2. INTRODUCTION
Q. What are Transport Phenomena ?
Ans. A combination of three closely related topics
Q. Why these transfer processes be studied together ?
1. They very frequently occur simultaneously in nature
2. The basic equations describing these transfer processes are very
closely related
3. The close similarity of these equations lead to “analogies”
4. Mathematics required for the three transfer processes equations
is very similar
5. The basic molecular mechanism of the three transfer processes is
very similar. The same molecules transfer momentum, energy
and mass, through viscosity, thermal conductivity and diffusivity
Momentum Transfer/Transport
Energy Transfer/Transport
Chemical Species Mass Transfer/Transport
Fluid Dynamics
Heat Transfer
Mass Transfer
4. Viscosity and Newton’s Law of Viscosity
Example of two parallel plates
Shear force acting on the second
molecular layer of fluid is due to
the difference in the velocities of
the two adjacent layers
• Top layer stationary,
• Bottom layer moves with constant velocity V
• A fluid is filled between the plates
• No slip condition between fluid and plates at both the plate surfaces
5. x
y
x
y
Viscosity and Newton’s Law of Viscosity, contd.
-2
Common sense suggests the following.
1. A constant force F is required to
maintain the motion of lower plate
2. This force is directly proportional to
1. Area of plates
2. Velocity of lower plate
3. This force is inversely proportional
to
1. Distance between the plates
Mathematical Interpretation Of Common Sense
F V F V
A Y A Y
V/Y is the gradient or slope
x
dv
V
Y dy
The force applied, F is the shear force
Y t < 0
t = 0
x
y
x
y
small t
large t
V
V
vx(y)
V
vx(y, t)
Fluid initially
at rest
Lower plate set
in motion
Velocity buildup
in unsteady flow
Final velocity
distribution in
steady flow
6. Viscosity and Newton’s Law of Viscosity,
contd. -3
The shear stress exerted in the x-direction on a
fluid surface of constant y by the fluid in the
region of lesser y is designated as
τ yx
fluid surface of constant y, Shear
force on unit area perpendicular to
the y-direction
x-direction
Shear Stress
The shear stress is moving in the
direction of y because the bottom layer
of fluid exerts a shear stress
on the next layer which then exerts
a shear stress on subsequent layer
Shear stress is induced by the
motion of the plate. Shear stress
can be induced by a pressure
gradient or a gravity force.
Pressure force is a force acting on a
surface while the gravity force is the
force acting on a fluid volume
7. Viscosity and Newton’s Law of Viscosity,
contd. -4
The shear stress is a function of
1. Velocity gradient
2. Properties of the fluid
If this functional dependence is linear:
fluids are called Newtonian Fluids
x
yx
dv
dy
Where, vx = fluid velocity in the x-direction
μ = fluid viscosity, a property of the fluid, not the physical system
8. x-momentum is being transmitted through
the fluid in the positive у direction.
Momentum goes "downhill" from a region
of high velocity to a region of low velocity.
The velocity gradient can therefore be
thought of as a "driving force" for
momentum transport.
9. Viscosity and Newton’s Law of Viscosity,
contd. -4
The shear stress is a function of
1. Velocity gradient
2. Properties of the fluid
If this functional dependence is linear:
fluids are called Newtonian Fluids
x
yx
dv
dy
Where, vx = fluid velocity in the x-direction
μ = fluid viscosity, a property of the fluid, not the physical system
The viscosity of Newtonian fluids is constant
The temperature dependence is between T0.6 and T. Some theories are available.
Behaviour Of Gases At Moderate Pressures
Viscosity Is Independent Of Pressure Increases With Temperature
10. Viscosity and Newton’s Law of Viscosity,
contd. -5
Behaviour Of Liquids
Viscosity Is Independent Of Pressure Decreases With Temperature
Units of viscosity is g/cm/sec (poise) or Pa-s.
Magnitudes:
Air @ 20C 0.00018 g/cm/sec
Liquid water @ 20 C 0.001 Pa-s, 0.01 g/cm/s
