MEL242
HEAT AND MASS TRANSFER
Prabal Talukdar
Associate Professor
Department
p
of Mechanical Engineering
g
g
IIT Delhi
[email protected]
MECH/IITD
Course Coordinator: Dr. Prabal Talukdar
Room No: III, 368
E-mail: [email protected]
Course webpage:
http://web.iitd.ac.in/~prabal/courses.html
Pre-requisite: Fluid Mechanics (AML 160)
Lectures: Tue, Wed, Fri: 9-9.50 a.m.
(Room No: IV LT1)
Tut: 1-1.50 p.m.
(Tentative Room no: III352
MEL 242: Heat and Mass Transfer (3-1-0)
•Syllabus (for total 42 lectures)
Introduction and basics of to heat transfer: Modes of heat transfer, Fourier’s law, conductivity, diffusivity.
Heat conduction equation:
q
1D Heat conduction,, General heat conduction equation,
q
, Boundary
y and initial
conditions, Heat generation.
Steady heat conduction: Heat conduction in plane wall, cylinder, sphere, network analysis, critical radius of
insulation, heat transfer from fins.
Transient heat conduction: Lumped system analysis, transient heat conduction in large plane walls, long
cylinders
li d and
d spheres
h
with
ith spatial
ti l effect,
ff t Heisler
H i l and
d Grober
G b charts
h t
Numerical methods of heat conduction: Finite difference formulation, numerical methods for 1D and 2D steady
state heat conduction.
(≈ 10 lectures)
Introduction to convection: Fundamentals, Velocity and thermal boundary layer, laminar, turbulent flows,
conservation equations for mass, momentum and energy, solution of boundary layer equations, Analogy between
heat and momentum transfer, Non-dimensional numbers
External heat transfer: Drag and heat transfer, parallel flow over flat plates, flow across cylinders and spheres
Internal heat transfer: Mean velocity and mean temperature, entrance region, constant heat flux and temperature
condition in pipe flow,
flow Hagen–Poiseuille
Hagen Poiseuille flow,
flow Turbulent flow and heat transfer
Natural/free convection: Equation of motion of Grashof number, natural convection over surfaces and inside
enclosures
(≈ 13 lectures)
Boiling and condensation: Boiling heat transfer, pool boiling, flow boiling, condensation heat transfer, film
condensation, heat transfer correlations.
((≈ 4 lectures)
Heat Exchangers: Types of heat exchangers, overall heat transfer coefficient, analysis of heat exchangers, the
log mean temperature method, ε-NTU method.
(≈ 4 lectures)
Introduction to radiation: Fundamentals, radiative properties of opaque surfaces, Intensity, emissive power,
radiosity,
di i Planck’s
Pl k’ law,
l
Wien’s
Wi ’ displacement
di l
law,
l
Black
Bl k andd Gray
G
surfaces,
f
Emissivity,
E i i i absorptivity,
b
i i Spectral
S
l andd
directional variations, Stephan Boltzmann law, Kirchhoff’s law
View factors: Definitions and relations, radiation heat transfer between two black surfaces, between diffuse gray
surfaces, network method above two surfaces, re-radiating surface, radiation shield, radiation effects on
temperature
p
measurements.
(≈ 7 lectures)
Mass Transfer: Introduction, analogy between heat and mass transfer, mass diffusion, Fick’s Law, boundary
conditions, steady mass diffusion through a wall, cylinder and sphere, water vapour migration in buildings,
transient mass diffusion, mass transfer in a moving medium, diffusion of vapor through a stationary gas: Stefan
Flow
(≈ 4 lectures)
Evaluation:
Tuts and Quiz (2 nos): 20% (Closed note, book)
Minor Test I: 20% (Open note,
note closed book)
Minor Test II: 25% (Open note, closed book)
Major Test: 35% (Open note, closed book)
Total: 100%
Textbook: Fundamental of Heat and Mass Transfer: F. P.
Incropera and D. P. Dewitt
Heat Transfer: Yunus A. Cengel
Heat Transfer: J.P. Holmann
P.TALUKDAR/IITD
Quiz
Tentative Date
Quiz 1
August 27
Quiz 2
November 5
Heat Transfer as a Course
• Has a “reputation” for being one of the most challenging,
fundamental, conceptual courses in ME. It is the “heart” of
thermal
h
l engineering
i
i
• Why??
– Physically diverse: thermodynamics,
thermodynamics material science
science, diffusion
theory, fluid mechanics, radiation theory
– Higher-level math: vector calculus, ODEs, PDEs, numerical
methods
– Physically elusive: heat is invisible; developing intuition takes
time
– Appropriate assumptions: required
i d to simplify
i lif andd solve
l most
problems
• However, Heat Transfer is interesting, fun, and readily
applicable to the real world
P.TALUKDAR/IITD
Heat Transfer Applications
• Heat transfer is commonly encountered in engineering systems and
other aspects of life, and one does not need to go very far to see some
application areas of heat transfer.
transfer
P.TALUKDAR/IITD
Human body
y
P.TALUKDAR/IITD
Heat Transfer - Thermodynamics
y
• Thermodynamics is concerned with the amount of heat transfer as a
system
y
undergoes
g
a process
p
from one equilibrium
q
state to another,
and it gives no indication about how long the process will take.
• A thermodynamic analysis simply tells us how much heat must be
transferred to realize a specified change of state to satisfy the
conservation of energy principle.
We are normally interested in how long it takes for the
hot coffee in a thermos to cool to a certain
temperature, which cannot be determined from a
thermodynamic analysis alone
alone.
• Determining the rates of heat transfer to or from a
system and thus the times of cooling or heating,
heating as well as the
variation of the temperature, is the subject of heat transfer
P.TALUKDAR/IITD
Definition
• Heat transfer is energy transfer due to a temperature difference in a
medium or between two or more media
• Different types of heat transfer processes are called different modes
of heat transfer
• Conduction heat transfer is due to a temperature gradient in a
stationary medium or media
• Convection heat transfer occurs between a surface and a moving
fluid at different temperatures
• Radiation heat transfer occurs due to emission of energy in the
f
form
off ele
electromagnetic
t
eti waves
e by
b all
ll bodies
b die above
b e absolute
b l te zero
e
temperature
– Net radiation heat transfer occurs when there exists a temperature
difference between two or more surfaces emitting radiation energy
P.TALUKDAR/IITD
Conduction
• Conduction heat transfer is due to random molecular and atomic
vibrational, rotational and translational motions
– High temperature and more energetic molecules vibrate more and
transfer energy to less energetic particles as a result of molecular
collisions or interactions
• The heat flux (a vector)
& ′′ (W / m2)
Q
x
is characterized by a transport property know as the
– Thermal Conductivity,
y k ((W / m · K))
– W = watts
P.TALUKDAR/IITD
m = Meters
K = temperature in Kelvin
• Conduction is the transfer of energy from the more energetic
particles of a substance 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 the collisions and diffusion of the
molecules during their random motion. In solids, it 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 through a medium depends on the
geometry of the medium, its thickness, and the material of the
medium, as well as the temperature difference across the medium
P.TALUKDAR/IITD
Fourier’s Law
T2 − T1
ΔT
&
= − kA
Q cond = − kA
Δx
Δx
(W)
• In the limiting case of x →0, the equation above reduces to the
differential form
Fourier’s law of heat
dT
&
Q cond = −kA
dx
(W)
• The negative sign ensures that heat
transfer in the positive x direction is a
positive quantity
P.TALUKDAR/IITD
conduction after J. Fourier,
who expressed it first in his
heat transfer text in 1822
T1=
T2 =
Thermal Conductivity
y
• Specific heat Cp is a measure of a material’s ability to store thermal
energy.
gy For example,
p , Cp = 4.18 kJ/kg·°C
g
for water and Cp = 0.45
kJ/kg·°C for iron at room temperature, which indicates that water
can store almost 10 times the energy that iron can per unit mass.
• Likewise
Likewise, the thermal conductivity k is a measure of a material
material’ss
ability to conduct heat. For example, k = 0.608 W/m·°C for water
and k = 80.2 W/m·°C for iron at room temperature, which indicates
that iron conducts
cond cts heat more than 100 times faster than water
ater can.
can
• Thus water is a poor heat conductor relative to iron, although
water is an excellent medium to store thermal energy
P.TALUKDAR/IITD
Range
g of Thermal Conductivity
y
• The thermal conductivities of gases
such as air vary by a factor of 104
from those of pure metals such as
copper.
• Note that pure crystals and metals
have the highest thermal
conductivities and gases and
conductivities,
insulating materials the lowest.
P.TALUKDAR/IITD
A simple experimental setup to
determine the thermal conductivity
of a material
material.
P.TALUKDAR/IITD
The range of
thermal conductivity
of various materials
at room temperature
P.TALUKDAR/IITD
• The thermal conductivity of a substance is
normally highest in the solid phase and lowest
in the gas phase.
• Unlike gases, the thermal conductivities of
most liquids
li id decrease
d
with
i h increasing
i
i
temperature, with water being a notable
exception.
• In solids, heat conduction is due to two
effects: the lattice vibrational waves induced
by tthee vvibrational
b at o a motions
ot o s oof tthee molecules
o ecu es
positioned at relatively fixed positions in a
periodic manner called a lattice, and the
energy transported via the free flow of
electrons in the solid .
The thermal conductivity of a solid is obtained by adding the lattice
and electronic components.
components The relatively high thermal conductivities
of pure metals are primarily due to the electronic component.
P.TALUKDAR/IITD
• The lattice component of thermal conductivity strongly depends on
the way the molecules are arranged
• Unlike metals, which are good electrical and heat conductors,
crystalline
lli solids
lid suchh as diamond
di
d andd semiconductors
i d
suchh as
silicon are good heat conductors but poor electrical conductors. As a
result, such materials find widespread use in the electronics industry.
For example, diamond, which is a highly ordered crystalline solid,
has the highest known thermal conductivity at room temperature.
Even small amounts in a pure metal of “foreign”
molecules that are good conductors themselves
seriously
i l disrupt
di
t the
th flow
fl off heat
h t iin that
th t metal.
t l
For example, the thermal conductivity of steel
containing just 1 percent of chrome is 62 W/m·°C,
while the thermal conductivities of iron
and chromium are 83 and 95 W/m·°C,
P.TALUKDAR/IITD
• The variation of
the thermal
conductivity of
various solids,
liquids and gases
liquids,
with temperature
(from White)
P.TALUKDAR/IITD
Thermal Diffusivity
y
• The product ρCp, which is frequently encountered in heat transfer
y
is called the heat capacity
p
y of a material. Both the
analysis,
specific heat Cp and the heat capacity ρCp represent the heat
storage capability of a material.
•
But Cp expresses it per unit mass whereas ρCp expresses it per unit
volume, as can be noticed from their units J/kg·°C and J/m3·°C,
respectively.
• Another material property that appears in the transient heat
conduction analysis is the thermal diffusivity, which represents
how fast heat diffuses through a material and
is defined as
P.TALUKDAR/IITD
The larger the thermal diffusivity,
the faster the propagation of heat
into the medium. A small value of
tthermal
e a d
diffusivity
us v ty means
ea s tthat
at heat
eat
is mostly absorbed by the material
and a small amount of heat will be
conducted further
• Note that the thermal diffusivity
ranges from 0.14 x 10-6 m2/s for
water to 174 x 10-6 m2/s for silver,
which is a difference of more than a
thousand times.
• Also note that the thermal
diffusivities of beef and water are the
same. This is not surprising, since
meat as well as fresh vegetables and
fruits are mostly water,
water and thus they
possess the thermal properties of
water.
P.TALUKDAR/IITD
Forced Convection
Natural Convection
B ili
Boiling
C d
Condensation
i
P.TALUKDAR/IITD
Convection
• Convection heat transfer involves both energy transfer due to random
molecular motions and by bulk motion of the fluid
– Convection heat transfer includes both forced convection and natural
convection
• IIn convection
i heat
h transfer,
f the
h transfer
f off heat
h is
i between
b
a surface
f
and a moving fluid (liquid or gas), when they are at different
temperatures. The rate of transfer is given by Newton’s Law of
Cooling.
q '' = h (Ts − T∞ )
T∞
q’’
Moving fluid
Ts
Ts > T∞
P.TALUKDAR/IITD
Typical values of convection
h t ttransfer
heat
f coefficient
ffi i t
Process
h (W / m2 K)
Free Convection
Gases
2-25
Liquids
50 -1000
Forced Convection
Gases
35 -250
250
Liquids
50 -20,000
with Phase Change
Boiling or
Condensation
P.TALUKDAR/IITD
2500 -100,000
Radiation
•
•
•
All surfaces of finite temperature emit energy in the form of electromagnetic
waves
In the absence of an intervening medium, there is a heat transfer by radiation
between two surfaces at different temperatures
The maximum flux, E (W / m2), at which radiation may be emitted from a
bl kb d surface
blackbody
f
is
i given
i
by:
b
– Stefan Boltzmann Law
E b = σT
4
s
where
Eb or E = Surface emissive power (W / m2)
T = absolute temperature (K)
σ = Stefan-Boltzmann constant = 5.67 x 10-8 (W / m2 ּ◌ K4)
P.TALUKDAR/IITD
Eb
Ts
• For a real surface:
E = εσTs4
• For a surface with absorptivity
p
y α,, the incident radiation (G,
( , W/m2)
that is absorbed by the surface is given by:
Gabs = α ⋅ G
where
G = incident radiation (W / m2)
T = absolute temperature (K)
ε = surface emissivity (0 ≤ ε ≤ 1)
α = surface absorptivity (0 ≤ α ≤ 1)
P.TALUKDAR/IITD
G
Gabs
• For a gray surface α = ε
• When radiant energy is incident on a transparent surface, it can be
absorbed, reflected, or transmitted through the material. Hence,
G = G absorbed + G transmitted + G reflected = (α + τ + ρ) G
α + τ+ρ =1
where
ρ = materials surface reflectivity
τ = materials transmissivity
P.TALUKDAR/IITD
• Consider a small gray surface at temperature Ts that is completely
enclosed by the surroundings at temperature Tsur.
• The net rate of radiation heat transfer from the surface is:
Tsur
'
4
q 'rad
= E s − αG sur = εσTs4 − ασTsur
qsur’’
qs’’
'
q 'rad
=
Ts
q
4
= εσTs4 − ασTsur
= h r (Ts − Tsur )
A
• Where hr is the radiation heat transfer coefficient, W / m2 K
(
2
hr = ε ⋅ σ(Ts + Tsur ) Ts2 + Tsur
P.TALUKDAR/IITD
)
Conduction example
P.TALUKDAR/IITD
Convection
example
Calculate the heat flux
from your hand when it is
exposed to moving air
and water, assuming the
surface temperature of
your hand is 30°C.
P.TALUKDAR/IITD
Radiation ex.
An instrumentation package
has a spherical outer surface
of diameter D = 100 mm and
emissivity ε = 0.25.
0 25 The
package is placed in a large
space simulation chamber
whose walls are maintained
at 77 K. Iff the operation off
the electronic components is
restricted to the temperature
range of 40 ≤ T ≤ 85
85°C,
C, what
is the range of acceptable
power dissipation for the
package?
P.TALUKDAR/IITD