1. HEAT TRANSFER MAPPING OF DRUM
FLAKER(CHILLROLLS)
A MAJOR PROJECT REPORT
Submitted in partial fulfillment of the
requirements for the award of the degree
of
Master of Technology
in
CHEMICAL ENGINEERING
(With Specialization in Process Design Engineering)
By
MEDHA SINGH
DEPARTMENT OF CHEMICAL ENGINEERING
UNIVERSITY OF PETROLEUM & ENERGY STUDIES, DEHRADUN
UTTARAKHAND-248007, INDIA
April -2016
2. 2
CANDIDATE’S DECLARATION
I hereby declare that the work, which is being presented in this dissertation, Entitled “TOPIC’’,
submitted in partial fulfillment of the requirement for award of the degree of Master of
Technology in Chemical Engineering with the specialization in Process Design Engineering
(PDE), is an authentic record of my own work carried out under the supervision of , Professor,
Department of Chemical Engineering, University of Petroleum & Energy Studies, Dehradun and
Guide 2 Name from industry.
Date - 20th April, 2016
Place – Dehradun Medha Singh
This is to certify that the above statement made by the candidate is correct to the best of my
knowledge.
Ms Ankitha R Kartha
Professor, Dr Rajeshwar Mahajan NMB Plant Head
Department of Chemical Engineering Hindustan Unilever Limited,
University of Petroleum & Energy Studies Haridwar Uttarakhand
Dehradun, Uttarakhand-248007
INDIA
3. 3
ACKNOWLEDGEMENT
I am using this opportunity to express my gratitude to everyone who supported me
throughout the course of this M.Tech project. I am thankful for their aspiring guidance,
invaluably constructive criticism and friendly advice during the project work. I am sincerely
grateful to them for sharing their truthful and illuminating views on a number of issues related to
the project.
I express my warm thanks to Ms Ankitha R Kartha for their support and guidance at Hindustan
Unilever Ltd.
I would also like to thank my project internal guide Dr .Rajeshwar Mahajan and all the people
who provided me with the facilities being required and conductive conditions for my M.Tech
project.
Dated: April 20th 2016 Medha Singh
Place:Dehradun
4. 4
ABSTRACT
This report explores the parametric influence of spray cooling for thick walled metal drum with a
thin layer of soap on it. Using the point-source depiction of a spray, an analytical model is
derived to determine the heat and mass balance throughout the system. By setting boundary
conditions for the sprayed portion a heat diffusion model is constructed. This mathematical
model would help in heat transfer mapping and will provide a temperature curve for every point
along the sprayed surface.
5. 5
Contents
CANDIDATE’S DECLARATION.........................................................................2
ACKNOWLEDGEMENT.......................................................................................3
ABSTRACT..............................................................................................................3
LIST OF FIGURES .................................................................................................7
LIST OF TABLES ...................................................................................................8
NOMENCLATURE.................................................................................................9
1. INTRODUCTION ...........................................................................................11
2. LITERATURE REVIEW...............................................................................14
2.1 Working Principle and Parameters ............................................................15
2.2 Features Of The Drum Flaker(Chill rolls).................................................16
2.3 Specifications.................................................................................................16
2.3.1 The Drum ................................................................................................16
2.3.2 Coolant Circulation................................................................................17
2.3.3 Scrapper Assembly.................................................................................17
2.3.4 The Drum’s Material..............................................................................17
2.4 The Purpose Of Flaking ...............................................................................18
2.5 Parameter and the Tendency of the Product.............................................18
2.6 Types of nozzles.............................................................................................19
2.6.1 Hollow cone nozzles-Disc and core type...............................................20
2.6.2 Flat Fan Nozzles......................................................................................20
2.6.3 Floodjet nozzles.......................................................................................20
2.7 Cooling System In The Drum......................................................................20
6. 6
2.8 Applications...................................................................................................22
2.8.1 Food industry ..........................................................................................22
2.8.2 Fine Chemical..........................................................................................22
2.8.3 Healthcare ...............................................................................................22
3. MATHEMATICAL MODELLING.................................................................23
3.1 Methodology..................................................................................................23
3.2 Mathematical Modelling ..............................................................................23
3.3 Assumptions:.................................................................................................24
3.4 Mass balance for semi-differential control volume of water flowing in the
z direction inside the pipe...................................................................................24
3.5 Heat Balance for the water flowing inside drum......................................25
3.6 Heat Transfer Through The Walls. ............................................................26
3.7 Mass Balance For The Cake .......................................................................27
3.8 Heat Transfer Balance (Cake).....................................................................28
4. SOLUTION........................................................................................................30
4.1 Final Equations To Solve .............................................................................30
5. RESULT AND DISCUSSION........................................................................33
6. REFERENCES ................................................................................................36
APPENDIX.............................................................................................................37
7. 7
LIST OF FIGURES
No of Figure Name of Figure Page No
2.1 Drum flaker (Chill Roll) 15
2.2 Over of Drum flaker (Chill Roll) 16
2.3 Spray Nozzle Configuration 19
2.7.1 Full water type 21
2.7.2 Jacket type 21
2.7.3 Sprayer type 21
3.6.1 Assumed Flow Model (Heat and Fluid) Inside the Drum 27
8. 8
LIST OF TABLES
No of Table Name of Table Page No
2.5.1 Table of Parameter and
Tendency
18
9. 9
NOMENCLATURE
Vz(z) mean z- velocity of liquid inside pipe
Δ(z) thickness of the (“boundary” layer )of liquid in the drum
qw flow rate of water being sprayed inside the drum (constant)
𝑚3/𝑠
𝑚2 𝑎𝑟𝑒𝑎
T(z) mean temperature of the water flowing inside the drum
Twf temperature of the water being sprayed (constant)
Rp inside radius of the pipe
Q(z) heat flux (kj/m2
s)
T0(z) temperature of the outer wall
km thermal conductivity (kj/m-s-k) of the metal
tm thickness of metal wall
tcake thickness of cake
ya*(r,z) mass fraction of water (a) in cake at (r,z)
cpw specific heat of water
Dab mass diffusivity of a through cake(constant)
Ky mass transfer coefficient in the air film
ya**(z) mass fraction at equilibrium with mass fraction at outer film
yab mass fraction in atmosphere
Tair temperature of air in the bulk
Tcake temperature of cake
kcake thermal conductivity of cake
10. 10
Greek symbols
λw (Tcake) latent heat of vaporization of water at cake temperature r = (Rp +tm+tcake)
ρ density of water
11. 11
1. INTRODUCTION
Hindustan Unilever Limited (HUL) is India's largest Fast Moving Consumer Goods Company
with a heritage of over 80 years in India and touches the lives of two out of three Indians.
HUL works to create a better future every day and helps people feel good, look good and get
more out of life with brands and services that are good for them and good for others.
With over 35 brands spanning 20 distinct categories such as soaps, detergents, shampoos, skin
care, toothpastes, deodorants, cosmetics, tea, coffee, packaged foods, ice cream, and water
purifiers, the Company is a part of the everyday life of millions of consumers across India. Its
portfolio includes leading household brands such as Lux, Lifebuoy, Surf Excel, Rin, Wheel, Fair
& Lovely, Pond’s, Vaseline, Lakmé, Dove, Clinic Plus, Sunsilk, Pepsodent, Closeup, Axe,
Brooke Bond, Bru, Knorr, Kissan, Kwality Wall’s and Pureit.
The Company has over 16,000 employees and has an annual turnover of INR 30,170 crores
(financial year 2014 – 15). HUL is a subsidiary of Unilever, one of the world’s leading suppliers
of fast moving consumer goods with strong local roots in more than 100 countries across the
globe with annual sales of €48.4 billion in 2014. Unilever has 67.25% shareholding in HUL.
In 1931, Unilever set up its first Indian subsidiary, Hindustan Vanaspati Manufacturing
Company, followed by Lever Brothers India Limited (1933) and United Traders Limited (1935).
These three companies merged to form HUL in November 1956; HUL offered 10% of its equity
to the Indian public, being the first among the foreign subsidiaries to do so. Unilever now holds
67.25% equity in the company. The rest of the shareholding is distributed among about three
lakh individual shareholders and financial institutions.
The erstwhile Brooke Bond's presence in India dates back to 1900. By 1903, the company had
launched Red Label tea in the country. In 1912, Brooke Bond & Co. India Limited was formed.
Brooke Bond joined the Unilever fold in 1984 through an international acquisition. The erstwhile
12. 12
Lipton's links with India were forged in 1898. Unilever acquired Lipton in 1972, and in 1977
Lipton Tea (India) Limited was incorporated.
Pond's (India) Limited had been present in India since 1947. It joined the Unilever fold through
an international acquisition of Chesebrough Pond's USA in 1986.
Since the very early years, HUL has vigorously responded to the stimulus of economic growth.
The growth process has been accompanied by judicious diversification, always in line with
Indian opinions and aspirations.
The liberalisation of the Indian economy, started in 1991, clearly marked an inflexion in HUL's
and the Group's growth curve. Removal of the regulatory framework allowed the company to
explore every single product and opportunity segment, without any constraints on production
capacity.
Simultaneously, deregulation permitted alliances, acquisitions and mergers. In one of the most
visible and talked about events of India's corporate history, the erstwhile Tata Oil Mills
Company (TOMCO) merged with HUL, effective from April 1, 1993. In 1996, HUL and yet
another Tata company, Lakme Limited, formed a 50:50 joint venture, Lakme Unilever Limited,
to market Lakme's market-leading cosmetics and other appropriate products of both the
companies. Subsequently in 1998, Lakme Limited sold its brands to HUL and divested its 50%
stake in the joint venture to the company.
HUL formed a 50:50 joint venture with the US-based Kimberly Clark Corporation in 1994,
Kimberly-Clark Lever Ltd, which markets Huggies Diapers and Kotex Sanitary Pads. HUL has
also set up a subsidiary in Nepal, Unilever Nepal Limited (UNL), and its factory represents the
largest manufacturing investment in the Himalayan kingdom. The UNL factory manufactures
HUL's products like Soaps, Detergents and Personal Products both for the domestic market and
exports to India.
13. 13
1.1 Motivation for the work
In Hindustan unilever Limited, in NMB plant (soap plant). The drum flaker is used primarily to
process chemical and pharmaceutical products. The drum flaker transforms a molten product into
a solid. The process that takes place is a solidification and/or crystallisation process. The product
begins to solidify the moment it comes into contact with the cold, rotating drum. After one
revolution the completely solidified layer is removed from the drum by a knife and typically
breaks into easy to handle flakes. It is suitable to produce soap flakes at a temperature of 38-
40°C approx. from liquid soap at 80-90°C. But the problem arises when the drum’s temperature
increases upto 35°C, which has to be maintained at 15-17°C.
I took this project as this is a real life industrial problem, where I can apply my basics and logic
of transport phenomena to build a mathematical model of this whole process.
The objectives of this study are as follows
To develop a mathematical model.
To examine the effects of operating parameters.
Development of computer programme to solve the mathematical model in MATLAB .
14. 14
2. LITERATURE REVIEW
The drum flaker is used primarily to process chemical and pharmaceutical products.
However, more and more applications for these machines are also being found in the food
industry. The closed design is ideally suited for processing of toxic or offensively smelling
products. With the drum flaker, a molten product is converted into a solid form.
A thin layer of the liquid product adheres to the outside of the rotating, internally cooled drum in
a continuous process. Heat is extracted from the product by contact with the cooled drum
surface, and the product solidifies and cools to the required final temperature. A stationary knife
removes and breaks up the solidified layer.
The required flake size is achieved by controlling circumferential speed, layer thickness, and
knife angle. Careful design ensures optimum use of the drum surface area to maximize capacity
at the chosen operating conditions. The drum flaker is primarily used to produce flakes, but there
are also ways of converting your product into easily manageable pastilles or prills.
It has a two, counter-rotating stainless steel rolls equipped with a sprayer with nozzles from
which cold water is sprayed around the inner surface of the drum, to give a uniform heat
transmission.
The drums are equipped with rotary joints for proper water distribution and consistent water
recycling through siphon. Separate motor-reducers drive each drum and the product discharge
conveyor
These independent drives allow easy maintenance and flexibility of operation. Liquid soap
slurry falls on the rolls that spread it evenly among them, in a 0,3 — 0,5 mm thick layer that is
quickly cooled down and solidified.
15. 15
Product is then scraped off the rolls, by the doctor blades, in form of flakes and fall onto a
discharge conveyor belt. It is suitable to produce soap flakes at a temperature of 38-40°C approx.
from liquid soap at 80-90°C.
To maintain this surface temperature a detailed study has been done on the structure and the
whole process.
2.1 Working Principle and Parameters
A detailed literature review has been done to understand the process of chill roll (drum flaker).
Liquid soaps slurry falls on the rolls that spread it evenly among them, in a 0.3 — 0.5 mm thick
layer that is quickly cooled down and solidified.
Product is then scraped off the rolls, by the doctor blades, in form of flakes and fall onto a
discharge conveyor belt. It is suitable to produce soap flakes at a temperature of 38-40°C approx.
from liquid soap at 80-90°C.
Figure 2.1 Drum flaker (chill rolls)
16. 16
Figure 2.2 Overview of Drum Flaker (Chill rolls)
2.2 Features of the Drum Flaker (Chill rolls)
The Drum Flaker enables processing of molten products into excellent quality flakes. The well-
considered concept of the drum flaker has led to a number of features:
• Compact unit, little floor space required;
• Completely closed cooling system, absolutely no cross-contamination between cooling medium
and product;
• Low operational and maintenance costs
• Gastight enclosures
• Easy inertisation of the process;
• Unit designed with good access for maintenance and cleaning
• Construction material ranges from carbon steel to various grades of stainless steel, Haste alloy,
etc.
2.3 Specifications
2.3.1 The Drum
Cooling drums are available in a choice of materials selected in accordance with the chemical
properties and adhesion ability of the product to be processed. The materials range from fine
grain cast iron and carbon steel to Haste alloy, etc. The drums are specially designed for
maximum geometric stability. Distortion due to differential temperature gradient or mechanical
forces is
17. 17
impossible in normal operation. The drum design ensures equal heat transfer over the entire
drum surface, ensuring uniform flake size distribution. For products with poor adhesion to metal
surfaces, drums with special grooved surfaces are available.
2.3.2 Coolant Circulation
When liquid refrigerants are used, these are sprayed by a central spray tube over the internal
drum surface. The turbulent flow ensures maximum heat transfer over the full drum surface,
including over shell ends and heads. Consequently, an equal temperature is guaranteed over the
total length of the drum, resulting in uniform flakes with low fines content. The liquid is
siphoned off from the lowest part in the drum to avoid an accumulation of refrigerant there.
The siphoning action is assisted by some slight overpressure inside the drum. The entire system,
made of stainless steel, is easily detachable without disassembly of the drum. This design enables
feed and discharge of the refrigerant through one and the same shaft, while the other shaft is used
for the drive. Moreover it offers excellent accessibility to the inside of the drum for cleaning and
inspection. Some options are available, such as refrigeration through direct evaporation of Freon
or ammonia.
2.3.3 Scrapper Assembly
Rigid construction designed to ensure a uniform pressure against the drum over the full length
and to eliminate vibrations. The knife pressure is effected and controlled by means of a
pneumatic pressing system. For entirely enclosed machinery, the knife’s pressing system is
located outside the process environment. Scraper knives are available in a range of materials,
from steel to technical plastics. The flake size can be determined in advance by the choice of
scraper system.
2.3.4 The Drum’s Material
The drums are mostly made of stainless steel. Besides the choice of many types of stainless steel,
chromium-plated, Haste alloy, or cast iron drums are also possible. The exact choice will depend
on your product, the work site environment, available space, and the process to be performed.
The result is a durable drum with high dimensional stability and uniform heat distribution over
its entire surface.
18. 18
2.4 The Purpose of Flaking
The purpose of flaking is to cool and solidify fusion liquid. The solidified product is shaped thin
flake. The flake is capable of conveyance, safekeeping, transportation, and discharging.
2.5 Parameter and the Tendency of the Product
When the following parameter is changed, it’s possible to change the several conditions of the
flake.
・Rotation speed of the drum
・Temperature of the cooling water
・Clearance of the drum and the levelling roll
Table 2.5.1 Table of Parameter and Tendency
19. 19
Fig. 2.3 Spray nozzle configuration
This is a spray nozzle arrangement along the axis of a cylindrical thick-walled tube. Water is fed
through an axial supply channel that is fitted with radial oriented spray nozzles. The supply
channel and nozzles are fully retractable. They are inserted initially along the axis after the
heated part is removed from the furnace to initiate the quench, and retracted upon completion of
the quench. To maximize spray impact area and ensure both effective
and predictable spray distribution, the nozzles are positioned such that the spray impact zones
along the inner curved surface of the tube are tangent to one another with no spacing or overlap.
This arrangement limits the nozzle-to-surface distance to less than the radius of the tube.
2.6 Types of nozzles
A spray nozzle is a precision device that facilitates dispersion of liquid into a spray. Nozzles are
used for three purposes
To distribute a liquid over an area.
To increase liquid surface area.
To create impact force on a solid surface.
20. 20
A wide variety of spray nozzle applications use a number of spray characteristics to describe the
spray.
2.6.1 Hollow cone nozzles-Disc and core type
These are used primarily where plant foliage penetration is essential for effective insect and
disease control, and where drift is not a major consideration. At pressures of 40 – 8- psi hollow
cone nozzles give excellent spray coverage to the undersides of reduces penetration
correspondingly
2.6.2 Flat Fan Nozzles
Flat Fans are most commonly used spray nozzles. They produce a range of droplet sizes from
coarser to finer depending on pressure which makes them suitable to use. Flat Fan provides a
very good spray distribution over a wide range of pressures.
2.6.3 Flood jet nozzles
These are ideal for high application rates and speeds, because they produce a wide-angle, flat fan
pattern. Operating flood-jet nozzles at 5-25 psi minimizes drift, but pressure changes critically
affect the width of the spray pattern.
Generally, the spray generated by the flood jet is not as uniform as the flat-fan type.
2.7 Cooling System in the Drum
There are 3 ways of cooling system of drum flake
1- Cooling water is filled in the lower half inside the drum. The structure is easiness, but because
the water which became lukewarm is left, the cooling ability falls.
21. 21
.
Figure 2.7.1: Full water type
2- Cooling water flows in the jacket. Without being left, lukewarm water will be discharged
immediately
Figure 2.7.2: Jacket type
3- Cooling water is sprayed in the drum. The ability is high, but refuse is sometimes jammed
into a sprayer nozzle. Compressed air is needed.
Figure 2.7.3: Sprayer type
22. 22
2.8 Applications
Chilled roll flaker is a multi-purpose drying device. It is generally used in industries where the
product is temperature sensitive. Some examples are stated below
2.8.1 Food industry
1. Cheese
2. Chocolate
3. Dough
4. Vegetables
2.8.2 Fine Chemical
1. Fatty acids
2. Oleo chemicals
3. Phtalic Anhydride
4. Maleic Anhydride
5. Calcium Chloride
6. Caprolactam
7. Resins
8. Bisphenol A
9. Sulphur
2.8.3 Healthcare
1. Stearate
2. Soaps
23. 23
3. MATHEMATICAL MODELLING
3.1 Methodology
The objective of my project is to study and Construct a heat transfer model of the system by heat
and mass balance of the overall system to trouble shoot the problem of overheating the surface
.Modelling requires understanding of engineering systems.
– By observation and experiment.
– Theoretical analysis and generalization.
– Assumptions.
Modelling of this system includes taking a small section and forming differential equation for it.
Then solving it with some boundary conditions, to get heat and mass balance equations which
can be solved using MATLAB to get temperature profile, velocity profile and of the system.
3.2 Mathematical Modelling
Mathematical modelling is the art of translating problems from an application area into tractable
mathematical formulations whose theoretical and numerical analysis provides insight, answers,
and guidance useful for the originating application.
Mathematical modelling
is indispensable in many applications
is successful in many further applications
gives precision and direction for problem solution
enables a thorough understanding of the system modelled
prepares the way for better design or control of a system
allows the efficient use of modern computing capabilities
24. 24
Learning about mathematical modelling is an important step from a theoretical mathematical
training to an application-oriented mathematical expertise, and makes the student fit for
mastering the challenges of our modern technological culture.
3.3 Assumptions:
• Constant flow of fluid
• Stationary system.
• constant density and viscosity
• Heat transfer only through conduction and convection
• flow in only z direction
3.4 Mass balance for semi-differential control volume of water flowing in the z
direction inside the pipe.
Steady state
Vz2πRp. δ(z) + qw. dz2πRp = Vz2πRp. δ(z) + qw. dz + 2πRp(Vzδ)dz
Or
2πRp.
d(Vz.δ)
dz
. dz = qw. dz2πRp
Or
2πRp.
d(Vz. δ)
dz
= qw2πRp
After cancelling all the common terms we get
d(Vz.δ)
dz
= qw (3.1)
25. 25
Integrate above equation over z
Vzδ = qwz + C1
Boundary conditions
At z = 0, Vz = δ = 0 therefore C1 = 0
We get
Vzδ = qwz (3.2)
3.5 Heat Balance for the water flowing inside drum.
Cold water is being sprayed inside the drum, spreads evenly inside at the wall of the drum. This
flowing water takes heat from the cake (falling on the outer surface of the drum) through the
metal wall. Water which are spraying inside the drum gets collected at the bottom forming a
thick layer which is increasing due to syphoning process. As this whole process is a continuous
process i.e at the same time the cold water is coming in and the hot water is going out.
Considering Heat is transferring from outside to inside through the walls of the drum (metal
wall) to water.
ρw[Vz. 2πRp. δ]Cpw + ρw[2πRp. dz]qw. Cpw. Twf = ρw 2πRpCpwVz. Δ.T + ρw
2πRpCpw
d
dz
(Vz δT)dz -Q 2πRpdz
After cancelling all the common terms we get,
qwTwf =
d
dz
(VzδT) +
Q
Cpwρw
(3.3)
From equation (2) substitute the value of Vzδ
26. 26
qw. Twf =
d
dz
(qwz. T) +
Q(z)
Cpwρw
Or
qw. Twf = qw
d
dz
(z. T) +
Q(z)
Cpwρw
Or
qw. Twf = qw [z
dT
dz
+ T. 1] +
Q(z)
Cpwρw
Or
qw (Twf − T) = qw z
dT
dZ
+
Q(z)
Cpwρw
(3.4)
3.6 Heat Transfer through the Walls.
Heat is transferred from cake to the metal wall followed by conduction process.
Fourier’s law of conduction
Q(z) =
Km (T(z) − T0)
tm
(3.5)
27. 27
Fig 3.6.1 Assumed Flow Model Inside The Drum (Heat and Fluid)
3.7 Mass Balance For The Cake
Assuming only radial direction
a = water
b = solid
ya*= fraction of a at (r,z)
In this process when hot soap slurry falls on a drum , it contains some moisture. After several
rotations this moisture diffuses into the atmosphere and then the mixture becomes solid.
A small portion from cake is considered let’s say r , r+dr in radial direction through which liquid
is diffusing into the atmosphere.
28. 28
Mass Balance (steady state)
In-Out=0
-
-Dab.2πrdz.
dya
∗
dr
-[- Dab.2πrdz.
dya
∗
dr
- Dab.2πdz.
d
dr
(r .
dya
∗
dr
)dr ]=0
or
d
dr
[r
dya
∗
dr
] = 0 (3.6)
Boundary Conditions
At r = Rp + tm
dya
∗
dr
= 0
At r = Rp + tm + tcake
−Dab.
dya
∗
dr
= −ky(ya ∗∗ −yab)
3.8 Heat Transfer Balance (Cake)
Heat transfer balance includes conduction and convection through the surface
−kcake. 2πrdz. Kcake. 2πdz (r
dTcake
dr
) − Kcake. 2πdz
d
dr
(r
dTcake
dr
) dr = 0
29. 29
Or
d
dr
[r
dTcake
dr
] = 0 (3.7)
Boundary conditions
At r = Rp + tm Tcake = T0
At r = Rp + tm + tcake
−Kcake. 2π(Rp + tm + tcake)dz
dTcake
dr
hair. 2π(Rp + tm + tcake )dz(Tair −
Tcake) = λw(Tcake). Ky(Ya
∗∗
− Yab). 2π(Rp + tm + tcake)
or
hair(Tair − Tcake) − kcake
dTcake
dr
= λw(Tcake). Ky(Ya
∗∗
− Yab) (3.8)
30. 30
4. SOLUTION
4.1 Final Equations To Solve
Vzδ = qwz (3.2)
qw (Twf − T) = qw z
dT
dZ
+
Q(z)
Cpwρw
(3.4)
Q(z) =
Km (T(z) − T0)
tm
(3.5)
d
dr
[r
dya
∗
dr
] = 0 (3.6)
Boundary Conditions
r = Rp + tm
dya
∗
dr
= 0
r = Rp + tm + tcake
−Dab.
dya
∗
dr
= −ky(ya − yi)
d
dr
[r
dTcake
dr
] = 0 (3.7)
31. 31
Boundary Conditions
At r = Rp + tm
Tcake = T0
At r = Rp + tm + tcake
hair(Tair − Tcake) − Kcake
dTcake
dr
= λw(Tcake). Ky(ya
∗∗
− yab)
After rearranging above equation
Vzδ = qwz (4.1)
dT
dz
= − (
km
ztmCpwρwqw
+
1
z
) T +
kmT0
ztmCpwρw
+
Twf
z
(4.2)
dya
∗
dr
=
ky
Dab
(ya
∗∗
− yab) (4.3)
ya
∗
= B −
B−B∗
ln(
r1
r2
)
. ln(r/r1 )
dTcake
dr
=
C1
r
(4.4)
32. 32
At r = r1 Tcake = T0
At r = r2 −k
dTcake
dr
= λw. Tcake. ky(ya
∗∗
− yab) − hair(Tair − Tcake)
C1 = −
r2
k
[λw. Tcake. ky(ya
∗∗
− yab) − hair(Tair − Tcake)] =
(Tcake−T0)
lnr1
33. 33
5. RESULT AND DISCUSSION
This study examined the problem of spray cooling thick walled metal. An analytical model was
constructed to determine the temperature variation throughout the curved inner wall of the drum,
the computational model provides curves for every point within the sprayed surface of the wall.
This study examined the problem or increasing the surface temperature of drum flaker(chill
roll).Which could be improved by adjusting the flow rates, siphoning process, by adjusting
blades, by adjusting nozzle to inside surface length, by adjusting size of nozzle, spray angle.
Figure3.1 Shows straight line which means the velocity and the thickness of the water flowing
inside the drum increasing along the length of the drum.
Figure 3.1 velocity profile of water
0 0.5 1 1.5 2 2.5
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
Length (m)
(Vz*del)(m2/s)
34. 34
Figure 3.2 Shows the change in temperature (T) profile (mean temperature of the water flowing
inside the drum) along the length (L) of the drum. It first gradually increases and then becomes
constant. This is the temperature which has to be maintained below 6 ͦCelsius throughout the
process. Because this temperature causes the problem of overheating of the drum. If this
temperature remains constant below 6 ͦ Celsius automatically the temperature of the outer
surface of the drum will gradually decrease and could be maintained at the desired
temperature.
Figure 3.2 temperature (T) profile of water
0 0.5 1 1.5 2 2.5
4
4.005
4.01
4.015
4.02
4.025
4.03
4.035
4.04
4.045
length (m)
temperature(T)C
35. 35
Figure 3.3 Shows the change in mass fraction of the water (inside the cake) along the radius of
the drum. During the solidification process the amount of water in the cake gets evaporate into
the atmosphere.
Figure 3.3 Concentration profile of water in the cake
1.5 1.505 1.51 1.515 1.52 1.525 1.53 1.535
0.175
0.18
0.185
0.19
0.195
0.2
radius (m)
massfractionofwater(ya)
36. 36
6. REFERENCES
1 R.B.Bird , W.E.Stewart and E.N Lightfoot. Transport Phenomena. John Wiley & Sons,
New York. Second edition , 2002
2 Robert H Perry , Don W Green. Perry’s Chemical Engineers Handbook. Mc Graw Hill ,
New York. Seventh edition , 1999
3 N. Mascarenhas, I. Mudawar / International Journal of Heat and Mass Transfer 55 (2012)
2953–2964
37. 37
APPENDIX
MATLAB Solution
Solution for equation (1)
Chill roll call
function dT= chillroll(z,T)
qw=0.07;
clear all
clc
zspan=[0 2.5];
a0=0;
[z,a]=ode45('chillroll',zspan,a0)
plot(z,a)
xlabel('Length (m)');
ylabel('(Vz*del) (m^2/s) ');
Solution for equation (2)
function dT= chilltemp(z,T)
km=16.2;%W/mK
tm=.03;%m
cpw=4120;%kJ/kgK
rhow=1000;%kgm^-3
qw=0.07;%m^3/h
T0=15;%K
Twf=4;%K
% dT=-(km/(z*tm*cpw*rhow*qw)+1/z)*T+(km*T0)/(z*tm*cpw*rhow*qw)+Twf/z;
dT=((km/(tm*cpw*rhow*qw))-1)*(T/z)+(((km*T0)/(z*tm*cpw*rhow*qw))+Twf/z);
38. 38
Call Function
clear all
clc
zspan=[.01 2.5];
t0=4;
[z,T]=ode15s('chilltemp',zspan,t0);
plot(z,T);
xlabel('length (m)')
ylabel('temperature(T)C')
Solution for equation (3)
Mass balance
function dya=massbalance(r,ya)
ky=8*10^-6;
Dab=.3*10^-6;
yaeq=.04;
yab=.07;
dya=((ky/Dab)*(yaeq-yab));
clear all;
clc;
zspan=[1.503 1.533];
[r,ya]=ode45('massbalance',zspan,.2);
plot(r,ya)
xlabel('radius (m)');
ylabel('mass fraction of water(ya)');
