P13 E1 Saravanan Raj

Experiment Title

:

Linear and Radial Heat Conduction

Course

:

UEME3213 Heat and Mass Transfer

Program

:

Chemical Engineering

Name of Student

:

Saravanan Raj

Student ID No

:

1600167

Year and Trimester :

Y4 T1

Date of Experiment:

28th February 2019

Name of Lecturer :

Dr. Ng Chai Yan

TITLE Linear and radial heat conduction experiment OBJECTIVE The objective of this experiment is to examine the temperature profile and to determine the rate of heat transfer for both linear and radial conduction and to obtain the coefficient of thermal conductivity with the aid of the Fourier’s law. INTRODUCTION The Linear and Radial Heat Conduction Apparatus is used to study the basic principles of conduction heat transfer. With the aid of the apparatus, we are able to determine the relationship between the rate of heat transfer and temperature gradient, the cross-sectional area and length of the conducting path and thermal conductivity of the material. Thermal conduction is basically the the exchange of energy between adjacent molecules and electrons in the conducting medium. There are two ways where heat can be conducted in solids, which is by transportation of energy by free electrons and by lattice vibrations. In good conductors, a large number of free electrons move about in the lattice structure of the material. It always takes place from a region of higher temperature to a region of lower temperature. The portion of energy transported by free electrons is larger than that by lattice structure. An increase in temperature causes increase in both the lattice vibration and the speed of electrons, but increased vibration of lattice disturbs the movement of free electrons causing reduction in transport of energy by free electrons which means the overall conduction is reduced. A solid is chosen for the experiment of pure conduction because both liquids and gasses exhibit excessive convective heat transfer. A heat source placed in a material causes temperature changes due to heat conduction. The relationship between temperature and the distance from the heat source must be linear after some time in the case of linear heat conduction and it must have a logarithmic distribution in the case of radial heat conduction. For practical situation, heat conduction occurs in three dimensions, a complexity which often requires extensive computation to analyze. In the experiment, it is seen that heat will flow through the homogeneous shaped brass bar in the linear part and the circular brass plate (cylindrical) in the radial part. In relation to that, sensors connected to the module is to measure the temperature reading of the bar after it’s heated up by

the surrounding hot water which supplies the heat to the test modules which creates the temperature gradient. Then, few equations including the Fourier’s Law is used to calculate the thermal conductivity, k of the brass material.

THEORY Linear Conduction Heat Transfer (Homogeneous Bar) Fourier’s Law is an empirical relationship between the conduction rate in a material and the temperature gradient in the direction of energy flow, which concludes that the heat flux resulting from thermal conduction is proportional to the magnitude of the temperature gradient and opposite to it in sign. For a unidirectional conduction process this observation may be expressed as: Q=kA

dT dx

Where, Q

=

heat flow rate, [W]

[ ] W k⋅m

k

=

thermal conductivity of the material,

A

=

cross-sectional area of the conduction, [m2]

dT

=

changes of temperature between two points, [k]

dx

=

changes of displacement between two points, [m]

Fourier's Law thus provides the definition of thermal conductivity and forms the basis of many methods of determining its value. Fourier's Law, as the basic rate equation of the conduction process, when combined with the principle of conservation of energy, also forms the basis for the analysis of most conduction problems.

Radial Conduction Heat Transfer (Cylindrical) For cylindrical systems, the temperature difference produces conduction in the radial direction only. Hence, it is said to be one-dimensional. For radial conduction, the heating element is attached to the c

entre part of the circular brass plate. The heat flows radially and since the

area increases with radius, hence the temperature gradient must decrease with radius. The heat flow rate (Q) is: Q=−

where,

2 π Lk (T i −T o ) R ln o Ri

Q

=

heat flow rate, [W]

k

=

thermal conductivity of the material,

L

=

thickness of the conduction, [m]

Ti

=

inner section temperature, [K]

To

=

outer section temperature, [K]

Ro

=

outer radius, [m]

Ri

=

inner radius, [m]

[ ] W k⋅m

DESCRIPTION Unit Assembly The equipment comprises two heat-conducting specimens, a multi-section bar for the examination of linear conduction and a metal disc for radial conduction. A control panel supplies electrical power to the heaters and shows readings for all relevant measurements. A small flow of cooling water provides a heat sink at the end of the conducting path in each specimen.

1 7

2 3

8

4 9

5 6

Figure 1: Unit Assembly for Heat Conduction Study Bench (Model: HE 105)

1. Control Panel

6.

Thermocouple Connectors

2. Heater Power Indicator

7.

Thermocouples

3. Heater Power Regulator

8.

Radial Module

4. Temperature Indicator

9.

Linear Module

5. Temperature Selector Specifications



Linear Module Consists of the following sections: i)

Heater Section Material : Brass Diameter: 25 mm

ii)

Cooler Section Material : Brass Diameter: 25 mm

iii)

Interchangeable Test Section - Insulated Brass Test Section with Temperature Sensors Array (Diameter = 25mm, Length = 30 mm)



Radial Module Material

: Brass

Diameter : 110 mm Thickness : 3 mm  Instrumentations Linear module consists of a maximum of 9 type K thermocouple temperature sensors at 10 mm interval. For radial module, 6 type K thermocouple temperature sensors at 10 mm interval along the radius are installed. Each test modules are installed with a 100 Watt heater. APPARATUS There are two experimental models to study the heat transfer by conduction: 1. Linear Heat Conduction 2. Radial Heat Conduction

Control panel, heater power indicator, heater power regulator, temperature indicator, temperature selector, thermocouple connectors, thermocouples, radial module, and linear module.

PROCEDURE Linear Conduction Heat Transfer 1. The main switch was initially made sure switched off. A brass conductor (25mm diameter) intermediate section was inserted into the linear module and clamp together. 2. The temperature sensors T1 until T9 were installed to the test module and the sensors lead were connected to the panel. 3. The heater supply lead for the linear conduction module was connected to the power supply socket on the control panel. 4. The water supply was turned on and ensured that the water is flowing from the free end of the water pipe to drain. This should be checked at intervals. 5. The heater power control knob control panel was turned to the fully anticlockwise position. 6. The power supply and the main switch was switched on, the digital readouts were illuminated. 7. The heater was switched on and the heater power control was turned to 20 Watts and sufficient time was allowed to achieve steady state condition before recording the temperature at all temperature points as well as the input power reading on the wattmeter (Q).This procedure was repeated for other input power between 0 to 20 watts. After each change, sufficient time was allowed to achieve steady state condition again. 8. The graph of the temperature, T versus distance, x was plotted. The thermal conductivity of the test section was calculated.

Note: i)

Care should be taken when assembling the sample between the heater and the cooler sections, to match the shallow shoulders in the housings.

ii)

The temperature measurements are ensured to be aligned along the longitudinal axis of the unit.

iii)

The insulation material of the test module can withstand up to 100 degree Celsius. The heater power is reduced immediately when the temperature nearest to the heater is too high.

Radial Heat Transfer 1. The main switch initially is made sure turned off. 2. The temperature sensors (T1 until T6) were installed to the radial test module and the sensors leads to the panel were connected. 3. The heater supply lead for the radial conduction module was connected into the power supply socket on the control panel. 4. The water supply was turned on and ensured that water is flowing from the free end of the water pipe to drain. This was checked at intervals. 5. The heater power control knob control panel was turned to the fully anticlockwise position. 6. The power supply and main switch was switched on, the digital readouts were illuminated. 7. The heater was switched on and the heater power control was turned to 20 Watts and sufficient time was allowed to achieve steady state condition before the temperature at all temperature points as well as the input power reading on the wattmeter (Q) was recorded. After each change, sufficient time was allowed to achieve steady state conditions again. 8. The graph of the temperature, T versus distance, x was plotted. The thermal conductivity of the test section was calculated.

Note: The insulation material of the test modules can withstand up to 100 degrees celsius only. The heater power is reduced immediately if the temperature nearest to the heater is too high.

RESULTS Linear Conduction Heat Transfer

Linear Heat Conduction Comparison with Theory Points (experimental data), Line (theory) Temperature (deg C)

60 50 40 30 20 10 0 1

2

3

4

5

6

Distance along Axis (cm)

Graph 1

Radial Heat Transfer

7

8

9

Temperature (deg C)

Radial Heat Conduction Comparison with Theory Points (experimental data), Line (theory) 50 45 40 35 30 25 20 15 10 5 0 0

1

2

3

4

5

Radial Distance from Centre of Cylinder (cm)

Graph 2

6

7

Radial Heat Conduction Comparison with Theory Points (experimental data), Line (theory) 45

Temperature (deg C)

40 35 30 25 20 15 10 5 0 0

1

2

3

4

5

Radial Distance from Centre of Cylinder (cm)

Graph 3

CALCULATION Calculation done for Q = 5.0 W (linear):

dx = 0.01m Area, A =

π ( 0.025 m)2 =0.000491m2 4

At sensor 2: T2 = 305.5 K and T1 = 305.7 K dT = 0.2 k=

Q dx 5 0.01 W = =509.16 A dT 0.000491 0.2 m. K

( )

( )

At sensor 3: T3 = 305.4 K and T2 = 305.5 K dT = 0.1

6

7

k=

5 0.01 W =1018.33 0.000491 0.1 m. K

( )

At sensor 4: T4 = 305.1 K and T3 = 305.4 K dT = 0.3 k=

5 0.01 W =339.44 0.000491 0.3 m.K

( )

At sensor 5: T5 = 302.2 K and T4 = 305.1 K dT = 2.9 k=

5 0.01 W =35.12 0.000491 2.9 m. K

( )

At sensor 6: T6 = 303.3 K and T5 = 302.2 K dT = -1.1 k=

5 0.01 W =−92.58 0.000491 −1.1 m .K

( )

At sensor 7: T7 = 302.3 K and T6 = 303.3 K dT = 1 k=

5 0.01 W =101.83 0.000491 1 m. K

( )

At sensor 8: T8 = 302 K and T7 = 302.3 K dT = 0.3 k=

5 0.01 W =339.44 0.000491 0.3 m.K

( )

At sensor 9: T9 = 301.9 K and T8 = 302 K dT = 0.1

k=

5 0.01 W =1018.33 0.000491 0.1 m. K

( )

Average

k

=

509.16+ 1018.33+ 339.44+35.12−92.58+101.83+339.44+1018.33 W =408.7 8 m.K

Calculation done for Q = 5.0 W (radial):

Pi, π

= 3.142

Thickness, L = 0.003m At sensor 2: dT = (Ti – To) = 305.1 – 308.4 = -3.3 K Ro = 0.02, Ri = 0.01 −Q ln ∴ k=

Ro Ri

( )

2 πL ( T i −T o )

−5 x ln =

( 0.02 0.01 )

2 x 3.142 x 0.003 x (−3.3 )

At sensor 3: dT = 303.2 – 305.1 = -1.9 K Ro = 0.03, Ri = 0.02 −5 x ln k=

( 0.03 0.02 )

2 x 3.142 x 0.003 x (−1.9 )

At sensor 4: dT = 302.6 – 303.2 = -0.6 K Ro = 0.04, Ri = 0.03

=56.60

W m. K

=55.71

W m. K

−5 x ln k=

( 0.04 0.03 )

2 x 3.142 x 0.003 x (−0.6 )

=127.17

W m.K

At sensor 5: dT = 301.7 – 302.6 = -0.9 K Ro = 0.05, Ri = 0.04 −5 x ln k=

( 0.05 0.04 )

2 x 3.142 x 0.003 x (−0.9 )

∴ Average k=

=65.76

W m. K

55.71+ 56.60−127.17+65.76 W =76.31 4 m. K

DISCUSSION The experiment is led to examine the temperature profile and decide rate of heat exchange for both linear and radial conduction. Conduction is something that occurs in our daily life. Convection occurs when heat is transferred through a gas or liquid by the hotter material moving into a cooler area. The better the conductor, the more quickly heat will be exchanged. This happens because of the substances are in direct contact with each other. Furthermore, heat is led in solids in two routes; transport of energy by free electrons and grid vibration. In a way, there are numerous other wonders resembles this that operates based on this hypothesis of heat flow. Actually, conduction happens when a substance is warmed, particles will acquire power, and vibrate more. These molecules at that point catch nearby particles and exchange some of their energy to them. At this point, it proceeds and passes the vitality from the hot end down to the colder end of the substance. In addition, materials that have higher free electron portability have a tendency to be great conductors of heat. Hence, the heat move through materials is not effectively computed at a steady state. In this way, it is required to get the temperature distribution equation through a solid. In this experiment, there are two types of conductions which are linear and radial conductions. A homogeneous brass bar is placed in the linear module for linear conduction as

part of this experiment and heated at an end. The heat passes from the water to the bar through conduction. A total of nine temperature sensors were installed along the module to calculate the thermal conductivity by determining the temperature at different locations of the bar with distance around 0.01m from each other. The values of temperature were obtained, recorded and tabulated against the heat power used. A total of 5 different heat powers were used which are 5,10,15 and 20 Watts. The thermal conductivity, k was calculated based on Fourier’s Law equation using the area of 0.000491m2. The average thermal conductivity of each heat flow rate is calculated which is then used to calculate the overall average conductivity value of linear conduction in a brass specimen. A circular brass plate is used for the radial heat transfer part. The plate has a thickness, L of 0.003m. It was also heated with five different powers which are 5,10,15 and 20 Watts. Unlike linear conduction, for this experiment only six temperature sensors where installed along then module with distance of 0.01m. These values which are recorded is then substituted into the equation below, to find the thermal conductivity, k: Q=−

2 π Lk (T i −T o ) Ro ln Ri

The overall average conductivity is obtained from all the different values of Q. The overall average thermal conductivity for the linear part calculated is 232.65 W/m. K and for the radial part is 130.07 W/m.K. Based on the graph obtained in this experiment comparing the theoretical and the experimental value shows that the trend of both the graphs plotted for each part is seen to be abnormal and does not decrease linearly. In fact, it is also seen that the experimental value differs from the theoretical value for the linear conduction heat transfer part especially at sensor 6. The temperature obtained at sensor 6 supposed to be lower than sensor 5 but it seems to be higher. While for radial heat transfer part, the experimental data obtained at sensor 4 differs than the theoretical value as the temperature obtained is higher than sensor 3 which supposed to be lower. This is because the sensor 6 in the linear experiment and sensor 4 in the radial experiment

are less sensitive due to the problem in the terminals. Thus, the temperature readings are different from what it should be and this causes the abnormality in the trend. Lastly, there are several precaution steps that should be taken into consideration when conducting this experiment. First off, during the assembly of the sample between the cooler and heater sections, care should be exercised to match the shallow shoulders in the housings. Besides, ensure that the sensors are connected well to the module to get a better reading. Next, the insulation is to ensure that no heat is loss to the surrounding. In addition, the insulation material of the test modules can only withstand a temperature of up to 100 ℃ , hence the heater power should be reduced immediately in occasion of the temperature being too high. CONCLUSION The overall average thermal conductivity of linear conduction is 232.65 W/m. K and the overall average thermal conductivity of radial conduction is 130.07 W/m.K.

REFERENCE 1. Incropera, F. P., De Witt, D.P., Fundamentals of Heat and Mass Transfer, John Wiley & Sons, Singapore, 1990 2. Thermal Conductivity (n.d). Retrieved March 7, 2019 from

https://www.sciencedirect.com/topics/chemistry/thermal-conductivity