Heat Transfer

© Group 6 Heat Transfer 2013
Conduction, Convection and
Radiation

Heat Transfer
A temperature difference must exist for
heat transfer to occur.
Heat is always transferred in the direction
of decreasing temperature.
• Temperature is a scalar
• Heat flux is a vector quantity.

● Conduction- transfer of energy between
objects that are in physical contact.
● Convection- transfer of energy between
an object and its environment due to fluid
motion.
● Radiation- transfer of energy to or from a
body by means of the absorption of
electromagnetic radiation.
Heat energy only flows when there is a temperature
difference from a warmer area to a cooler area.
During heat transfer, thermal energy always moves in the same
direction:
HOT COLD

Metals are good conductors of heat. The outer electrons of
metal atoms are not attached to any particular atom. They
are free to move between the atoms.
When a metal is heated, the free
electrons gain kinetic energy.
How do metals conduct heat?
heat
This means that the free electrons
move faster and transfer the
energy through the metal.
This makes heat transfer in
metals very efficient.
Insulators do not have free
electrons and so they do not
conduct heat as well as metals.

How do non-metals conduct heat?

The rate of heat flux is linearly proportional to the
temperature gradient.
Fourier’s Law
Equation :

L
Q
k
t1
t2
A
For the steady
state,
unidirectional flow,
Fourier’s Equation:
Units metric English
Q (Heat)
A (Area)
t (Temp)
L (Thickness)
(heat flux)
(Temp.Gradient) F/in .
F/ft2
k (thermal conductivity) Btu*in/f
t2-F-hr
W
m In, ft

Conversion of Units
English
x
Metric

Variation of Thermal Conductivity
Thermal conductivity varies depending on temperature.
Depending on the material of the conductor, as the temperature
rises the thermal conductivity of the material often raises as well,
increasing the flow of energy.
Material Temperatur
e
T
Volume
V
Density Pressure
P
Thermal
Conductivity
K
Solids increase ------ ------ ------ increase
Metals increase ------ ------ ------ decrease
Liquids increase -------- decrease -------- decrease
Gases increase decrease increase increase increase

1. The conductivities of all homogeneous solid materials
are relatively high; practically all good (heat) insulators
are porous, cellular, fibrous, or laminated materials.
2. In general, the conductivity increases with the
density.
3. With rare exceptions, the conductivity of insulating
materials increases very materially with the
temperature.
4. The absorption of moisture greatly impairs the
insulating value of porous materials.
Generalizations concerning conductivities of solids

Sample Problem # 1
K= 80 W/m.k
A= 5000 cm2 = 0.5m2
T1 = 150 C + 273 = 423 K
T2 = 140 C + 273 = 413 K
L = 2 cm = .02m
Compute the amount of heat per second through an iron
plate 2 cm thick and area of 5000 cm2 if one face has a temperature
of 150 C and the other face is 140 C. The thermal conductivity for
iron is 80W/m.k.
Given Solution
Q = (80 W/m—K * 0.50m2 )(10K/.02m)
Q = 20000 J/s or
20 kW
Q = kA(t1-t2)/L

DAISY

Conduction through plane wall

Steady-state flow
same area (A)
different
area (A)

Any one section of the wall
Thermal Conductance
(c)
Unit Conductance
Thermal Resistance (R) Unit Resistance
Composite plane wall
Thermal Conductance
(c)
Unit Conductance
Thermal Resistance (R) Unit Resistance

FILM COEFFICIENT(h)
-film conductance, surface conductance
Some examples of the surface coefficients:
 Inside building walls, still air, design value h = 1.65 Btu/hr-ft2-°F
 Outside walls, 15-mph, design value h = 6.00 Btu/hr-ft2-°F
 Evaporating refrigerants in tube, typical value h = 200 Btu/hr-ft2-°F
 Condensing steam in tube, typical value h = 2000 Btu/hr-ft2-°F

maj

Conduction through a hollow sphere
Consider a hollow sphere having inner radius ri and
outer radius ro. The inner and outer surface temperature of the
sphere is maintained at ti and to (ti>to) respectively.
From the FOURIER’S Law
we can write

To calculate the total rate of heat transfer, we have to integrate
the previous equation.
or
2
1
2
1
or
General Formula
Conduction through a hollow sphere

Sample Problem # 3
; and t1 = 426.7 C. If the heat from the sphere is 439.6 W,
what is to ?
Solution
Let 0.0763 m
0.127m
699.7 K
Find: to

Solution

CONDUCTION THROUGH CURVED WALL
( CYLINDER)

i
w

Multilayered Cylinder

Sample Problem # 5
Calculate:
The rate of heat loss per unit
length of pipe.
Given
R1= 5.25/2 = 2.625 cm
R2= 6.03/2 = 3.015 cm
R3= 3.015 + 2 = 5.015cm
L = 1 m

Jass

How does convection in a liquid occur?

How does convection in a gas occur?

Flow of Fluids

Combination of Conduction , Radiation and Transport of fluid
Free Convection -
Forced Convection -
occurs when the fluid circulates, the heavier parts of
the fluid moving downward under the force of gravity
When work is done to blow or pump the fluid
What is Convection Heat?

Why is the freezer compartment at the top of a fridge?
The freezer compartment is
at the top of a fridge because
cool air sinks.
This warmer air rises and so
a convection current is set
up inside the fridge, which
helps to keep the fridge cool.
Why is convection important in fridges?
The freezer cools the air at
the top and this cold air cools
the food on the way down.
It is warmer at the bottom
of the fridge.

What is Film Coefficient (h) ?
Three (3) Conditions
1. Forced Convection
with Turbulent flow
2. Forced Convection
with Laminar flow
3. Free Convection
General Equation for (h)
Where :
L = length of the pipe/duct
D = diameter of pipe/duct
h = film coefficient

Film Coefficient , Turbulent Flow

Sample problem #

arnel

Laminar Flow
For laminar flow inside
pipe
Re<2100
Equation A
where
ṁ = mass flow rate
L = heated length of the straight
pipe
c = specific heat of the liquid
0.14
b b
0.14

Equation B (Sieder – Tate
Equation)
0.14
0.14
Laminar Flow

Sample Problem #
2

0.14
0.14

Film Coefficient for annular space
Double pipe
Heat
Exchanger
that consists
of two
concentric
tubes
Drawing TBC
For turbulent flow through concentric annular
area
0.8 n
b b
where :

For laminar tube through concentric annular area
0.14
where :

Sample Problem #

Rachel

Logarithmic Mean of Temperature Difference
The LMTD is a logarithmic average of the temperature
difference between the hot and cold streams at each end of the
exchanger.

Two primary classifications of flow arrangement
Parallel-flow arrangement
Fluids flow in the same direction through
the heat exchanger

Counter flow arrangement
The fluids enter the exchanger from opposite ends

Sample Problem #
When a heat exchanger was designed its overall heat transfer co-
efficient was 600 kcal/hr mt²°C. The heat transfer area provided =
10mt². Over a period of time, its overall heat transfer co-efficient
has fallen to 450 kcal/hr mt²°C due to fouling.
Data:
Specific heat of hot fluid = 1 kcal/kg °C
Hot fluid entering temperature = 80°C
Hot fluid leaving temperature = 60°C
Cold fluid entering temperature = 25 °C
Cold fluid leaving temperature = 40°C
Calculate:
How much additional area is to be added to maintain the same rate
of heat transfer?
Assumption: Flow is assumed in counter current direction

infrared
waves
The Earth is warmed by heat energy from the Sun.
There are no particles
between the Sun and the
Earth, so the heat cannot
travel by conduction or by
convection.
?
The heat travels to Earth by
infrared waves. These are
similar to light waves and
are able to travel through
empty space.
How does heat travel through space?
How does this heat energy travel from the Sun to the Earth?

Heat can move by travelling as infrared waves.
This means that infrared waves act like light waves:
 They can travel through a vacuum.
 They travel at the same speed as light – 300,000,000 m/s.
 They can be reflected and absorbed.
What are infrared waves?
Infrared waves heat objects that absorb them and are also
known as thermal radiation.
These are electromagnetic waves, like light waves, but
with a longer wavelength.

Investigating thermal emission

Emitting thermal radiation
All objects emit (give out) some thermal radiation.
Matt black surfaces are the best emitters of radiation.
white silver
matt
black
best emitter worst emitter
Certain surfaces are better at emitting thermal radiation
than others.
Shiny surfaces are the worst emitters of radiation.
Which type of kettle would cool down faster: a black kettle
or a shiny metallic kettle?

Investigating thermal absorption

Absorbing thermal radiation
Infrared waves heat objects that absorb (take in) them.
best emitter worst emitter
best absorber worst absorber
white silver
matt
black
Matt black surfaces are the best absorbers of radiation.
Certain surfaces are better at absorbing thermal radiation
than others. Good emitters are also good absorbers.
Shiny surfaces are the worst emitters because they reflect
most of the radiation away.
Why are solar panels that are used for heating water
covered in a black outer layer?

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 absorptance
(symbol α). Other fractions of
incident radiation which are
reflected and transmitted are
called reflectance(symbol ρ)
and transmittance(symbol τ),
respectively. The sum of these
fractions should be unity
α + ρ + τ = 1.

States that the amount of radiation from a black body is
proportional to the fourth power of the absolute temperature, where σ
= ( 0.1713) (10-8) is the Stefan-Boltzmann constant when Q is in
Btu/hr, and A is the radiating area in square feet of the black body
whose surface temperature is T°R.
STEFAN-BOLTZMANN LAW
Q= σAT4
The amount of radiation with
emissivity Ɛ is
Q= ƐσAT4

Sample Problem #
A solid metal sphere (emissivity = 0.65) has a
radius of 5 cm is heated to 600ºC and suspended from a
thin wire in the center of a room. At what rate is heat
released to the room?

Iana

Radiation between Gray Bodies
Let the amount of radiant heat q, leaving
surface A, be

From the equation

In an analogous circuit we have the form shown in this figure
W1 J1
q1
Resistance due to the space configuration

Example – Two Gray Surfaces in Shape
W1
J1
Total Resistance

4 4
44
44

4 4

Configuration Space Factors for Radiation Equation

RADIATION BETWEEN ELEMENT
AND RECTANGULAR PARALLEL
SURFACE ABOVE ELEMENT

RADIATION SHAPE FACTOR
FOR PARALLEL,
CONCENTRIC, DISCS

FOR PARALLEL, DIRECTLY
OPPOSED, RECTANGLES

FOR PERPENDICULAR
RECTANGLES WITH S
COMMON EDGE.

FOR CONCENTRIC
CYLINDERS OF FINITE
LENGTH.

FOR INFINITESIMAL
PLANES AND SPHERES

Conduction
Soldering iron
• Iron rod is a good conductor
of heat with copper tip.
• The handle is made of plastic
which is a good insulator.
Home electrical appliances
• The handles of kettles, hot
iron, cooking utensils are
made of wood and plastics
which are the good insulators
of heat.

Convection
Electric kettle
• The heating element is always placed at the bottom of the
kettle.
• So that hot water at the bottom which is less dense will rise
up.
• Cooler water at the top which is denser will sink to the bottom.
• Convection current is set up to heat up the water.
Refrigerator
• The freezer is always placed at the top of the refrigerator.
• So that cold air at the top will sinks to the bottom.
• Warmer air at the
bottom will rise
to the top.
• Convection current is set up to cool down the
refrigerator.

Radiation
Cooling fins at the back of a refrigerator
• A black and rough surface is a good
radiator of heat.
White paint for houses
• In hot countries, houses are painted in
white to reduce absorption of heat
energy from the Sun
Teapot
• Has smooth, shiny and silvery surface.

Vacuum Flask
•The shiny bright silvering
surface on glass wall
reduces heat loss by
radiation.
•cork stopper which is
made of poor conductors
reduces heat loss by
conduction and convection

Glossary
 absorber – A material that takes in thermal radiation.
 conduction – The method of heat transfer in solids.
 conductor – A material that lets heat flow through it.
 convection – The method of heat transfer in fluids, which
occurs because hot fluids are less dense than cold fluids.
 emitter – A material that gives out thermal radiation.
 free electrons – Electrons in a metal that are free to move
through the metal.
 heat transfer – The flow of heat energy from a hotter area
to a colder area.
 radiation – Heat energy transferred by infrared waves.
This method of heat transfer does not need particles.

Heat Transfer

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Heat Transfer