Post on 08-Mar-2023
IUBAT- International University of Business Agriculture and Technology
Founded 1991 by Md. Alimullah Miyan
COLLEGE OF ENGINEERING AND TECHNOLOGY(CEAT)
Course Title: Heat and Mass Transfer
Course Code : MEC 313
Course Instructor: Engr. Md. Irteza Hossain
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
Heat of Conduction through a hollow Cylinder
• Case : Uniform conductivity
Assumption:
• Length of the cylinder is very large compared to
diameter, so the heat flow only in radial direction
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
2
Heat of Conduction through a hollow Cylinder
As per Fourier's Law:
Boundary Condition
When t = t1 , r= r1
t= t2 , r= r2
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
3
dr
dtrkQ
dr
dtkAQ
rr
rr
2
th
r
R
t
kL
r
r
ttQ
2
ln
)(
1
2
2
1
Hot fluid
L
r2
r1
Heat of Conduction through a hollow Cylinder
• The thermal resistance
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
4
)2
)ln(1
2
kL
r
r
Rth
Heat of conduction through a composite cylinder
• Consider flow of heat through a composite cylinder as shown in the
following figure:
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
5
Heat of conduction through a composite cylinder
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
6
LrhLk
rr
Lk
rr
Lrh
ttQ
cfBA
hf
cfhf
3
2312
1 2
1
2
)/ln(
2
)/ln(
2
1
)(
outconvAconductiveAconductivei
cfhf
RRRR
ttQ
cov
)(
Heat flow through radial system
CBALk
rr
Lk
rr
Lk
rr
TTQ
2
)/ln(
2
)/ln(
2
)/ln(
)(
342312
41
thCthB RRR
TTQ
cylinderMultilayerforquationfloweheatThe
thA
)41(
:
Logarithmic Mean Area for Hollow Cylinder
• It is Consider convenient to have an expression for the heat flow
through a hollow cylinder of the same form as that for a plane wall
• r2- r1 is the equivalent wall thickness and Am is the equivalent
area of A
Where: Ai,Ao Inside and
area of the cylinder
Am = 2πrmL
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
10
)ln(Ai
A
AAA
o
io
m
oA
)ln(
)(2
1
2
12
r
r
rrLAm
Logarithmic Mean Area for Hollow Cylinder
The above Am is known as Logarithematic area of the
plane wall and hollow cylinder.
By use this expression a cylinder can be transformed in
to a plan e wall and the problem can be solved easily.
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
11
)(
)(
0 i
oim
RR
TTKAQ
Problem and solution
• A thick walled tube of stainless steel with 20 mm inner diameter
is covered with a 30 mm layer of asbestos insulation (K =0.2
W/m oC. If the insider wall temperature of the pipe is maintained
at 600 oC. and outside insulation at 1000 oC., cal
• calculate the heat loss per meter length.
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
12
Problem and solution
• A steel pipe with 50 mm OD is covered with a 6.4 mm
asbestos insulation ( K = 0.166 W/moK ) followed by a 25
mm layer of fiber glass insulation ( K= 0.0485 W/moK).
The pipe wall temperature is 393 oK and outside
insulation temperature is 311 oK. Calculate the interface
temperature between asbestos and fiber galss.
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
13
Problem and solution
• A pipe ( K= 180 W/moC) having inner and outer diameter 80 mm and
100 mm in a space at 25oC.Hot gases at temperature 160oC flow
through the pipe neglecting the surface heat transfer coefficient ,
calculate
• The heat loss through the pipe per unit length.
• The temperature a point half way between the inner and outer
surface
• The surface area normal to the direction of heat flow so that the
heat transfer through the pipe can be determined by considering
material of pipe as a plane wall of the same thickness
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
14
CRITICAL RADIUS OF INSULATION
• Insulation:
A material which retards the flow of heat with reasonable
effectiveness is known as insulation.
Insulation serves the following two purposes:
1. It prevents the heat flow from the system to the surroundings
2. It prevents the heat flow from the surrounding to the system
• Application:
1. Boiler and stem pipes
2. Air conditioning system
3. Food preserving stores and refrigerators
4. Insulation bricks ( in different furnace)
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
15
INSULATION OF PIPING:
CODES AND STANDARDS
• Insulation is often regulated by code requirements. The individual sections of any
code must be carefully read in order to determine how flame-spreading or smoke-
developing characteristics restrict the use of particular materials in specific areas
of a building.
INSULATION MATERIAL AND THICKNESS SELECTION
• The general criteria needed to make a choice among various insulation materials
are as follows:
o The reason insulation is needed
Condensation prevention
Reduction of heat loss
Personnel protection (max surface temperature ~49C [120F])
Noise reduction
o Service temperature expected
o Code requirements
o The location where insulation will be installed
o Accessibility for the insulated pipe
o Installed cost of the complete insulating system
CRITICAL RADIUS OF INSULATION
• Adding more insulation to a wall, i.e the thicker the
insulation the lower the heat transfer rate.
• This is expected since the heat transfer Area A is
constant and adding insulation always increases the
thermal resistance of the wall with out increasing the
convection resistance
• Adding insulation to a cylindrical pipe or a spherical
shell is different because : The addition insulation
increases the conduction resistance of the insulation
layer but decreases the convection resistance of the
surface because of the increase in the outer surface
area of the convection.
• The heat transfer from the pipe may increase or
decrease depending on which effect dominates.Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
19
Critical thickness of insulation for cylinder
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
20
•Considering a cylindrical pipe
•r 1 is the outer radius of pipe
•T1 constant surface temperature
•Insulation radius r2
•Surrounding temperature T∞
•Convective heat transfer
coefficient h
Critical thickness of insulation for cylinder
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
21
The variation of with outer radius of the insulation r2 is
plotted in Fig. The value of r2 at which q reaches a maximum
is determined from d /dr2=0( Zero slope)
Q
Q
Critical thickness of insulation for cylinder
• The relation represents the condition for minimum
resistance and consequently maximum heat flow rate.
• The insulation radius at which resistance to heat flow is
minimum is called “ critical radius( rcr )
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
22
h
krcr
Problem and solution
• A small electric heating application uses wire of 2 mm diameter with
0.8mm thick insulation ( k= 0.12 W/m oC ). The heat transfer
coefficient ( h) on the insulated surface is 35 W/m2 oC . Determine
the critical thickness of insulation in this case and percentage of
change in the heat transfer rate if the critical thickness is used,
assuming the temperature difference between the surface of the
wire and surrounding air remains unchanged.
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
23
Problem and solution• Calculate the critical radius of insulation for
asbestos(K=0.17W/moC) surrounding a pipe and exposed to
room air at 20oC with h = 30 W/m2oC). Calculate the heat loss
form a 200 oC, 5.0 cm dia pipe when covered with the critical
radius of insulation and with out insulation.
• Explain the effect of heat transfer using fiber glass insulation
(k=.04W/moC) considering the critical radius of fiber glass.
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
24
Engr. Md. Irteza Hossain, Faculty,
Mechanical Engineering
27
Problem and solution
Consider a 2-m high electric hot water heater that has a
diameter of 40 cm and maintains the hot water at 55 0C .
The tank is located in a small room whose average
temperature is 27 0C and the heat transfer coefficients on
the inner and outer surfaces of the heater is 50 and 12
W/m20C respectively. The tank is placed in another 46 cm
diameter sheet metal tank of negligible thickness and the
space between the two tanks is filled with foam insulation
( k=0.03 W/m0C). The thermal resistances of the water
tanks and the outer thin sheet metal shell are very small
and can be neglected. The price of electricity is $0.08/kwh
and the home owner pays $ 280 a year for water heating.
Determine the fraction of the hot water energy cost of this
household that is due to the heat loss from the tank. Hot
water tank insulation kits consisting of 3 cm thick fiber
glass insulation (k=0.035 W/m0C) large enough to wrap
the entire tank are available in the market for about $30.If
such an insulation is installed on this water tank by the
home owner himself, how long will it take for this
additional insulation to pay for itself?
Dr. Şaziye Balku 28
RADIATIONEnergy emitted by matter in the form of electromagnetic waves(or photons) as a result of the changes in the electronic configurations of the atoms or molecules
All bodies at a temperature above absolute zero emit thermal radiation
•Does not require an intervening medium
• Fastest (at the speed of light)
• Possible also in vacuum
•Example: energy of sun reaching the earth
•Thermal radiation: form of radiation emitted by bodies because of their temperature
•different from other forms of electromagnetic radiation; X-rays, gamma rays, microwaves, and television waves that are not related with temperature
29
STEFAN-BOLTZMANN LAWThe maximum rate of radiation that can be emitted from a surface at an
absolute temperature is;
Stefan-Boltzman constant
=5.67 10-8 W/m2.K4
Black body: an idealized surface that emits radiation at this maximum rate
Black body radiation: radiation emitted by blackbodies
Real surfaces emit less radiation
1
10 For real bodies
For black bodies
Emissivity of the surface
4
max, SSemitTAQ
4
SSemit TAQ
30
Radiation heat transfer between a surface
and the surfaces around it
When a surface is completely
enclosed by a much larger (or
black) surface at temperature Tsurr
separated by a gas (such as air)
that does not intervene with
radiation, the net rate of radiation
heat transfer between these
two surfaces is given by
31
)( 44
surrSSrad TTAQ
)(
TTAhQSStotal
Combined heat transfer coefficient includes effects of both
convection and radiation in such an example and conduction heat
transfer may be neglected.
= heat transfer per unit time (W)
A = surface area for heat transfer (m2)
σ = Stefan-Boltzmann constant, 5.67x10-8 W/m2K4
= emissivity
Ts = absolute temperature of surface (K)
Tsurr = absolute temperature of surroundings (K)
radQ