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### Lab Report-Thermal Conduction in Solids ( Aluminum and Composite) ## Aim

Aim of this lab work is to understand the thermal conduction in solids

## Objectives

Following are the objective of this lab work of thermal  conduction in solids

1. To measure the thermal conduction of copper

2. Plotting the thermal conductivity characteristic curve for composite wall comprising of aluminum and copper

## Theory

According to the law of energy or heat transfer, heat or energy always from the area of high potential to the area of low potential in free natural state or conditions. Heat from area of high potential to area of low potential in three different ways conduction, convection and radiation from these three methods of heat transfer conduction is the methods of heat transfer which transfer heat between metals.

Conduction
Conduction is mode of heat transfer from high potential source to low potential source of single body with the help of its vibrating molecules

Convection
Convection is mode of the transfer from high potential source to low potential source in fluid or from fluids.

Radiation is mode of the transfer from high potential source to low potential source without the help of any medium.

## Rate of heat flow

I the case when there is a heat transfer between region of high potential to the region of low potential trough the solid then it is important to calculate the amount of heat transfer Q in time t through a particular cross section area A of solid having x thickness.

Q= -KA*t*∆T/∆x= -KA/x(T_2-T_1)
Here
U=  k/x
For composite wall
U=  K_1/x_1 +  K_2/x_2
So
Q= -UA(T_2+T_1)

## Apparatus

Following are the apparatuses which are required for carrying out the experiment of find the thermal conductivity of solids

1. Stop watch

2. Thermal conductivity of solids equipment’s

3. Beaker

4. Specimens of aluminum  and copper both have  30 mm length and 40 mm diameter

5. Heat conductive paste

## Apparatus Setup

1. The heater of the apparatus must be switched on

2. All the thermocouples should be on front panel and in Dewar vessel

3. The flowing water which is used for cooling must covers the overflow present on the constant water pressure device

## For Aluminum

 Time 0 3 6 9 12 15 18 27 24 T2 32.5 34.6 35.4 36.9 37.9 38.6 38.7 38.4 38.4

T1 = 43.4 T2 = 38.4
t1 = 19 t2 = 15

Mass of empty beaker = 0.104 Kg
Time to get 200 ml of water = 80 sec
Beaker mass with water= 0.29 kg

Mass flow rate =(Mass of water and beaker – Mass of beaker)/time

Mass flow rate=(0.29 – 0.104)/80  =2.325*〖10〗^(-3)

Calculating K

Q= m ̇*Cp*(t_1-t_2  )

Cp = 4190 J/KgK

Q= 2.32*〖10〗^(-3)*4190*(t_1-t_2  )

Q= 38.967

Ka= -Q/A*∆x/∆T=-Q/A*((x_1-x_2))/((T_2-T_1))

Ka=-38.967/0.001256*0.025/((38.4-43.4) )=168.5

## For composite Wall

 Time 0 3 6 9 12 15 18 21 24 27 T2 31.3 33 33.7 34.5 34.8 35 35.3 35.4 35.5 35.6

T1 = 50.3 T2 = 40.4T3 = 38.3 T4 = 35.7t1 = 19 t2 = 15

Q= 38.967

Kc= -Q/A*∆x/∆T=-Q/A*((x_1-x_2))/((T_4-T_3))

Kc=-38.967/0.001256*0.025/((35.7-38.3) )=298.16

Composite Wall Theory

U=Kc/xc+Ka/xa

U=298.16/0.025+168.5/0.025  =16848.4

Q= -UA(T_4-T_1)

Q= -16848.4*0.001256(35.7-50.3)

Q= 309.11

## Difference in value of Thermal conductivity

From the text book of heat transfer author Cengel chapter 1 basics of heat transfer, it is founded that the thermal conductivity of copper is 401 W/m C and thermal conductivity of aluminum is 237 W/m C. This value of thermal conductivity of copper and aluminum is very different from what was obtained from experiment 298 for copper and 168 for aluminum. Reason for difference in values can be anything from human error to faulty apparatus. If the worker performing the experiment is not skilled and well educated then there are possibilities that worker has not done experiment according to the recommended procedure and has taken wrong readings. Other than this is the apparatus which is being used is faulty then the experiment perform by skilled worker according to the recommended procedure will produce wrong values of thermal conductivity of copper and aluminum.

## Difference in Heat Transfer

The predicted value of heat transfer through the composite wall is much more than the value that was calculated using the power absorb by the water theory. For composite wall the value of heat transfer is 309.11 which is 270.143 more than the value of heat transfer using power absorb in water. Reason for difference in these values is the method of calculating the heat transfer means the variable involve in the calculation of heat transfer in both methods. In composite wall theory variable which effect the heat transfer are heat transfer coefficient, area of plate and temperature difference where as in power absorb by water method variables which effect the heat transfer are mass flow rate of water, specific heat capacity of water and total time. This mean than if mass flow rate of water is increased or decrease, the heat transfer will change for power absorb in water method but will not change for composite wall theory. Likewise if area of wall or overall temperature difference is changed then heat transfer through composite wall theory will change but heat transfer through power absorb in water will not change.