fundamental momentum transfer
TRANSCRIPT
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Transport Process(KNC2153)
Dr Khairuddin Sanaullah
Dr Ivy Tan Ai Wei
Dept. of Chemical Engineering & Energy SustainabilityFaculty of Engineering
Semester II, 2011-2012
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Course Outline
Chapter 1: Fundamentals of Momentum Transfer & Transport Properties
(Wk 1): Modes of momentum transfer, Newton‘s Law of viscosity, Types of fluid flow &
Reynolds Number, Momentum Transfer in a Fluid, Continuity Equation.
Chapter 2: Momentum Equation (Navier Stoke‘s) & It‘s Applications (Wk 2 & 3):
Derivation of Navier Stoke‘s Equation, Shell momentum balance & velocity
profile in laminar flow, Design equations for laminar & turbulent flow in
pipes, Compressible flow of gases, Boundary-layer flow & Turbulence.
To be Continued
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Course Outline
Books
Geankoplis, C.J., [2003],Transport Processes and Separation Process Principles ,
Prentice Hall
Joel Plawsky [2010], Transport Phenomena Fundamentals, CRC Press
Bird, R., [2002] Transport Phenomena, John Willey
Holland & Bragg [1995], Fluid Flow for Chemical Engineers (2nd Ed.), Butterworth.
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Fundamental Principles of Momentum Transfer
Modes of Momentum Transfer
• Shear
• Pressure
• Convection
Shear & Normal Stresses (Internal Fluid Forces): Differences in shear and normal
stresses across the control volume result in a flow of momentum from the higher to thelower stress. Shear & Normal stresses normally arise from two sources:
1. Pressure in the fluid
2. Velocity Gradients
The pressure gives rise to a normal stress component whereas velocity gradients give riseto the shear stress components and can contribute to the total normal stress.
External Foreces: The most important foreces are due to the pressure gradient
& gravity (body force - ρg). Both are generation terms.
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Fundamental Principles of Momentum Transfer
Modes of Momentum Transfer
Convection: Momentum may flow into and out of the control volume in a variety of
ways:
(i) By convection (i.e. by bulk fluid flow)
(ii) By molecular transfer (i.e. by velocity gradients)
(iii) By external forces acting on the body such as gravity or pressure (e.g. Pump).
The first mechanism mentioned above arises due to the fluid acceleration through the
control volume and the second arises from shear stress acting on the fluid.
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Transport Property (Momentum)
Momentum Transport –Newton’s Law of Viscosity:
When a fluid is flowing through a pipe or between two flat plates, either of two types o
flow may occur, depending on the velocity of this fluid (i.e. Laminar or turbulent). Here
the discussion is limited to laminar flow.
An elastic solid deforms by an amount proportional to the applied stress. However, a fluid
when subjected to a similar applied stress will continue to deform, i.e. to flow at a
velocity that increases with increasing stress. A fluid exhibits to this stress, Viscosity is
that property of a fluid which gives rise to forces that resist the relative movement o
adjacent layers in the fluid.
The ideas can be clarified by a more quantitative discussion of viscosity: refer figure in
the next slide.
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Transport Property (Momentum)
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Transport Property (Momentum)
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Transport Property (Momentum)
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Fundamental Principles of Momentum Transfer
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Fundamental Principles of Momentum Transfer
Types of Fluid Flow & Reynolds Number
Laminar flow ─ the flow is characterized
by smooth streamlines and
highly-ordered motion.
Turbulent flow ─ the flow is
characterized by velocity
fluctuations and
highly-disordered motion.
The transition from laminar
to turbulent flow does not
occur suddenly.
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Fundamental Principles of Momentum Transfer
Types of Fluid Flow & Reynolds NumberThe velocity profile in turbulent flow is much fuller than that in laminar flow, with a
sharp drop near the surface.The turbulent boundary layer can be considered to consist of four regions:
Viscous sublayer
Buffer layer
Overlap layer
Turbulent layerThe intense mixing in turbulent flow enhances heat and momentum transfer, which
increases the friction force on the surface and the convection heat transfer rate.
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Fundamental Principles of Momentum Transfer
Inertia forces
ReViscous forces
c cVL VL
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Fundamental Principles of Momentum Transfer
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Fundamental Principles of Momentum Transfer
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Transport Property (Mass)
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Transport Property (Mass)
Example: A mixture of He and gas is contained in a pipe at 298 K and 1 atm total
pressure which is constant throughout. At one end of the pipe at point 1 the partial
pressure of He is 0.60 atm and at the other end 0.2 m (20 cm) = 0.20 . Calculate the flux of He at steady state if of the mixture is
0.687×10− /. Use SI units.
Solution
Since total pressure P is constant, then the concentration c is constant, where c is as
follows for a gas from the ideal gas law. = ≫
=
=
Where n is kg mol a + b, V is volume in , T is temperature in K, R is gas constant,
expressed as 8314.3.
.or 82.057 × 10− .
.and c is kg mol a + b/ .
For steady state the flux in equation (4) is constant, also for a gas is constant.Rearranging equation (4) and integrating,
=
=(−)
− …. (i)
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Transport Property (Mass)
Also, from the ideal gas law, = , and
=
=
…. (ii)
Substituting (ii) into (i) = (−)(−)
Now substitute values in this equation, = 0.6 atm = 0.2 atm. Here pressures in
atm are used with SI units.
=(.6×)(.6−.)
(.6×)()(.−) = . × −
.
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Transport Property (Mass)
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Transport Property (Energy)
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Transport Property (Energy)
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i
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Transport Properties
T P i
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Transport Properties