# Solution Library

# Calculate the Thermal Conductivity of a Bar of Material

**Question**

The following arrangement is used to determine the thermal conductivity of a bar of material. At one end of the bar, an electrical heater is attached. The horizontal surfaces of the bar are covered in insulation. At the other end of the bar, a heat sink is located. The heat sink maintains the respective surface at 20°C. Three thermocouples are located along the length of the bar, one at the mid-point. At steady-state, the temperatures are as indicated below.

The bar has a square cross-section of side 2 cm. Note that the second thermocouple is located at the mid-point along the length of the bar. Only the metal surface is connected to the electrical heater. All the heat flow enters the bar at the metal surface.

(a) What do you understand by steady-state, given that initially, before the heated is switched on, the entire bar is at a temperature of 20°C?

(b) Using Excel (preferably), sketch the temperature profile along the bar. What can you deduce from this temperature profile? What does this tell you about the insulation?

(c) Write down the integrated form of Fouriers Law for plane-wall conduction. Explain why, for the above situation. it is not appropriate to use the integrated form of Fourier's Law to determine the thermal conductivity of the metal.

(d) Calculate the heat-transfer area (A) for plane-wall conduction through the bar.

(e) Using your graphical plot of the profile. estimate the thermal conductivity (k) of the metal bar. You are advised to plot the temperature data as an Excel or Mathcad file. By comparing your calculated value of k with published data, what do you estimate to be the material of the bar?

(f) Estimate the rate of heat loss through the insulation.

Hint: This is the difference between the value of Q entering the bar at the heater and the value of Q leaving at the heat sink.

(g) How do you define pettect insulation? Sketch the temperature profile along the bar if the present insulation were replaced with a perfect insulation. Also, for perfect insulation, sketch the temperature profile across the bar (in a vertical direction. as shown by the red line).

**Summary**

The question belongs to Chemical Engineering and the question is about thermal conductivity of a material. The material is being heated. Questions such as steady state, temperature profile, insulation, integrated form of Fouriers Law, etc have been answered clearly in the solution.

Download Full Solution

## Comments

Rashathis is a very good website

maaniI have 50 questions for the same test your page is showing only 28

joeannehi can you please help or guide me to answer my assignments. thanks

joeannehi can anyone help or guide me to my assignments. thanks

MonikCristinaThis solution is perfect ...thanks

JaneteHello Allison,I love the 2nd image that you did! I also, had never heard of SumoPaint, is something that I will have to exolpre a bit! I understand completely the 52 (or so) youtube videos that you probably watched. Sometimes they have what you want, sometimes they don't! However, it is always satisfying when you are able to produce something that you have taught yourself. Great job!Debra 0 likes

SandeepPerfect bank of solution.

Oxanagreat !

Paul Brandon-Fritziusthanks for the quick response. the solution looks good. :)

tina Johnsonthnx for the answer. it was perfect. just the way i wanted it.

Giuseppeworks fine.