KMU 401 - Chemical Engeineering Basic Measurements Laboratory

Experiment 4: Computer Controlled Thermal Conduction & Computer Controlled Thermal Radiation

GROUP C2

Buket Gürsel / #20628864Berkan Koca / #20622742

Duygu Temizkan /#20622938Gökhan Uzun /#20622962

Instructor: Prof. Dr. Deniz TanyolaçResearch Assistant: Yasemin Günaydın

Date of Experiment: November 5, 2010Date of Submission: November 12, 2010

November 12, 2010

Dear Prof. Dr. Deniz Tanyolaç

The experiment “Computer Controlled Thermal Conduction & Computer Controlled

Thermal Radiation” had been done on 5th November, 2010. Essential aim of the experiment

was getting information about basic mechanisms of heat transfer, Thermal Conduction&

Thermal Radiation on top of all this, determination of thermal conductivities different kind of

metarials (such as brass and stainless steel) that heat flows through a multilayer wall., It is

assumed to occur only one dimensional heat transfer because of the insulation around of the

metarials. All part of the study; even if they are worked at unsteady state conditions, it is

formed as steady state except one part of the experiment.

Research Assistant Yasemin Günaydın was contributed to our work during the

experiment. The experiment had been taken four and a quarter hours. We did not have any

kind of problem likewise heating the brass or stainless steel of linear conduction heat transfer

experiment system, or setting up the position of adjustable part placed in the linear conduction

heat transfer experiment system. There is no hand made labor except setting up the

temperature sensors on the radial cunduction heat transfer experiment system. All part of the

systems controlled by computer. Thereby, it was very good and disciplined group working.

Buket Gürsel

Berkan Koca

Duygu Temizkan [Responsible for the Experiment]

Gökhan Uzun

ii

TABLE of CONTENTS

Cover Page……………………………………………………………………………………..iPresentation Letter……………………………………………………………….……...……..iiTable of Contents……………………………………………………………….……….…….iiiSummary……………………………………………………………………….………..…….iv1. Theory………………………………………………………….………..……………11.1. Heat Transfer…………………………………………………………………………11.1.1. Basic Mechanisms of Heat Transfer…………………………………………………11.1.1.1.Conduction Heat Transfer……………………………………………………………11.1.1.2.Convection Heat Transfer……………………………………………………………21.1.1.3.Radiation Heat Transfer…………………………………….…………………………31.1.2. Definition of Heat Transfer……………………………………………..……………41.1.2.1.Fourier's Law of Heat Conduction………………………………….………………41.1.2.2.Thermal Conductivity…………………………………………….…….……………51.1.3. Conduction Heat Transfer……………………………………………………………71.1.3.1.Conduction Through A Flat Slab or Wall……………………………..……………71.1.3.2.Conduction Through Plane Wall In Series…………………………………………81.1.3.3.Conduction Through A Hollow Cylinder……………………………………………91.1.4. Thermal Radiation…………………………………………………………………..101.1.5. Absorptivity, Reflectivity and Transmittivity………………………………………121.1.6. Radiation Behaviour of Surface……………………………………………………121.1.7. Stefan-Boltzmann Law………………………………………………………………131.1.8. Kirchhoff's Law………………………………………………………………………142 Experimental Method………………………………………………………………162.1. The Aim of The Experiment………………………………………………..………162.2. Description of Apparatus……………………………………………………………162.3. Experimental Procedure……………………………………………………….……173. Result and Discussion………………………………………………………………183.1. Experimental Procedures of Computer Controlled Conduction…………..………183.1.1. Conduction in a Simple Bar…………………………………………………………183.1.2. Conduction in a Radial Element……………………………………………………213.1.3. Radiationn Heat Transfer…………………………………………..………………224. Conclusion………………………………………………………………………….255. Nomenclature………………………………………………………………………266. Referrences…………………………………………………………………………277. Appendices…………………………………………………………………………28

iii

SUMMARY

The following laboratory report summarizes and discusses the two of the basic

mechanisms of the heat transfer. Theoretical information about heat transfer is followed by

the procedure and results of the computer controlled thermal conduction and radiation.

Thermal conduction is analysed in a linear and radial heat transfer system. Thermal radiation

part of the experiment is done by a radio meter source which emitting thermal radiation and

related data is recorded by the computer.

Heat transfer which is one the case of the transport phenomena is expressed in three

basic mechanisms: Conduction, Convection, and Radiation. Though one of these mechanisms

can be dominant in a system, they generally take place all together.

Heat may be conducted in all aggregations of matters. In the gas and liquid forms, heat

is conducted by the transfer of the nergy of motion between adjacent molecules. Heat is

transferred by vibration of atoms in solids and mostly by free electrons in metallic solids.

Convective heat transfer is subject to the bulk transport and mixing of macroscopic

elements of warmer portions with cooler portions of a gas or liquid. This case may also refers

to the energy exchange between a solid surface and a fluid. A distinction must be made

between forced convection heat transfer, where a fluid is forced to flow past a solid surface by

a pump, fan or blower. Natural or free convection takes place where a density difference or

buoyancy forces are present.

Thermal radiation is the third action of a heat transfer system in which no physical

medium is required. Radiation is the transfer of energy through space by means of

electromagnetic waves. The most important example of radiation is the transport of heat to the

earth from the sun.

To sum up, the experiment named Computer Controlled Thermal Conduction &

Thermal Radiation is accomplished and examined in-detail in this report. Related calculations

are done with the discussions of experimental error ratios which are tabulated in ralevant

section.

iv

1. THEORY

1.1. Heat Transfer

In the simplest of terms, the discipline of heat transfer is concerned with only two

things: temperature, and the flow of heat. Temperature represents the amount of thermal

energy available, whereas heat flow represents the movement of thermal energy from place to

place. [1]

On a microscopic scale, thermal energy is related to the kinetic energy of molecules. The

greater a material's temperature, the greater the thermal agitation of its constituent molecules

(manifested both in linear motion and vibrational modes). It is natural for regions containing

greater molecular kinetic energy to pass this energy to regions with less kinetic energy.

Several material properties serve to modulate the heat tranfered between two regions at

differing temperatures. Examples include thermal conductivities, specific heats, material

densities, fluid velocities, fluid viscosities, surface emissivities, and more. Taken together,

these properties serve to make the solution of many heat transfer problems an involved

process. [1]

1.1.1. Basic Mechanisms of Heat Transfer

Heat is energy transferred due to a difference in temperature. There are three modes of

heat transfer: conduction, convection, and radiation. All three may act at the same time.

Conduction is the transfer of energy between adjacent particles of matter. It is a local

phenomenon and can only occur through matter. Radiation is the transfer of energy from a

point of higher temperature to a point of lower energy by electromagnetic radiation. Radiation

can act at a distance through transparent media and vacuum. Convection is the transfer of

energy by conduction and radiation in moving, fluid media. The motion of the fluid is an

essential part of convective heat transfer. [2]

1.1.1.1. Conduction Heat Transfer

Conduction is heat transfer by means of molecular agitation within a material without

any motion of the material as a whole. If one end of a metal rod is at a higher temperature,

then energy will be transferred down the rod toward the colder end because the higher speed

particles will collide with the slower ones with a net transfer of energy to the slower ones. For

heat transfer between two plane surfaces, such as heat loss through the wall of a house, the

rate of conduction heat transfer is:

1

where

Q: Heat transferred in time = t k: Thermal Conductivity of a Barrier A: Area T: Temperature d: Thicknessof the barrier [3]

1.1.1.2. Convection Heat Transfer

Convection is heat transfer by mass motion of a fluid such as air or water when the

heated fluid is caused to move away from the source of heat, carrying energy with it.

Convection above a hot surface occurs because hot air expands, becomes less dense, and rises.

Hot water is likewise less dense than cold water and rises, causing convection currents which

transport energy. [3]

2

(Eq. 1)

Figure 1.1 – The heat flows from high temperature to low temperature. [4]

Figure 1.2 – The Convective HeatTransfer. [5]

1.1.1.3. Radiation Heat Transfer

Radiation is the transfer of heat energy through empty space by means of

electromagnetic waves. All objects with a temperature above absolute zero radiate energy. No

medium is necessary for radiation to occur, for it is transferred by electromagnetic waves;

radiation takes place even in, and through, a perfect vacuum. For instance, the energy from

the Sun travels through the vacuum of space before warming the Earth. Radiation is the only

form of heat transfer that can occur in the absence of any form of medium (i.e., through a

vacuum).[7]

3

Figure 1.3 – Bouyancy Effect in Circulation. [6]

Convection can also lead to circulation in a

liquid, as in the heating of a pot of water over

a flame. Heated water expands and becomes

more buoyant. Cooler, more dense water near

the surface descends and patterns of

circulation can be formed, though they will not

be as regular as suggested in the drawing. [3]

Figure 1.4 - Hot metalwork from a blacksmith. The yellow-orange glow is the visible part of

the thermal radiation emitted due to the high temperature. Everything else in the picture is

glowing with thermal radiation as well, but less brightly and at longer wavelengths than the

human eye can see. An infrared camera will show this radiation.[8]

Radiation heat transfer is concerned with the exchange of thermal radiation energy

between two or more bodies. Thermal radiation is defined as electromagnetic radiation in the

wavelength range of 0.1 to 100 microns (which encompasses the visible light regime), and

arises as a result of a temperature difference between 2 bodies.[9]

No medium need exist between the two bodies for heat transfer to take place (as is

needed by conduction and convection). Rather, the intermediaries are photons which travel at

the speed of light. [9]

The heat transferred into or out of an object by thermal radiation is a function of

several components. These include its surface reflectivity, emissivity, surface area,

temperature, and geometric orientation with respect to other thermally participating objects. In

turn, an object's surface reflectivity and emissivity is a function of its surface conditions

(roughness, finish, etc.) and composition. [9]

1.1.2. Definition of Heat Transfer

1.1.2.1. Fourier’s Law of Heat Conduction

The law of Heat Conduction, also known as Fourier's law, states that the time rate of

heat transfer through a material is proportional to the negative gradient in the temperature and

to the area, at right angles to that gradient, through which the heat is flowing. We can state

this law in two equivalent forms: the integral form, in which we look at the amount of energy

flowing into or out of a body as a whole, and the differential form, in which we look at the

flow rates or fluxes of energy locally. [10]

The heat flux due to conduction in the x direction is given by Fourier’s law,

where Q is the rate of heat transfer (W), k is the thermal conductivity [W/(m⋅K)], A is the

area perpendicular to the x direction, and T is temperature (K). For the homogeneous, one-

dimensional plane shown in Fig. 1.5-a, with constant k, the integrated form of (Eq.2) is,

where Δx is the thickness of the plane. Using the thermal circuit shown in Fig. 1.5-b, (Eq. 3)

can be written in the form

where R is the thermal resistance (K/W). [2]

4

(Eq. 2)

(Eq. 3)

(Eq. 4)

1.1.2.2. Thermal Conductivity

The thermal conductivity k is a transport property whose value for a variety of gases,

liquids, and solids is tabulated also provides methods for predicting and correlating vapor and

liquid thermal conductivities. The thermal conductivity is a function of temperature, but the

use of constant or averaged values is frequently sufficient. Room temperature values for air,

water, concrete, and copper are 0.026, 0.61, 1.4, and 400 W/(mK). Methods for estimating

contact resistances and the thermal conductivities of composites and insulation are

summarized by Gebhart.[2,11]

In physics, thermal conductivity, k, is the property of a material that indicates its

ability to conduct heat. It appears primarily in Fourier's Law for heat conduction. Thermal

conductivity is measured in watts per kelvin per metre (W·K−1·m−1). Multiplied by a

temperature difference (in kelvins, K) and an area (in square metres, m2), and divided by a

thickness (in metres, m) the thermal conductivity predicts the rate of energy loss (in watts, W)

through a piece of material.[12]

The reciprocal of thermal conductivity is thermal resistivity. [12]

5

Figure 1.5 - Steady, one-dimensional conduction in a homogeneous planar wall with constant k.

The thermal circuit is shown in (b) with thermal resistance Δx/(kA).[2]

Table 1- Thermal Conductivities from CRC Handbook [13]

MaterialThermal conductivity(cal/sec)/(cm2 C/cm)

Thermal conductivity(W/m K)*

Diamond ... 1000

Silver 1.01 406.0

Copper 0.99 385.0

Gold ... 314

Brass ... 109.0

Aluminum 0.50 205.0

Iron 0.163 79.5

Steel ... 50.2

Lead 0.083 34.7

Mercury ... 8.3

Ice 0.005 1.6

Glass,ordinary 0.0025 0.8

Concrete 0.002 0.8

Water at 20° C 0.0014 0.6

Asbestos 0.0004 0.08

Snow (dry) 0.00026 ...

Fiberglass 0.00015 0.04

Brick,insulating ... 0.15

Brick, red ... 0.6

Cork board 0.00011 0.04

Wool felt 0.0001 0.04

Rock wool ... 0.04

Polystyrene (styrofoam) ... 0.033

Polyurethane ... 0.02

Wood 0.0001 0.12-0.04

Air at 0° C 0.000057 0.024

Helium (20°C) ... 0.138

Hydrogen(20°C) ... 0.172

Nitrogen(20°C) ... 0.0234

Oxygen(20°C) ... 0.0238

Silica aerogel ... 0.003

1.1.3. Conduction Heat Transfer

1.1.3.1. Conduction Through A Flat Slab or Wall

6

*Most from Young, Hugh D., University Physics, 7th Ed. Table 15-5. Values for diamond and

silica aerogel from CRC Handbook of Chemistry and Physics.

For one dimensional conduction in a plane wall, temperature is a function of

the x coordinate only and heat is transferred exclusively in this direction. In Figure 1.6, a

plane wall separates two fluids of different temperatures. Heat transfer occurs by convection

from the hot fluid at   to one surface of the wall at   , by conduction through the

waconvection from the other surface of the wall at   to the cold fluid at   . [14]

For steady state conditions with no distributed source of sink of energy within the wall, the

appropriate form of the heat equation is,

 to determine the conduction heat transfer rate,

Note that A is the area of the wall normal to the direction of heat transfer and for the

plane wall, it is a constant independent of x. The heat flux is then

Equations 6 and 7 indicate that both the heat rate qx and heat flux qx’’ are constants,

independent of x. [14]

1.1.3.2. Conduction Through Plane Wall In Series

7

Figure 1.6 - Heat Transfer Through a Plane Wall [14]

(Eq. 5)

(Eq. 6)

(Eq. 7)

Equivalent thermal circuits may also be used for more complex systems, such as

composite walls. Such walls may involve any number of series and parallel thermal

resistances due to layers of different materials. Consider the series composite wall of Fig. 1.7.

The one dimensional heat transfer rate for this system may be expressed as,

where is the overall temperature difference and the summation includes all thermal

resistances. [14] Hence,

Alternatively, the heat transfer rate can be related to the temperature difference and resistance

associated with each element. [14] For example,

8

Figure 1.7 – Equivalent Thermal Circuit for a Series Composite Wall [14]

(Eq. 8)

(Eq. 9)

(Eq. 10)

With the composite systems, it is quite often convenient to work with an overall heat

transfer coefficient, U, which is defined by the expression analogous to Newton's law of

cooling. Accordingly,

where is the overall temperature difference. The overall heat transfer coefficient is related

to the total thermal resistance, and from Equations 8 and 11 we see that UA = 1/Rtot. Hence,

for the composite wall of Fig.1.7. [14]

In general, we may write,

1.1.3.3. Conduction Through A Hollow Cylinder

A common example is the hollow cylinder, whose inner and outer surfaces are

exposed to fluids at different temperatures (Figure. 2.12). For steady state conditions with no

heat generation, the appropriate form of the heat equation, [14]

where, for a moment k is treated as a variable. The physical significance of this result

becomes evident if we also consider the appropriate form of Fourier's law. The rate at which

energy is conducted across the cylindrical surface in the solid may be expressed as

where A = 2ΠrL is the area normal to the direction of heat transfer. Since, Eq. 14 dictates that

the quantity kr(dT/dr) is independent of r, it follows from Eq. 15 that the conduction heat

transfer rate qr (not the heat flux qr″ ) is a constant in the radial direction. [14]

9

(Eq. 11)

(Eq. 12)

(Eq. 13)

(Eq. 14)

(Eq. 15)

1.1.4. Thermal Radiation

Heat transfer by thermal radiation involves the transport of electromagnetic (EM)

energy from a source to a sink. In contrast to other modes of heat transfer, radiation does not

require the presence of an intervening medium, e.g., as in the irradiation of the earth by the

sun. Most industrially important applications of radiative heat transfer occur in the near

infrared portion of the EM spectrum (0.7 through 25 μm) and may extend into the far infrared

region (25 to 1000 μm). For very high temperature sources, such as solar radiation, relevant

wavelengths encompass the entire visible region (0.4 to 0.7 μm) and may extend down to 0.2

μm in the ultraviolet (0.01- to 0.4-μm) portion of the EM spectrum. Radiative transfer can

also exhibit unique action-at-a-distance phenomena which do not occur in other modes of heat

transfer. Radiation differs from conduction and convection not only with regard to

mathematical characterization but also with regard to its fourth power dependence on

temperature. Thus it is usually dominant in high-temperature combustion applications. The

temperature at which radiative transfer accounts for roughly one-half of the total heat loss

from a surface in air depends on such factors as surface emissivity and the convection

coefficient. For pipes in free convection, radiation is important at ambient temperatures. For

fine wires of low emissivity it becomes important at temperatures associated with bright red

heat (1300 K). Combustion gases at furnace temperatures typically lose more than 90 percent

of their energy by radiative emission from constituent carbon dioxide, water vapor, and

particulate matter. Radiative transfer methodologies are important in myriad engineering

10

Figure 1.8 – Hollow Cylinder with Convective Surface Conditions. [14]

applications. These include semiconductor processing, illumination theory, and gas turbines

and rocket nozzles, as well as furnace design.[2]

λ = c / v = 1 / η

where,

λ: Wavelength

c: Speed of Ligth (3 x 1010) [cm/sec]

v: Frequency

E =hv

where,

E : Amount of Energy

h : Planck’s Constant (6.625 x 10-27) [erg-sec]

v :Frequency

11

Figure 1.9 – Electromagnetic Spectrum [15]

(Eq. 16)

(Eq. 17)

1.1.5. Absorptivity, Reflectivity and Transmittivity

Thermal radiation is the energy radiated from hot surfaces as electromagnetic waves. It

does not require medium for its propagation. Heat transfer by radiation occur between solid

surfaces, although radiation from gases is also possible. Solids radiate over a wide range of

wavelengths, while some gases emit and absorb radiation on certain wavelengths only. [16]

When thermal radiation strikes a body, it can be absorbed by the body, reflected from the

body, or transmitted through the body. The fraction of the incident radiation which is

absorbed by the body is called absorptivity (symbol α). Other fractions of incident radiation

which are reflected and transmitted are called reflectivity (symbol ρ) and transmissivity

(symbol τ), respectively. The sum of these fractions should be unity i.e. [16]

α + ρ + τ = 1

 An object is called a black body if, for all frequencies, the following formula applies[17]:

α + ε = 1

1.1.6. Radiation Behavior of Surface

In physics, a black body is an idealized object that absorbs all electromagnetic

radiation falling on it. Blackbodies absorb and incandescently re-emit radiation in a

characteristic, continuous spectrum. Because no light (visible electromagnetic radiation) is

reflected or transmitted, the object appears black when it is cold. However, a black body emits

a temperature-dependent spectrum of light. This thermal radiation from a black body is

termed blackbody radiation. In the blackbody spectrum, the shorter the wavelength, the higher

the frequency, and the higher frequency is related to the higher temperature. Thus, the color of

a hotter object is closer to the blue end of the spectrum and the color of a cooler object is

closer to the red.[18]

At room temperature, black bodies emit mostly infrared wavelengths, but as the

temperature increases past a few hundred degrees Celsius, black bodies start to emit visible

12

Figure 1.10 – Representation of Total

Radiation Properties. [16]

(Eq. 18)

(Eq. 19)

wavelengths, appearing red, orange, yellow, white, and blue with increasing temperature. By

the time an object is white, it is emitting substantial ultraviolet radiation.

The term black body was introduced by Gustav Kirchhoff in 1860. When used as a compound

adjective, the term is typically written as one word in blackbody radiation, but sometimes also

hyphenated, as in black-body radiation. [18]

Blackbody radiation is electromagnetic radiation in thermal equilibrium with a black

body at a given temperature. Experimentally, it is established as the steady state equilibrium

radiation in a rigid-walled cavity. There are no ideal (perfect) black bodies in nature, but

graphite is a good approximation, and a closed box with graphite walls at a constant

temperature gives a good approximation to an ideal black body. [19, 20, 21]

An object at temperature T emits radiation, which is a visible glow if T is high enough.

The Draper point is the name given to the point at which all solids glow a dim red (about 798

K). [22, 23]

A black body is an object that absorbs all light that falls on it, and emits light in

a wavelength spectrum determined solely by its temperature. A black body can be

approximated by, for example, an oven: a cavity surround by walls at temperature T and with

a small opening through which light can enter and leave. At 1000 K, the opening in the oven

looks red; at 6000 K, it looks white. No matter how the oven is constructed, or of what

material, as long as it is built such that almost all light that enters is absorbed, it will be a good

approximation to a blackbody, so the spectrum, and therefore color, of the light that comes

out will be almost entirely a function of its temperature alone. A plot of the amount of energy

inside the oven per unit volume per unit frequency interval versus frequency (or per unit

wavelength interval, versus wavelength), at a temperature T, is called theblackbody curve. [18]

Two things that are at the same temperature stay in equilibrium, so a body at

temperature T surrounded by a cloud of light at temperature T on average will emit as much

light into the cloud as it absorbs, following Prevost's exchange principle, which refers

to radiative equilibrium. The principle of detailed balance says that there are no strange

correlations between the process of emission and absorption: the process of emission is not

affected by the absorption, but only by the thermal state of the emitting body. This means that

the total light emitted by a body at temperature T, black or not, is always equal to the total

light that the body would absorb were it to be surrounded by light at temperature T. [18]

1.1.7. Stefan-Boltzmann Law

The Stefan-Boltzmann law states that the emissive power, P, from a black body is

directly proportional to the forth power of its absolute temperature i.e.[23]

13

P= σ T4

where σ is the Stefan-Boltzmann constant,

σ= 5.6705 x 10-5 [erg-cm-2.K-4.sec-1]

The emitted power, P, for a non-black body with emissivity, ε, is[23]: 

P= εσT4

1.1.8. Kirchhoff’s Law

In thermodynamics, Kirchhoff's law of thermal radiation, or Kirchhoff's law for short,

is a general statement equating emission and absorption in heated objects, proposed by Gustav

Kirchhoff in 1859, following from general considerations of thermodynamic equilibrium and

detailed balance.

An object at some non-zero temperature radiates electromagnetic energy. If it is a

perfect black body, absorbing all light that strikes it, it radiates energy according to the black-

body radiation formula. More generally, it is a "grey body" that radiates with some emissivity

multiplied by the black-body formula. Kirchhoff's law states that[24]:

“At thermal equilibrium, the emissivity of a body (or surface) equals its absorptivity.”

Here, the absorptivity (or absorbance) is the fraction of incident light (power) that is

absorbed by the body/surface. In the most general form of the theorem, this power must be

integrated over all wavelengths and angles. In some cases, however, emissivity and absorption

may be defined to depend on wavelength and angle, as described below.

Kirchhoff's Law has a corollary: the emissivity cannot exceed one (because the

absorptivity cannot, by conservation of energy), so it is not possible to thermally radiate more

energy than a black body, at equilibrium. In negative luminescence the angle and wavelength

integrated absorption exceeds the material's emission, however, such systems are powered by

an external source and are therefore not in thermal equilibrium.

This theorem is sometimes informally stated as a poor reflector is a good emitter, and

a good reflector is a poor emitter. It is why, for example, lightweight emergency thermal

blankets are based on reflective metallic coatings: they lose little heat by radiation.

14

(Eq. 19)

(Eq. 20)

Kirchhoff’s Law

Qrad = εσAs(Ts4 – Tsurr

4) (W)

where,

ε, Surface of Emissivity

As, Surface of Area

σ, Stefan – Boltzmann Constant

15

(Eq. 21)

2. EXPERIMENTAL METHOD

2.1. The Aim of the Experiment

The aim of the experiment that is accomplished is examination of thermal conduction

and thermal radiation with a computer controlled equipment system. The practical objective

of the part I of the experiment is the demonstration of Fourier’s Law of Conduction,

observation of temperature gradient on a linear bar and circular disk. Solid phase is chosen for

the pure conduction and radiation demonstration, since fluids show convective heat transfer

properties at all conditions. Related data recorded by the computer is analyed and thermal

conductivities are calculated for conduction part of the experiment. The radiation part is

involved with the verification of inverse of the distant square law.

2.2. Description of Apparatus

Part I: Computer Controlled Conduction

o Saced-TCCC Software for computer

o TCCC equipment

o Conductor cylindirical bar with interchangeable brass (10 mm and 25 mm ID) and

stainless steel (25 mm ID) parts

o TCCC equipment, circular disk accessory made of brass

The equipment listed above are used in the thermal conduction part of the experiment. The

experimental data is recorded by the computer while the heat flux is subjected to brass and

stainless steel cylinders. All the sensors on the linear bar functioned well as well as the

sensors on the radial element of the equipment system.

Part II: Computer Controlled Radiation

o Saced-TXC Software for computer

o TXC-RC equipment

o Radiometer SR-1

o Plate with the thermocouple ST-1 (Black body)

Computer controlled thermal radiation experiment is done with the devices listed here.

The data for the radiation of the source directly on the radio meter is recorded on the data

sheet whereas the data for the blackbody radiation is recorded by the computer. The only

problem about the blackbody was the loose connection of the ST-1 plate on the equipment

system. The data are recorded when the ST-1 is holded by hand.

16

2.3. Experimental Procedure

PART I: Computer Controlled Conduction

Thermal conduction part of the experiment is started firstly with the 8 W power source

to reach the steady-state. The 25 mm ID Brass cylinder is attached to the experiment set-up

and temperature data is recorded with 11 thermo-sensors placed on equal distances. This data

acquisition is repeated for 8, 10, 12, 14 W heat fluxes.

Then, the 10 mm ID brass is attached to system and temperatures are recorded on each

sensor as well. The stainless steel with 25 mm diameter is plugged into the set-up and same

recordings are done at 8,10,12,14 W.

Conduction measeruments are completed with radial conduction experiment in which

a 110 mm diameter of radial brass disk is observed under 10, 15, 20 W heat rates. The

ralevent data are recorded for calculations.

PART II: Computer Controlled Radiation

Thermal radiation of a radiation source is measured by a radio meter firstly as a

reference. The distance of the radiometer is changed with time and different fluxes. The

radiation flux versus distance data is recorded for this section of experiment.

Then, ST-1 plate as a blackbody is plugged into the system. Same measurements are

done for ST-1 while the distance is changed by time. These data is recorded by computer.

17

3. RESULTS & DISCUSSION

3.1. Experimental Procedures Of Computer Controlled Conduction

3.1.1 Conduction in a Simple Bar

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

45

50

x (m)

T (°

C)

Figure 3.1 10 mm radius Brass For The intermediate Section T(°C) vs x(m) @8,10,12,14 W

The graph above shows that increasing heat flux increases the slope of eachline.

According to the graph, the distance is inversely proportional to the temperature different.

This can also be verified in Fourier’sLaw of Conduction. Theslope of heat fluxlines (Q),

denotes the temperature gradient (dT/dx). This is as well direct proportional to Fourier’s Law.

Temperature gradient increases when the heat flux (Q/A) is increased gradually. The highest

slope is obtained at highest Q which is 14 W. Consequently at the different Q values at the

same material ,it is seen dissimilar lines that they have distinc slopes from eachother.this

situation can be caused from the increasing of the temperature gradient.

18

0 2 4 6 8 10 12 140

5

10

15

20

25

30

35

40

x (m)

T (°

C)

Figure 3.2 25 mm radius Brass For The intermediate Section T(°C) vs x(m) @8,10,12,14 W

The graph above shows that increasing heat flux increases the slope of eachline.

According to the graph, the distance is inversely proportional to the temperature different.

This can also be verified in Fourier’sLaw of Conduction. Theslope of heat fluxlines (Q),

denotes the temperature gradient (dT/dx). This is as well direct proportional to Fourier’s Law.

Temperature gradient increases when the heat flux (Q/A) is increased gradually. The highest

slope is obtained at highest Q which is 14 W. Consequently at the different Q values at the

same material ,it is seen dissimilar lines that they have distinc slopes from eachother.this

situation can be caused from the increasing of the temperature gradient.

The only difference with the 25 mm and 10 mm radiusBrass is that increasing cross

sectional area does not yield a step slope.Heat flux is decreased when the cross sectional area

which is proportional to Radius is increased. Therefore, the slope of the lines for 25 mm and

10 mm Radius of Brass are different at same heat rate values (Q).

19

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

45

50

x (m)

T (°

C)

Figure3.3 25 mm radius Stainless Steel For The intermediate Section T(°C) vs x(m) @8,10,12,14 W

Stainless steel has a lower thermal conductivity (k) with respect to brass at same radii.

As well as the graphs above, the distance is inversely proportional to the temperature different

the slope verifies the Fourier’s Law of Conduction again. The slope of heat rate lines (Q),

denotes the temperature gradient (dT/dx). The slope of the stainless steel having a radius of 25

mm is steeper at higher temperature gradients than 25 mm brass.According to Fourier’s Law,

the differences of the temperature gradients between brass and stainless steel shows that

stainless steel has a lower conductivity.

20

3.1.2.Conduction in a Radial Element

0 1 2 3 4 5 6 70

5

10

15

20

25

30

35

r (m)

T (°

C)

Figure 3.4 110 mm radius S. Steel For The intermediate Section T(°C) vs x(m) @ 8,10,12,14 W

Conduction in a radial element also obeys the Fourier’s Law. The difference between

the linear conduction and radial conduction is that radial conduction is expressed in radial

coordinates whereas the linear conduction is expressed in cartesian coordinates. This

difference causes that the curve is more concave at radial coordinates. Since these curves are

more concave than the linear conduction lines, the decreasing of the temperature gradients is

faster. it is caused from the Formula of the radial coordinate systems. Should the occasion

arise ,the difference of the heat source to at the end of the radial distance is expressed as

ln(r1/r2) .For the reason of this difference at the Formula increases to the temperature gradient

through the higher value.

21

3.1.3 Radiation Heat Transfer

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.150

50

100

150

200

250

300

350

400

f(x) = 5898.9731825878 x − 540.306335681906R² = 0.88372869014085

1/ X2 (m-2)

R (W

/m

2)

Figure 3.5 Inverse Square Law At Radiation Heat Transfer, R(W/m2) vs 1/ X2 (m-2)

The inverse of distance squares (1/ X2 ) and thermal radiation flux (R) is plotted on

the graph above. As shown on the graph, radiation flux is direct proportional to inverse of the

distance squares. The inverse-square law is very common in physics and states that the

strength of a physical quantity is inversely proportional to the square of the distance from the

source of that physical quantity.Typical examples of the inverse square law can be found in

the study of light, gravitation and acoustics. A radiation sensor measures the relative intensity

of the incident thermal radiation. It displays the measured intensity as a voltage when

connected to a voltmeter. If it is considered the lamp to be the source of radiation, then the

measured intensity will decrease as you move the sensor away from it.

22

Table 3.1. Average k Values That İs Calculated Using The Fourier’s Law

Material Radius(mm)

ktheoretical [25]

(W/m C°)kexperimental, average

(W/m C°)%Error

Brass 10 111 503,00 % 353,15

Brass 25 111 146,34 %31,83

Stainless Steel

25 16 80,38 % 402,3

Table 3.2. Average k Values Of The Heating And Cooling Reagions Of The Simple Conduction Heat Transfer Device

Material Radius(mm)

ktheorical

(W/mC°)k experimental,average

(W/m C°) (Heating reagion)

k experimental,average

(W/m C°)(Cooling reagion)

%Error(Heatin

g reagion)

%Error(Cooling reagion)

Brass 110 111 488,2 136,4

23

Table 3.3. Kirchhoff’s Law - Radiation Heat Transfer

Time(s) Q/Aexp.(W/m2) Q/Atheo. (W/m2) % Error

100 28,42 59,47 52,20

110 30,10 60,8 50,50

120 33,16 63,29 47,59

130 37,93 76,53 50,43

140 42,04 68,35 38,50

150 47,77 71,45 33,14

160 52,55 74,41 29,37

170 54,77 77,7 29,24

180 60,63 80,85 25,00

Table 3.4. Unsteady State Condition - Radial Coordinate System

Q (W) ktheoretical (W/mK) kexperimental(W/mK) % Error

10 111 102.2 7.47

15 111 76.7 30.9

20 111 127.5 14.8

4. CONCLUSION

24

Basic heat transfer mechanisms are observed in this experiment. Parameters which

effect thermal conductivity of materials are discussed. Main aim of the experiment is to

determine the thermal conductivity values of brass and stainless steel. It is learned that

thermal conductivity depends on chemical composition, phase, crystalline structure,

homogeneous material or not, temperature and pressure. Thermal conductivity of metals is

directly proportional to the absolute temperature and mean free path of the molecules. In pure

metals thermal conductivity decreases with increasing temperature. But presence of impurities

or alloying elements, even in minute amounts, thermal conductivity increases with

temperature.

For the first part of the experiment, Brass cylinders having different radii is used to show

the relation between cross sectional area and the temperature gradient. For brass 25 mm

kexperimental,average is found to be 146,34 W/m C°. %31,83 error ratio is obtained for this result.

Similarly, brass for 10 mm kexperimental,average is found to be 503,00 W/m C° an also percent error

is % 353,15. For stainless steel which has 25 mm radius, kexperimental,average is found to be 80,38

W/m C° and percent error is 402,3 .

Some errors are present while determining the thermal conductivity of brass and

stainless steel. It might be caused even if the situation of the system is unsteady state, it is

used the Fourier’s law that is suitable for only steady state systems. And if we waited more

along time for getting of the system to the steady state condition, more sensitive results could

have gained.

First part of the experiment is completed with the calculation of thermal conductivity

from unsteady state radial conduction measurements. Using the graph that is attached on

appendix, k values for each heat rates are obtained by using the trial and error method. At

Q=10,15,20 W, percent errors are %7,47,%30,9,%14,8. This errors were occurred because

some mistakes can be done while reading the k/hr values from the chart because it is really

difficult to read the exact value from the chart.

The thermal radiation is examined in the second part of the experiment. Radiative heat

transfer to a black body is measured for this part. Relatively lower error ratios are calculated

as presented above. The error is caused due to the existence of other heat transfer mechanisms

while the source is emitting thermal radiation.

5. NOMENCLATURE

25

AcdE

: Area (m2): Speed of Light: Thickness (m): Amount of Energy

hkLP

: Planck’s Constant: Thermal Conductivity: Length (m): Emitted Power

qx : Heat Rateqx

’’  Q

: Heat Flux: Heat Transfer Rate

r : Radius (m)Rt

: Resistance (K/W): Time (s)

Ts

Tsurr

Uv

: Temperature of Surface: Temperature of Surrounding: Overall Heat Transfer Coefficient: Frequency

Greek lettersλσεηρατα

: Wavelength: Stefan-Boltzmann Constant: Surface of Emissivity: Number of Wave: Reflectivity: Absorbtivity: Transmissivity: Absorptivity

6. REFERENCES

26

[1] http://www.efunda.com/formulae/heat_transfer/home/overview.cfm[2] Malooney, J. O., Perry's Chemical Engineering Handbooks, 8th Ed., Section 5: Heat and Mass Transfer, pg. 5.3, 5-16,[3] http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.html[4] http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/imgheat/htcd1.gif[5] http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/imgheat/cvec.gif[6] http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/imgheat/convectpot.gif[7] http://en.wikipedia.org/wiki/Heat_transfer[8] http://upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Hot_metalwork.jpg/300px-Hot_metalwork.jpg[9] http://www.efunda.com/formulae/heat_transfer/radiation/overview_rad.cfm[10] http://en.wikipedia.org/wiki/Conduction_(heat)[11] Gebhart, Heat Conduction and Mass Diffusion, McGraw-Hill, 1993, p. 399.[12] http://en.wikipedia.org/wiki/Thermal_conductivity[13] Young, Hugh D., University Physics, 7th Ed. Table 15-5. Values for diamond and silica aerogel from CRC Handbook of Chemistry and Physics.[14] http://www.cdeep.iitb.ac.in/nptel/Mechanical/Heat%20and%20Mass%20Transfer/Conduction/Module%202/main/2.6.1.html[15] http://en.wikipedia.org/wiki/File:Electromagnetic-Spectrum.png[16] http://www.taftan.com/thermodynamics/RADIAT.HTM[17] http://en.wikipedia.org/wiki/Thermal_radiation[18] http://en.wikipedia.org/wiki/Black_body[19] G. Kirchhoff (1860). On the relation between the Radiating and Absorbing Powers of different Bodies for Light and Heat, translated by F. Guthrie in Phil. Mag. Series 4, volume 20, number 130, pages 1-21, original in Poggendorff's Annalen, vol. 109, pages 275 et seq.[20] M. Planck (1914). The theory of heat radiation, second edition, translated by M. Masius, Blackiston's Son & Co, Philadelphia[21] Robitaille, P. (2003). "On the validity of Kirchhoff's law of thermal emission". IEEE Transactions on Plasma Science 31: 1263. doi:10.1109/TPS.2003.820958[22] "Science: Draper's Memoirs". The Academy (London: Robert Scott Walker) XIV (338): 408. Oct. 26, 1878.[23] J. R. Mahan (2002). Radiation heat transfer: a statistical approach (3rd ed.). Wiley-IEEE. p. 58. ISBN 9780471212706.[23] http://www.taftan.com/thermodynamics/BOLTZMAN.HTM[24] http://en.wikipedia.org/wiki/Kirchhoff%27s_law_of_thermal_radiation[25] Computer Controlled Radiation, Conduction, Experiment Sheets, Hacettepe University, 2010

7. APPENDICES

27

APPENDIX – 1DATA SHEET (Computer Format)

Brass 10 mm

ST-10 ST-11 SW-1

21,45921,27429 7,71417

21,43719

21,29288

7,843885

21,462221,27977

7,804818

21,45245

21,27752

7,822628

21,44002

21,30422

7,849949

21,47049 21,3522

7,837948

21,48496

21,40167

7,954066

21,54284

21,45043

7,822819

21,59668

21,50066

7,868398

21,61051 21,527

7,864696

21,60378

21,50446

7,760451

21,59786

21,53458

7,784198

21,62486 21,5385 7,7026821,63001

21,51562

7,710915

21,61224

21,51684

7,695722

21,61255

21,49637

10,23276

21,586121,46841

10,29506

21,56298

21,46023

10,30942

21,5412 21,4442 10,2766

5 7

21,529521,41262

10,17901

21,50333

21,39683

10,16598

21,51079

21,33693

10,11511

21,5011 21,307610,19854

21,50637

21,31341

10,13062

21,51957 21,3135

10,14798

21,53047

21,31722

10,19158

21,55984

21,32643

10,12085

21,55878 21,3369

10,19165

21,5521,32461

10,32557

21,58053

21,33358

17,47929

21,6025 21,3578 12,011821,62592

21,34365

11,99865

21,65194

21,39558

12,00727

21,70379

21,40057

12,02086

21,71556

21,43428

11,98499

21,72926

21,39467

12,12696

21,74958 21,4125

12,00899

21,77408

21,44079

11,83255

21,78877

21,46491 11,8967

21,81222

21,47303

11,99546

28

21,83312

21,46759

11,95888

21,825921,49996

11,95486

21,86511

21,46969

11,91751

21,887921,50738

13,04275

21,90003

21,53038

14,43227

21,91663 21,5667

14,54022

21,95185 21,5775

14,39984

21,95566

21,58301

14,41759

21,97439

21,55116

14,27849

22,00894 21,6106

14,56645

22,02308

21,62347

14,31162

22,03167 21,6426

14,63616

22,0606 21,7032 14,5326

4 822,09437

21,71047

14,62499

22,09294 21,722

14,50849

22,13471

21,72191

14,47498

22,15302

21,73387

14,35848

22,18729

21,74679

14,47651

22,214821,76538

14,37105

APPENDIX – 2THE GRAPH

29

30

APPENDIX - 3

ORIGINAL DATA SHEET

31

APPENDIX - 4

SAMPLE CALCULATIONS

32