The Conduction of Heat Along a Composite Bar and Evaluate the Overall Heat Transfer Coefficient

Table of Contents Text content Page a) Objective.................................................................................................2 b) Introduction.............................................................................................2 c) Material & Apparatus..............................................................................3 d) Procedure...............................................................................................3 e) Results & Discussion..............................................................................4 f) Conclusion..............................................................................................5 g) References..............................................................................................5

OBJECTIVE
This experiment was carried out to study the conduction of heat along a composite bar and evaluate the overall heat transfer coefficient.

INTRODUCTION
Conduction is defined as the transfer of energy from more energetic particles to adjacent less energetic particles as a result of interactions between the particles. In solids, conduction is the combined result of molecular vibrations and free electron mobility. Metals typically have high free electron mobility, which explains why they are good conductors. Conduction can be easily understood if we imagine two blocks, one hot and the other cold. If we put these blocks in contact with one another but insulate them from the surroundings, thermal energy will be transferred from the hot block to the cold block. This mode of heat transfer between the two solid blocks is termed as ‘conduction’.

Figure 1: Schematic of a long cylindrical insulated bar Provided that the heated, intermediate and cooled sections are clamped tightly together, so that the end faces are in good thermal contact, the three sections can be considered to be one continuous wall of uniform cross section and material.
According to Fourier’s law of heat conduction:

If a plane wall of thickness (Δx) and area (A) supports the temperature difference (ΔT) then the heat transfer per unit time (Q) by conduction through the wall is found to be: If the material of the wall is homogeneous and has a thermal conductivity K then: The heat flow is positive in the direction of temperature fall hence the negative sign in the equation. For convenience the equation can be rearranged to avoid negative sign as follows: For continuity, the steady heat flow through the successive sections must be the same so Fourier’s law can be applied to the three sections as follows: We may write it as Where U is an overall heat transfer coefficient for the composite wall.

MATERIAL AND APPARATUS
The SOLTEQ Heat Conduction Study Bench (Model : HE105) , Cooling Water, Temperature Sensor, brass conductor section, stainless steel section, heater power control knob control panel, power supply , thermocouple.

PROCEDURE 1. The main switch is switched off and then a stainless steel section of 0.025m diameter is inserted to the intermediate section into the linear module and clamped together. 2. Water supply and heater power are turned on and water flowing from the free end of the water pipe to drain is ensured and the heater power control knob is turned fully in anticlockwise position and connected to the sensor leads. 3. The power supply and main switch is switched on and the digital readouts will be illuminated. 4. The heater power is controlled from 0-40 watts and the temperature at the sensors is recorded in the following tables. 5. Graph is plotted for temperature, T versus distance, x and the Overall Heat Transfer Coefficient is calculated

RESULTS AND DISCUSSION

Heater power, Q (Watts) | TT1 (°C) | TT2 (°C) | TT3 (°C) | TT7 (°C) | TT8 (°C) | TT9 (°C) | 10 | 49.9 | 45.0 | 42.8 | 31.9 | 31.8 | 31.5 | 20 | 77.5 | 67.5 | 62.4 | 34.4 | 33.8 | 32.8 | 30 | 104.1 | 92.6 | 81.5 | 36.4 | 35.3 | 33.9 | 40 | 139.1 | 134.9 | 109.7 | 38.4 | 36.6 | 34.9 |

K=QAdTdx
K10W=100.00049087(262.83)=77.51Wm°C
K30W=300.00049087(793.33)=77.04Wm°C
K40W=400.00049087(1312)=62.11Wm°C

By using Fourier’s Law, thermal conductivity, k can be calculated. When power heater, Q is 10W the thermal conductivity is 77.51 W/m°C whereas for 30W, the thermal conductivity is 77.04 W/m°C and 62.11 W/m°C at 40W. The theoretical thermal conductivity differs from the actual thermal conductivity value of 119 W/m°C. This could be due to experimental errors such as heat loss from the thermocouple to the surrounding. Varying the input power affects the thermal conductivity value as it decreases when more input power is given.

CONCLUSION

From the experiment conducted, we have been able to investigate Fourier’s Law for the linear conduction of heat along a homogeneous bar.

REFERENCES

“Heat Transfer”. Wikipedia. Retrieved on 31 May 2011. <http://en.wikipedia.org/wiki/Heat_transfer#Conduction >

Yunus A. Cengel. “Heat Transfer A Practical Approach”, WBC McGraw-Hill (1998)

“Linear Heat Conduction”. Retrieved on 31 May 2011 <http://me.yeditepe.edu.tr/courses/me401/me401_linear_conduction.pdf >

References: K40W=400.00049087(1312)=62.11Wm°C By using Fourier’s Law, thermal conductivity, k can be calculated Yunus A. Cengel. “Heat Transfer A Practical Approach”, WBC McGraw-Hill (1998) “Linear Heat Conduction”