ME 304 Widener University Radial Heat Conduction Lab Report

ME 304

Widener University

ME 304

Question Description

I’m studying for my Engineering class and need an explanation.


i need you to do lab report for Radial Heat Conduction

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Widener University School of Engineering ME304 Mechanical Measurements II Experiment 5: Radial Heat Conduction Objective To measure temperature distribution for transient and steady-state 1-D heat conduction in a cylindrical wall and to determine the thermal conductivity k of the disk material. Theory When the inner and outer surfaces of a thick walled cylinder are each at a different uniform temperature, heat flows radially through the cylinder wall. The heat conduction in this case is governed by Fourier’s law for one-dimensional radial flow: Q = −kA(dT dR) = −2Rhk (dT dR) (here h is the cylinder height, or thickness) The disk can be considered to be constructed as a series of successive layers in the wall. The heat conducted across each layer must be constant if the flow is steady. But since the area to the successive layers increases with radius, the temperature gradient must decrease with radius. This leads to the following logarithmic temperature distribution along the radial direction: Q ln (Ra Rb ) = −2hk (Ta − Tb ) where Ta is the temperature at any radius Ra and Tb is the temperature at any radius Rb. Note that the equation is valid for any pair of radii within the radial domain. Thus, if two temperatures at two known radial positions are measured, the thermal conductivity k of the material can be found as: k= Q ln (Rb Ra ) − Q ln Rb − ln Ra = 2h(Ta − Tb ) 2h Tb − Ta (Eqn. 1) The radial specimen in the HT12 apparatus consists of a disk with the inside radius R1 = 5 mm, the outside radius R0 = 55 mm and thickness h = 3.2 mm. Six thermocouples are located at R1 = 5.7 mm, R2 = 9.9 mm, R3 = 20.3 mm, R4 = 30.1 mm, R5 = 40.1 mm and R6 = 50.5 mm. The outer diameter of the disk is cooled with water while electric heater is located at the disc center. The heat power generated can be determined from: Q = VI where V is heater voltage, I is heater current. Experimental Equipment 1. HT10X Heat Transfer service Unit 2. HT12 Radial Heat Conduction Accessory 3. IFD3 interface device Preliminary procedure 1. 2. Confirm that the six thermocouples on the HT12 unit are connected to the appropriate sockets of the service unit, with the labels on the thermocouple leads (T1-T6) matching the labels on the unit. Ensure that the cold water supply is connected to the inlet of the pressure regulating valve on HT12 and that the flexible cooling water outlet tube is directed to a suitable drain. Experimental procedure 1. 2. 3. 4. 5. 6. 7. 8. 9. Switch on the main power switch. Turn on the cooling water and adjust the flow to 1.5 liters/min +/- 0.2 liters/min Start the computer and bring the HT12 program on Start data acquisition, recording all temperatures every 10 seconds Set the heating power to 50% and record data for about 10 minutes Record all temperatures by hand Turn the heating power off and continue recording data for about 15 minutes Stop data acquisition and save the data file Re-start the software and repeat steps 4-8 for the heating power of 100% Calculations and Results 1. 2. 3. 4. 5. 6. 7. Calculate the average heat power Q added by the heater to the disc (use only data points when the heater was on) for 50% and 100% power. For each power setting, graph six curves: T1 through T6 as a function of time (two graphs, 6 curves each). For each power setting, estimate the steady-state temperature values T1 through T6 from the two graphs of point 2 (total of 12 values). Create a single log/linear plot of steady-state temperature (deg C) on the linear vertical axis as a function of radius (mm) on the logarithmic horizontal axis. Plot data for each power setting and draw two linear trend lines. The plot should be similar to the one shown. Estimate uncertainties on temperatures and radial positions and add them as error bars. Using the trend line equations, estimate temperature To at the outer periphery of the disk (Ro = 55 mm) for 50% and 100% power setting. Using the trend line equations (slopes, in particular) and manipulating the equations presented in the Theory section, calculate the thermal conductivity of the disk material for 50% and 100% power setting. Compare the two values with each other. Note: An alternative (not as good) way to calculate k is to use temperature values at any two selected positions. Do not use two adjacent thermocouples. Based on thermal conductivity values available in the literature, list most likely materials the disk is made of. References 1. Heat transfer unit HT10X manual, Armfiled Inc. Jackson, NJ 08527 2. Radial heat conduction HT12 manual, Armfiled Inc. Jackson, NJ 08527 ...
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Final Answer

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Lab Report


Radio heat conduction
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Lab Report


Radio heat conduction
An experiment for radio heat conduction was done using various sizes of conductors at
both 100% and 50%The average voltage when the heater was on at 100% power is 11.2, and the
average current of the same is 1.70. Applying the heat equation Q =VI with V is the heating
voltage and heat current as I, the average heat power Q calculated as:
Q=11.2 × 1.70 =19.04 Watts.
At 50%, the average voltage recorded as 5.6 and its respective current as 0.75. Thus by
definition of the heat equation,
Q= 5.6 × 0.75 = 4.2 Watts.
The heat equation implies that the amoun...

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