CHAPTER 1 INTRODUCTION
MAE 120: Heat and Mass Transfer
Bihter Padak
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What is Heat Transfer ?
Heat :
It is the form of energy that can be transferred
from one system to another as a result of
temperature difference.
Heat Transfer :
It is the science that deals with the determination
of the rates of such energy transfers.
Thermodynamics and Heat Transfer
They are called thermal sciences.
What is the difference?
Thermodynamics:
It concerns with the amount of heat transfer
(between equilibrium states).
Ø Time independent
Ø Equilibrium phenomenon
Ø Deals with the end states of the process
Ø Provides no information on the nature of
interaction or the time rate at which it occurs
Heat Transfer:
It deals with the rate
of heat transfer.
Ø Time dependent processes
Ø Non-equilibrium phenomenon
Ø Driving force: temperature difference
Ø Thermodynamic principles alone are not
enough for heat transfer analysis
The Difference between
Heat Transfer & Thermodynamics
How long will it take to
cool the coffee in a
thermos bottle from 90oC
to 70oC?
Which one, heat transfer
or thermodynamics, can
answer this question?
Heat transfer can calculate the time needed
Some application areas of heat transfer
Heat Transfer Mechanisms
Heat can be transferred in three different ways:
1. Conduction
2. Convection
3. Radiation
Ø All modes of heat transfer
require temperature
difference (driving force).
Ø All modes of heat transfer
are from the high
temperature medium to the
lower temperature one.
Conduction Heat Transfer
Energy transfers from the more
energetic particles to the adjacent
less energetic ones as a result of
interactions between the particles.
Conduction can
take place in solids,
liquids, or gases
In gases and liquids: Conduction is due
to collisions & diffusion of molecules
In solids: Conduction is due to the
combination of vibrations of the
molecules in a lattice and the energy
transport by free electrons.
The rate of heat conduction depends on:
Ø geometry
Ø material
Ø thickness
Ø temperature difference
Rate of heat conduction through wall:
Rate of heat conduction µ
dT
qcond = −kA
dx
(J / s or W)
k
dT/dx
A
dx
(Area) (Temperatu re difference)
Thickness
Fourier’s Law of
Heat Conduction
Steady heat transfer
through a large plane
wall of thickness of
Dx and area A
= thermal conductivity (W/m.K)
= temperature gradient (K/m)
= heat transfer area (m2)
= thickness of medium in x-direction (m)
Heat flux:
!!
qcond
dT
= −k
dx
Heat transfer rate in the xdirection per unit area
perpendicular
to
the
direction of heat transfer
(W/m 2 )
Convection Heat Transfer
The heat transfer between a solid surface and the
adjacent fluid (liquid or gas) that is in motion and
involves the combined effects of conduction and
fluid motion.
Convection = Conduction + Advection (fluid motion)
There are two convection types:
Free Convection:
Fluid moving naturally over the
surface (density difference)
Forced Convection:
Fluid is forced to flow over the
surface (fan, pump, etc.)
Heat transfer from a hot
surface to air by convection
u
The rate of convection heat
transfer is expressed by
Newton’s law of cooling:
qconv = hA (Ts − T∞ )
(J / s or W)
A
Newton’s Law of
Cooling
A = heat transfer area between two mediums (m2)
h = convection heat transfer coefficient (W/m2.K)
Ts = surface temperature of the solid (K)
T¥ = temperature of fluid moving over the body (K)
qconv = hA (Ts − T∞ )
h is influenced by numerous factors:
Ø surface geometry
Ø the nature of fluid flow
Ø fluid properties
Ø the bulk fluid velocity, etc.
Radiation Heat Transfer
The energy 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. No need of intervening
medium. Occurs most efficiently in vacuum.
In heat transfer studies we are interested in thermal
radiation (radiation emitted by bodies because of
their temperature).
Ø It is a volumetric phenomenon: all solids, liquids
& gases emit, absorb, or transmit radiation
Ø For opaque surface solids: it may be considered
as a surface phenomenon
Radiation Heat Transfer
The rate at which energy is released per area (W/m2)
è Surface emissive power: E
The maximum rate of radiation per area from a
surface at an absolute temperature Ts is :
4
s
Eb = σ T
2
(W/m )
Stefan-Boltzmann Law
TS = surface absolute temperature (K)
σ
= the Stefan-Boltzmann constant
(5.67x10 -8W / m 2 K 4 )
è has to be in K
Radiation Heat Transfer
Black body:
Eb
The idealized surface
that emits the max.
radiation is called “black
body” (Black body
radiation).
For real bodies:
The radiation is less
and expressed as
4
s
E = εσ T
2
(W/m )
e = the emisivity of the surface (0 < e < 1)
for black body:
e=1
Radiation Heat Transfer
Radiation may also be “incident” on a surface from
its surroundings
Radiation at which all such radiation is incident on
a unit area of a surface è Irradiation: G
G
The absorbed radiation:
Gabsorbed = α G
Gref = (1− α ) G
0 < a < 1)
Gabsorbed = α G
a=1: black body (perfect absorber)
Absorptivity (a): The fraction of radiation energy
incident on a surface that is absorbed by the surface
Radiation Heat Transfer
The absorbed radiation:
Gabsorbed = α G
G
Gref = (1− α ) G
0 < a < 1)
Gabsorbed = α G
•
a<1 and opaque surface è a portion of radiation is reflected
• a<1 and semi transparent surface è a portion of radiation
may be transmitted
Ø
In general: e & a depend on temperature &
wavelength of the radiation.
Ø
Kirchoff’s law of radiation: e & a of a surface at a
given temperature & wavelength are equal
Ø
In many practical applications:
average emissivity= average absorptivity
xample, the absorptivity of a surface to solar radiation may differ from its
to radiation emitted by the walls of a furnace.
Special case: Radiation between enclosed surfaces
E
q"conv
e of emissivity
orptivity ", and
ature Ts
(a)
1.6
ndings.
E
Gas
T, h
Gas
T, h
Surroundings
at Tsur
q"rad
q"conv
Surface of emissivity
! = " , area A, and
temperature Ts
Ts > Tsur, Ts > T
(b)
In case where a surface
of emissivity e and
Radiation
exchange:
(a) at a surface
(b) between a surface
and large
surface
area
A atandabsolute
temperature
TS is
completely enclosed by a much larger (black
body) surface at temperature Tsur, the
radiation heat transfer between two bodies is:
4
s
4
sur
qrad = εσ A(T − T )
Special case: Radiation between enclosed surfaces
4
s
4
sur
qrad = εσ A(T − T )
It may be convenient to express as:
qrad = hr A(Ts − Tsur )
2
s
2
sur
hr = εσ (Ts + Tsur )(T + T )
hr = the radiation heat transfer coefficient
Radiation heat transfer to & from a surface surrounded
by a gas can occur in parallel to convection.
qtotal = qconv + qrad
4
s
4
sur
= hA(T s −T∞ ) + εσ A(T − T )
Simultaneous Heat Transfer
Mechanisms
In many heat transfer processes heat may be
transferred with more than one mechanism.
Examples ?
Look around and find examples!
and energy advection.
The first law of thermodynamics addresses total energy, which consists of kinetic and
potential energies (together known as mechanical energy) and internal energy. Internal energy
can be further subdivided into thermal energy (which will be defined more carefully later)
Conservation Laws and Thermal Energy Balance
Ø Always define your system
Open
W
Closed
Q
•
tot
∆ Est
E in
(a)
•
•
E g, E st
•
E out
(b)
FIGURE 1.7 Conservation of energy: (a) for a closed system over a time interval
and (b) for a control volume at an instant.
Ø General balance equation
Accumulation = Input – Output + Generation - Consumption
• Integral form: Finite time period
• Rate form: All terms expressed as rates
Conserved properties: total mass, total energy
Conservation of mass
dM sys
= m in − m out
dt
Conservation of energy
dEsys 
= Ein − E out
dt
Heat and Other Forms of Energy
Ø Energy can exist in numerous forms such as:
-
Thermal
Kinetic
Electrical
Chemical
-
Mechanical
Potential
Magnetic
Nuclear
Ø Their sum constitutes the total energy of a
system.
Total Energy of a System (ε) = S all energies
Heat and Other Forms of Energy
Internal energy:
The sum of all microscopic forms of energy is
called the internal energy of a system, and is
denoted by u (J/kg) or U (J).
Microscopic energy:
Forms of energy related to the molecular
structure of a system and the degree of the
molecular activity.
Components of Internal Energy
Sensible energy/heat:
Portion
of
internal
energy
associated
with
translational,
rotational and vibrational motion of
molecules.
Temperature é Sensible heat é
Latent energy/heat:
The internal energy associated
with the phase change
Chemical energy:
The internal energy associated with the atomic
bonds in a molecule
Nuclear energy:
The internal energy associated with binding
forces of nucleus
Internal Energy and Enthalpy
Ø In the analysis of systems
that involve fluid flow, we
frequently encounter the
combination of properties
u and Pn.
Ø The combination is
defined as enthalpy.
h = u + Pv
Ø The term Pn represents
the flow energy of the
fluid (also called the flow
work).
Specific Heats of Gases, Liquids and Solids
Specific heat:
Energy required to raise
the temperature of a
unit mass of substance
by one degree (denoted
by °C).
Ø Two kinds of specific heat (kJ/kg.°C or kJ/kg.K):
1. Specific heat at constant volume (Cv)
2. Specific heat at constant pressure (Cp)
Specific Heats of Gases, Liquids and Solids
Ø The specific heat of a substance, in general, depend
on
two
independent
properties
such
as
temperature and pressure.
Ø For an ideal gas, they depend on temperature only.
Cp= Cv + R
Changes in the internal energy (u) and enthalpy (h)
of ideal gases :
Differential :
du = C V dT and dh = CPdT
Finite :
Du = C V ,ave DT and Dh = CP,ave DT
(J/kg)
DU = mC V ,ave DT and DH = mCP,ave DT
(J)
m = mass of the system (kg)
C ave = the average specific heat (kJ/kgo C)
Incompressible substance:
A substance whose specific volume (or density)
does not change with temperature & pressure
Ø Volume (density) ¹ f (T, P)
Þ CP = C V = C
Ø Specific heat depends on
temperature only
Therefore, for solids and liquids :
DU = mCave DT
Energy Transfer
Energy can be transferred to or from a given mass
by two mechanisms:
Ø Heat (Q)
Ø Work (W)
Heat transfer:
Driving force is temperature difference (DT ).
Q ~ DT Þ Q­, DT­ or
Q¯, DT ¯
Heat transfer rate:
The amount of heat transferred per unit time (J/s)
The First Law of Thermodynamics
It says: "Energy can neither be created nor destroyed"
Conservation of energy principle:
ìTotal energy ü ìTotal energy ü ìChange in the
ï
ï ï
ï ï
entering
the
leaving
the
í
ý í
ý = ítotal energy
ïsystem
ï ïsystem
ï ïof the system
î
þ î
þ î
εin − εout = Δε sys
εin
εout
Energy can be transferred
by heat, work and mass.
ε : Total energy
ü
ï
ý
ï
þ
εin = εout
The rate form:
εin − εout
Rate of net
energy transfer
by heat, work
and mass
Steady - State:
Rate of net
energy transfer
in by heat, work
and mass
dε sys
=
dt
(J / s or W)
Rate of change in
internal, kinetic,
potential, etc.,
energies
dε system
=0
dt
εin = εout
Rate of net
energy transfer
out by heat,
work
and mass
ε = E + E AO
Total
Thermal+ All other
mechanical
Thermal and mechanical energy balance:
E in − E out + E gen
dE sys
=
dt
Thermal and mechanical
energy generation
Ein − Eout + Egen = ΔEsys
change in thermal and
mechanical energy of system
Integral form
Energy Balance for Steady-Flow Systems
A large number of devices involve mass flow in
and out of the system and are modeled as
control volume.
Ø Steady - state: No change with time
Ø Unsteady-state (Transient): Changes with time
Ø Uniform: No change with position
In case of steady-flow process:
Ein = Eout
Þ
E tot = constant
Under steady conditions, the net rate of energy
transfer to a fluid in a control volume is equal to
the rate of increasing in the energy of the fluid
stream flowing through the control volume.
The Surface Energy Balance
A special case for which no volume or mass is
encompassed by the control surface.
E in − E out = 0
•
Applies for steady-state and transient conditions.
•
With no mass and volume, energy storage and
generation are not pertinent to the energy balance,
even if they occur in the medium bounded by the
surface.
The Surface Energy Balance
Consider surface of wall with heat
conduction, convection and radiation.
!! − qconv
!! − qrad
!! = 0
qcond
transfer
by
T1 − T2
4
k
− h(T2 − T∞ ) − εσ (T24 − Tsur
)=0
L
Analysis of Heat Transfer Problems
Solution Methodology
1. Known: State briefly what is known.
2. Find: State briefly what must be found.
3. Schematic: Draw a schematic of the physical system.
Mark the control volume. Identify relevant HT
processes by labeled arrows.
4. Assumptions: List all simplifying assumptions.
5. Properties: Compile property values needed.
6. Analysis: Apply appropriate conservation laws,
introduce the rate equations as needed. Develop the
analysis as completely as possible before substituting
numerical values. Perform the calculations.
7. Comments: Discuss your results (key conclusions, a
critique of assumptions, trends, parameter sensitivity).
Idealization of a System: Assumptions
Modeling of Heat
Transfer Problems
L
(?)
Example
Problem Statement:
The coating on a plate is cured by exposure to an
infrared lamp providing an irradiation of 2000W/m2.
It absorbs 80% of the irradiation and has an
emissivity of 0.50. It is also exposed to an air flow
and large surroundings for which temperatures are
20°C and 30°C, respectively.
If the convection coefficient between the plate and
the ambient air is 15 W/m2.K, what is the cure
temperature of the plate?
frared lamp. Heat transfer from the coating is by convection to ambient
xchange with the surroundings.
Solution
ind:
Coating
radiation
Known:
1. Cure
temperature
for h # 15with
W/m2 ! K.prescribed
properties is cured by irradiation from an 2
2. Effect of airflow
on the cure
temperature
for 2the
" h coating
" 200 W/m
infrared
lamp.
HT from
is ! K
which the cureconvection
temperature isto
50!C.
ambient air and radiation
chematic:
Find:
exchange with the surroundings.
Cure temperature for h = 15 W/m2.K.
Schematic:
Tsur = 30°C
Glamp = 2000 W/m2
q"conv
T∞ = 20°C
2 ≤ h ≤ 200 W/m2•K
Air
T
Coating,
α = 0.8, ε = 0.5
q"rad
α Glamp
Assumptions:
Ø Steady-state conditions
Ø Negligible heat loss from back surface
Ø No internal heat generation
Ø Plate is small object in large
surroundings and coating has an
absorptivity of a = 0.80.
Properties:
Analysis:
h = 15 W/m2.K, a = 0.80, e = 0.5,
Tsur = 30°C, T¥ = 20°C
Since the process is at steady-state conditions and
there is no HT at the back surface, the plate must be
isothermal (Ts=T). A control surface placed about the
entire plate and applying energy conservation law
will yied the desired temperature.
Conservation of Energy:
Ein − Eout + Egen = ΔEsystem
Steady-state and no internal heat generation:
Ein − Eout = 0
"" − qrad
"" = 0
(αG)lamp − qconv
4
(αG)lamp − h(T − T∞ ) − εσ (T 4 − Tsur
)=0
Insert numerical values and solve for T:
0.8 x 2000 W / m2 - 15 W / m 2K(T - 293 )K
- 0.5 x5.67 x10 -8 W/ m 2K 4 (T 4 - 303 4 )K 4 = 0
T = 377 K
= 104°C
st
lamp irradiation by the coating and outflow due to convection and net radiation transfer
to the surroundings, it follows that
Comments:
(!G)lamp # q%conv # q%rad ! 0
Final
characteristics
of and
the
including wear and
Substituting
from Equations 1.3a
1.7, coating,
we obtain
durability, are known
to depend on the4 ) temperature
at
(!G)lamp # h(T # T!) # "#(T 4 # Tsur
!0
which
curing occurs. An air flow system is able to control
Substituting numerical values
the air velocity,
hence the convection coefficient, on the
0.8 $ 2000 W/m2 # 15 W/m2 ! K (T # 293) K
cured surface. However, the process
engineer
needs
to
#8
2
4
4
4
4
# 0.5 $ 5.67 $ 10 W/m ! K (T # 303 ) K ! 0
know how the temperature
depends on the convection
and solving by trial-and-error, we obtain
coefficient.
T ! 377 K ! 104"C
"
Solving
the energy conservation equation for selected
2. Solving the foregoing energy balance for selected values of h in the prescribed range
values
of hthewill
result:
and plotting
results,
we obtain
240
200
T (!C)
160
120
80
50
40
0
0
20
40 51 60
h (W/m2•K)
80
100
Let’s see what we have learned!
1. How does heat transfer differ from
thermodynamics?
2. What is heat transfer?
3. Can you give a few examples of heat transfer
appliances in household or in your classroom?
4. What kinds of energy forms do you remember?
5. What does the first law of thermodynamics say?
6. What is specific heat? What is its unit?
7. How many specific heats are defined in
thermodynamics ?
8. What are the mechanisms of heat transfer?
How are they distinguished from each other?
9. What is a blackbody? How do real bodies differ from blackbody?