Equivalent forces
A commercial airliner is shown here with threedimensional information supplied. If engine 3 suddenly
fails, determine the resultant of the three remaining
engine thrust vectors, each of which has a magnitude of
90 kN. Specify the y nd z-
INTRODUCTION
TO
HEAT TRANSFER
Heat :
Heat is one of the first things understood by mankind.
Heat is the energy in transit between systems or
system and surroundings which occurs by virtue of
their temperature difference when they communicate.
The scien
Solidification
1
Processes involving solidification
g
o C
Casting
o Joining
Welding
Brazing
Soldering
g
2
How to measure temperature?
o
Contact M d
C t t Mode
Thermocouples
o
Non contact mode
Infrared pyrometers
3
Types of thermocouple
Type K
Chromel (90%
PhaseDiagrams
Phase Diagrams
1
2
WhatarePhaseDiagrams?
Phase diagrams are also called
o Equilibrium Diagrams
o Constitutional Diagrams
Phase diagrams are essentially stability maps
maps.
3
TypesofPhaseDiagrams
Based on number of components
Onecomponent
O
Counters Non compressive members
13.5kN
The diagonal members in the center panel of the
truss shown are slender and
act only in tension;
such members are called counters. Determine the
force in members BD and CE and in the counter
which is acting when P=1
Trusses
Trusses
Tension
member.
Forces will be
directed
towards the
pin.
Compression
member.
Forces will be
directed away
from the pin.
Trusses are composed of two force
members. This is a consequence of
the fact that trusses consist of pin
and roller joi
Method of sections
Determine the force in
each members AF and
EJ when P=Q=9.0 kN
YA
XA
XK
sin = 0.6, cos = 0.8
Method of sections
YA
sin = 0.6, cos = 0.8
XA
XK
F 0 X
F 0 Y
M 0
x
y
A
A
XK 0 XK XA
PQ
k
7.2 j X A i 5.4i ( P ) j 10.8i ( Q ) j 0
7.2 X A k 5
Zero load member
Pin
Sum of all vertical
components must be
zero for
equilibrium. Hence
the vertical
component of this
force must be zero
IN ABSENCE OF
ANY EXTERNAL
FORCE ON THE
PIN. Hence the
PIN
force itself must be
zero!
Two force
members all
Finding Z
Trusses
Trusses
Tension
member.
Forces will be
directed
towards the
pin.
Compression
member.
Forces will be
directed away
from the pin.
Trusses are composed of two force
members. This is a consequence of
the fact that trusses consist of pin
and roller joi
Equivalent forces
A force and a couple are applied to a beam.
(a) Replace this system by a force F applied at
point G, and determine the distance d.
(b) Solve part (a) assuming that the directions of
the two 600- N forces are reversed.
Equivalent forces
Y
Coordinate systems
Cartesian
Z
z
P(x,y,z)
x
X
y
Example of a
problem where a
Cartesian coordinate
system is a good
choice
Y
Coordinate systems
Z
Spherical
sin
P(sincos,
cos
sinsin,
cosY
)
X
sinsin
Example of a
problem where a
spherical system is
required
Equivalent forces
Three cables attached to a disk exert on it the
forces shown.
(a) Replace the three forces with an equivalent
force-couple system at A.
(b) Determine the single force which is equivalent
to the force couple system obtained in part a,
and
Equivalent forces
A force and a couple are applied to a beam.
(a) Replace this system by a force F applied at
point G, and determine the distance d.
(b) Solve part (a) assuming that the directions of
the two 600- N forces are reversed.
Equivalent forces
Y
Coordinate systems
Cartesian
Z
z
P(x,y,z)
x
X
y
Example of a
problem where a
Cartesian coordinate
system is a good
choice
Y
Coordinate systems
Z
Spherical
sin
P(sincos,
cos
sinsin,
cosY
)
X
sinsin
Example of a
problem where a
spherical system is
required
CharacterizationofMaterials
Characterization of Materials
1
Microstructural Characterization
Mechanical Property Characterization
Microstructural Characterization
(to bt i i f
(t obtain information about microstructures)
ti
b t i
t
t
)
Optical Microsco
Diffusion
Diffusion is material transport by atomic motion.
2
Wheredoweencounterdiffusion?
o Solidification
o Powder metallurgy (sintering)
o Joining processes (solid state or liquid state)
o Heat treatment processes
o Hardening of metals (bulk or surface
SCHOOL OF MECHANICAL SCIENCES
IIT BHUBANESWAR
Heat Transfer (MEA 3003)
B.Tech. (Mechanical Engineering) V Semester
L T P Cr
3 1 0 4
Introduction: Basic Concepts and Modes; Relationship to Thermodynamics.
Conduction: Mechanism; Fourier's General Conduction
Free CONVECTIVE
HEAT TRANSFER
Introduction :
Free or natural convection is the process of heat transfer which
occurs due to movement of fluid particles which is produced due
to change in density resulting from temperature gradients.
Natural convection i
BOILING
HEAT TRANSFER
Introduction :
Boiling constitute the convective heat transfer process that
involves a change of phase from liquid to vapour state.
Now-a-days, dissipation of large quantity of heat within a
limited space at small wall superheat is o
CONDENSATION
HEAT TRANSFER
Introduction :
Condensation occurs when the temperature of a
vapour is reduced below its saturation
temperature Tsat.
This is usually done by bringing the vapour into
contact with a solid surface whose temperature
Ts is below
RADIATION
HEAT TRANSFER
INTRODUCTION
All bodies at a temperature above absolute zero temperature
emit energy by a process of electromagnetic radiation. The
intensity of such radiation depends upon the temperature
and nature of the surface.
Heat Transfer
Transient Heat Conduction
Heating or Cooling of Infinite Plate with Finite Internal and Surface
Resistance (0 < Bi < 100)
(1)
The initial Condition is
[I]
The Boundary Conditions are
Infinite Plate
[I]
[II]
The solution of equation (1) is given by
(2)
Now
SCHOOL OF MECHANICAL SCIENCES
IIT BHUBANESWAR
HEAT TRANSFER (MEA 3003)
Topic : 2-D Steady State Heat Conduction and Unsteady Heat Conduction
Tutorial Sheet 4
[1]
The temperature along the edges of a rectangular plate of length a along X-axis and b along Y
SCHOOL OF MECHANICAL SCIENCES
IIT BHUBANESWAR
HEAT TRANSFER (MEA 3003)
Tutorial Sheet 5
Topic : Forced Convection Heat Transfer
[1]
Air at 100C and at a pressure of 100 kPa is flowing over a plate at a velocity of 3 m/s. If the plate is 30
cm wide and at
SCHOOL OF MECHANICAL SCIENCES
IIT BHUBANESWAR
HEAT TRANSFER (MEA 3003)
Tutorial Sheet 2
Topic : Steady State Heat Conduction with Heat Generation
[1]
What is heat generation? Give some examples related to real life applications.
[2]
Consider the uniform h
SCHOOL OF MECHANICAL SCIENCES
IIT BHUBANESWAR
HEAT TRANSFER (MEA 3003)
Tutorial Sheet 3
Topic : Heat Transfer from Extended Surfaces
[1]
Explain how the fins enhance heat transfer from a surface. Also, explain how the addition of fins may
actually decreas
SCHOOL OF MECHANICAL SCIENCES
IIT BHUBANESWAR
HEAT TRANSFER (MEA 3003)
Tutorial Sheet 1
Topic : Steady State Heat Conduction without Heat Generation
[1]
The temperature distribution across a wall, 1 m thick at a certain instant of time is given as :
Where
SCHOOL OF MECHANICAL SCIENCES
IIT BHUBANESWAR
HEAT TRANSFER (MEA 3003)
Tutorial Sheet 6
Topic : Free Convection Heat Transfer
[1]
Vertical door of a hot oven is 0.5 m high and is maintained at 2000C. it is exposed to atmospheric air
at 20 0C. Find (a) loc
CONVECTIVE HEAT TRANSFER
Important Terminology
Laminar Flow :
Laminar flow is that type of flow in which the fluid particles
move in a flat or curved un-mixing layer or streams and
follows a smooth continuous path in such a way that they
retain their rel
Time Allowed: 3 hours
Maximum Marks: 300
-.
om
Candidates should attempt any FIVE questions.
All questions carry equal marks.
'(
Let V and U be vector spaces over the field K and let V be of finite dimension. Let T: V. -+
U be a linear Map.
Prove that
dim