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
Top Related