read the Lab Manual write-up on this experiment along with the sections from your class textbook listed in the references section. NOTE: This PRELAB is due at the beginning of the lab. 2. What is the objective of this experiment? 3. Solve the system of equations eq.2 for TA(a), Tn(x), and Te(2) given the boundary conditions eq.3. 4. Prove the result of eq.6. 59 NAME DATE GRADE