ME315 – Fall 2019 _ LAB2












A: A Steady State Heat Conduction

B: The Fourier Rate Equation for Radial Heat Transfer


Table of Contents: Abstract 5 Objectives 6 Theory 6 Procedure 8 Complete Results 9 Results of the Measurements: 9 Temperature vs Radius Plots: 9 (T – r) Plot at 13 V: 10 (T – r) Plot at 14 V: 10 (T – r) Plot at 16 V: 11 Results of the Experimental Temperature (T3) for Each Electrical Power Input. 11 Experimental Temperature (T3) at 13 Volts: 11 Experimental Temperature (T3) at 14 Volts: 12 Experimental Temperature (T3) at 16 Volts: 12 Results of the Reading and Calculations of the and : 13 The Percentage Error for Heat Transfer: 17 Conclusion 18 References 19







List of figures:


Figure 1: Radial Head Conduction Setup. 7

Figure 8: (T – r) Plot at 1 3 V. 10

Figure 9: (T – r) Plot at 1 4 V. 10

Figure 10: (T – r) Plot at 1 6 V. 11
















List of Tables:

Table 1: Obtained Temperature Results. 9

Table 2: Experimental Temperatures Results. 12

Table 3: Heat Transfer Results. 13

Table 4: Comparison Between the Experimental and Theoretical Temperatures. 17

















In this laboratory, we will calculate the temperature using different voltage values and a cylindrical wall in a stable state with a centered heat point. We will use various readings, one of which will be unknown, and we will calculate it using Fourier’s law and excel graphs before measuring electrical heat transfer. We will use the calculated voltage and the current from the test unit, Q ̇_Elec will be defined as the Q ̇_Cond will be measured using the Fourier law. Readings will be measured to help with the application of calculations. In addition, students have to calculate the error value to test whether the experiment was successful or not. At the end of our experiment, we are going to compare the theoretical temperature with the experimental to know our percentage error. Finally, in our report we are going to list the steps of our experiment and list the procedure, theory, objectives, calculations, the graphs and the conclusion.







Some of the objectives for forming the experiment are: 1) Use the test readings and calculations to determine what is needed 2) Use excel to locate and determine the unknown temperature T3. 3) Measure the heat transfer of the conduction Q



In various modes of conductivity, convection and radiation heat transfer. You must see heat transfer in the conduction in this experiment. Leading of gasses, liquids and solids may take place. The conductivity in solids develops due to molecular vibrations, collision, and diffusion in gasses and liquids.

Heat conduction generally occurs in a number of scientific applications and can be measured by the Fourier Heat Conductivity Law:

̇ = − A /

The heat transfer in radial direction to the medium layers for a stable conductive feature in an enclosed cylindrical wall (disk), will depend on the radius of cylinder layers and the temperature of each layer. Take the cylinders surface 2αrL and the correct form of the general heat conduction will then be determined in radial direction by The following:

̇ = 2 (1 − 2) / ln ( 2 1)



Where: r1 and r2 are the internal and external surfaces, and L is the total cylinder length.


Figure 1: Radial Head Conduction Setup.

As in (Figure 1), the apparatus shows a metal disk with thermocouples at different radii and heat flow out of the center to the periphery. As a result, heat flow and the distribution of temperature can be investigated. There are six Thermocouples, which are placed on the disk and their purpose is to measure temperature gradient from the heated section (central core) to the cooled section.

As listed below we have the Fourier’s Law and the derived Fourier’s Law:


· K: the thermal conductivity.

· A: the area.

· : Temperature gradient.

By taking the area of the cylinder to be , and obtain another form of Fourier’s Law which is listed as the following:


Also, we used this formula:


· I: Current.

· V: Voltage.




1- Just continue your experiment after your teacher provides you with operating and security practices.

2- Make sure to supply water to the cold area.

3- Make sure the versatile water link to the drain.

4- Ensure every thermocouple is connected to the socket at the service unit component (K).

5- Make sure the switch (B) to the manual unit is set.

6- Make sure on the measurement selection switch (E) you pick V.

7- Switch on the key reserve switch (A).

8- See the readings of voltage in the top meter (D) panel (as V in step 6 was selected).

9- The voltage rises slowly to 13V from zero voltage.

10- Change the Measurement Set (E) to I at 13 V and read the corresponding current measurement value at meter (D).

11- Ensure you are located on T1 at the temperature switch (G) and change it later.

12- Watch the temperature on the adjacent panel meter (J) for 10min (for a steady state condition).

13- Take the read T1 and change the temperature reading switch to show further temperatures after reaching a steady state.

14- Fill in the table in different layers below the temperatures, and remember to mention the units. Remember that you cannot assess T3 from the third layer, this is measured later.

15- Repeat step 9 with 14 and 16V voltage change.





Complete Results


In the results part, we determined the experimental and theoretical third temperature. For the theoretical, we calculated it from the formula, but for the experimental we found by a logarithmic equation which is obtained from the plot drawn in Excel. After that, we found their percentage of error. We repeated these steps three times for 12 volts, 15 volts and 17 volts.


Results of the Measurements:

We have the obtained results from the unit service at the three different values for the voltage.


  T1 T2 T4 T5 T6
ri (mm) 7 10 30 40 50
T at 13 V


51.3 47 34.5 31.4 28.7
T at 14 V


55.2 50.3 35.8 32.2 29.2
T at 16 V


64.1 57.7 38.8 34.2 30.2


Table 1: Obtained Temperature Results.


Temperature vs Radius Plots:

For this section, we took the five obtained temp