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Thermal Conductivity – Resistance: Temperature

Abstract

The previous experiments employed the concept of thermal resistance between two points A and B in an attempt to observe a change in temperature difference between point A and B. Although thermal conductivity is calculated via thermal resistance, this experiment will maintain the same thermal resistance in all sample. The varying constant will, in this case, be amount of energy put through the system. Multiple simple set-up’s will be employed with varying heat magnitudes in an attempt to observe a difference in temperatures between point A and B on a single sample.

Introduction

The goal of this experiment will be to observe a variation in temperatures between point A and B using samples of the exact same thermal resistance. This will ultimately provide further insight into the concepts of Thermal Conductivity and Thermal Resistance.

Background Information and Equations

Background Information

Laboratory testing of Thermal Conductivity routinely involves the calculation of Thermal Resistance. From this value, thermal conductivity may be determined via use of other more readily measured values (length…).

Background Equation

Heat Flow Equation Q = ΔT / RΘ

  • Q = Heat flow in Watts
  • ΔT = Temperature difference in Degrees Celsius
  • RΘ = Thermal Resistance (l / k ⋅ A)
  • l = Length of a material in Meters
  • k = Thermal conductivity constant in W/m-K
  • A = Surface area in meters squared

This experiment will vary the bolded constant via different heat sources.

As with the other experiments, it is recommended to use a material with fairly high thermal conductivity in order to save time. Suitable materials may be found in the table below.

More materials may be found here

Materials and Experimental Set-up

The dimensions of the copper adaptor are:

  • d = 1 inch
  • d’ = 2 inch
  • l = 1/2 inch
  • l’ = 1 inch

Experimental Set-up

A steam generator and chamber will be used in this experiment in order to mimic a heat source of 100°C. For instructions on how to make a steam generator and steam chamber, visit the Lee’s Disc Method. To effectively use the steam generator, a hole with a diameter of 2 inch should be made. The hole will serve as the location of insertion for the copper adaptor.

The copper adaptor should be designed to have the exact same dimensions as the hole in the steam chamber. Wider holes may be used, however; bigger dimensions may not support the copper adaptor and would not be recommended. A hole should be machined into the copper adaptor with a diameter of 1 inch and a depth of ½ inches. This hole will provide a location of insertion for the metal rod to be tested.

If the machining process did not provide a clean cut, the hole left may be filled with thermal interface material. The rod can then be inserted in the hole and any excess thermal interface material wiped off.

On the left, a hypothetical representation of the copper adaptor supporting the testing material while in the steam chamber. On the right, a hypothetical representation of the copper adaptor supporting the testing material while on a hotplate.

Procedure

  • Obtain the desired material to be tested
  • Insert the material into the hole of the copper adaptor (with thermal interface material if needed)
  • Turn on the hot plate to a low setting (~50°C)
  • Allow the hot plate to reach a stable temperature (steady-state)
  • Record the temperature of the tip of the material to be tested
  • Place the copper adaptor with material on the hot plate
  • Allow the material to heat up for 5-10 minutes
  • Once the time has passed, record the temperature
  • Remove the adaptor and material allowing them to return to beginning temperature
  • Repeat steps 4-9 using the hot plate at a high setting (~150°C+) and steam chamber (100°C)

Observation

A trend of increasing temperature after 5-10 minutes with respect to an increase in the magnitude of the source of heat should be observed. Without using a thermometer, one could place a candle at the tip of the metal rod and record the degree to which the candle is melted after a certain period of time. Although three tests may prove to be adequate in order to demonstrate the effect temperature difference, the same software used in Part Three may be used to gain even further insight. Simply by accessing the Examples > Conduction > Conduction > Comparing Temperature Differences. Using this example, various magnitudes of temperature may be experimented with to gain further insight into the effect of the temperature level on heat flow rate.

Conclusion

The three previous experiments demonstrated that the temperature between point A and B may be manipulated via manipulation of the thermal resistance between point A and B. This experiment did not manipulate thermal resistance; however, the road analogy still holds true. Should you allow the cars to enter the road at high velocities, the rate at which the cars leave the road will increase. Decrease the entrance velocity of the cars and the exit velocity will also be lower.

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