Stress and Strains, large deformations, Nonlinear Elastic analysis,critical load analysis, hyper elastic materials, FE formulations for Non-linear Elasticity, Nonlinear Elastic Analysis Using Commercial Finite Element Programs, Fitting Hyper elastic Material Parameters from Test Data
Topics:
1. Introduction to Fluid Dynamics
2. Surface and Body Forces
3. Equations of Motion
- Reynold’s Equation
- Navier-Stokes Equation
- Euler’s Equation
- Bernoulli’s Equation
- Bernoulli’s Equation for Real Fluid
4. Applications of Bernoulli’s Equation
5. The Momentum Equation
6. Application of Momentum Equations
- Force exerted by flowing fluid on pipe bend
- Force exerted by the nozzle on the water
7. Measurement of Flow Rate
a). Venturimeter
b). Orifice Meter
c). Pitot Tube
8. Measurement of Flow Rate in Open Channels
a) Notches
b) Weirs
Stress and Strains, large deformations, Nonlinear Elastic analysis,critical load analysis, hyper elastic materials, FE formulations for Non-linear Elasticity, Nonlinear Elastic Analysis Using Commercial Finite Element Programs, Fitting Hyper elastic Material Parameters from Test Data
Topics:
1. Introduction to Fluid Dynamics
2. Surface and Body Forces
3. Equations of Motion
- Reynold’s Equation
- Navier-Stokes Equation
- Euler’s Equation
- Bernoulli’s Equation
- Bernoulli’s Equation for Real Fluid
4. Applications of Bernoulli’s Equation
5. The Momentum Equation
6. Application of Momentum Equations
- Force exerted by flowing fluid on pipe bend
- Force exerted by the nozzle on the water
7. Measurement of Flow Rate
a). Venturimeter
b). Orifice Meter
c). Pitot Tube
8. Measurement of Flow Rate in Open Channels
a) Notches
b) Weirs
Pressure Gradient Influence on MHD Flow for Generalized Burgers’ Fluid with S...IJERA Editor
This paper presents a research for magnetohydrodynamic (MHD) flow of an incompressible generalized
Burgers’ fluid including by an accelerating plate and flowing under the action of pressure gradient. Where the
no – slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is
introduced to establish the constitutive relationship of the generalized Burgers’ fluid. By using the discrete
Laplace transform of the sequential fractional derivatives, a closed form solutions for the velocity and shear
stress are obtained in terms of Fox H- function for the following two problems: (i) flow due to a constant
pressure gradient, and (ii) flow due to due to a sinusoidal pressure gradient. The solutions for no – slip condition
and no magnetic field, can be derived as special cases of our solutions. Furthermore, the effects of various
parameters on the velocity distribution characteristics are analyzed and discussed in detail. Comparison between
the two cases is also made.
Effects on Study MHD Free Convection Flow Past a Vertical Porous Plate with H...IJMTST Journal
This paper deals with the combined soret effect of thermal radiation and heat generation on the MHD free
convection heat and mass transfer flow of a viscous incompressible fluid past a continuously moving infinite
plate. Closed form of solution for the velocity, temperature and concentration field are obtained and
discussed graphically for various values of the physical parameters present. In addition, expressions for the
skin friction and Sherwood number is also derived and finally discussed with the graphs.
Decay Property for Solutions to Plate Type Equations with Variable CoefficientsEditor IJCATR
In this paper we consider the initial value problem for a plate type equation with variable coefficients and memory in
1 n R n ), which is of regularity-loss property. By using spectrally resolution, we study the pointwise estimates in the spectral
space of the fundamental solution to the corresponding linear problem. Appealing to this pointwise estimates, we obtain the global
existence and the decay estimates of solutions to the semilinear problem by employing the fixed point theorem
Approximate Analytical Solution of Non-Linear Boussinesq Equation for the Uns...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy perturbation transform method(HPTM). The solution is compared with the exact solution. The comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer
parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height of water table. The results resemble well with the physical phenomena.
Anomalous Diffusion Through Homopolar Membrane: One-Dimensional Model by Guilherme Garcia Gimenez and Adélcio C Oliveira* in Evolutions in Mechanical Engineering
Chemical Reaction on Heat and Mass TransferFlow through an Infinite Inclined ...iosrjce
The numerical studies are performed to examine the mass transfer flow with thermal diffusion and
diffusion thermo effect past an infinite, inclined vertical plate in a porous medium in the presence of chemical
reaction. First of all, the governing equations are transformed to a system of dimensionless coupled partial
equations. Explicit finite difference method has been used to solve these dimensionless equations for momentum,
concentration and energy equations. During the course of discussion, it is found that various parameters related
to the problem influence the calculated result. Finally, the profiles of velocity, concentration and temperature
are analyzed and illustrated with graphs.
APPROXIMATE ANALYTICAL SOLUTION OF NON-LINEAR BOUSSINESQ EQUATION FOR THE UNS...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy perturbation transform method(HPTM). The solution is compared with the exact solution. The comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height of water table. The results resemble well with the physical phenomena.
APPROXIMATE ANALYTICAL SOLUTION OF NON-LINEAR BOUSSINESQ EQUATION FOR THE UNS...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq
equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper
approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy
perturbation transform method(HPTM). The solution is compared with the exact solution. The
comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer
parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height
of water table. The results resemble well with the physical phenomena.
APPROXIMATE ANALYTICAL SOLUTION OF NON-LINEAR BOUSSINESQ EQUATION FOR THE UNS...mathsjournal
For one dimensional homogeneous, isotropic aquifer, without accretion the governing Boussinesq
equation under Dupuit assumptions is a nonlinear partial differential equation. In the present paper
approximate analytical solution of nonlinear Boussinesq equation is obtained using Homotopy
perturbation transform method(HPTM). The solution is compared with the exact solution. The
comparison shows that the HPTM is efficient, accurate and reliable. The analysis of two important aquifer
parameters namely viz. specific yield and hydraulic conductivity is studied to see the effects on the height
of water table. The results resemble well with the physical phenomena.
Numerical simulation on laminar convection flow and heat transfer over a non ...eSAT Journals
Abstract
A numerical algorithm is presented for studying laminar convection flow and heat transfer over a non-isothermal horizontal plate.
plate temperature Tw varies with x in the following prescribed manner:
T T Cx w
n 1
where C and n are constants. By means of similarity transformation, the original nonlinear partial differential equations of flow
are transformed to a pair of nonlinear ordinary differential equations. Subsequently they are reduced to a first order system and
integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity, and temperature profiles for various Prandtl number and n are illustrated graphically.
Flow and heat transfer parameters are derived. The results of the present simulation are then compared with experimental data in
literature with good agreement.
Keywords: Free Convection, Heat Transfer, Non-isothermal Horizontal Plate, Matlab, Numerical Simulation.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability
The numerical solution of helmholtz equation via multivariate padé approximationeSAT Journals
Abstract
In this study, we consider the numerical solution of the Helmholtz equation, arising from numerous physical phenomena and
engineering applications including energy systems. We make use of a Padé Approximation method for the solution of the
Helmholtz equation. Firstly, Helmholtz partial differential equation had been converted to power series by two-dimensional
differential transformation, then the numerical solution of the equation was put into Padé series form for accelerating
convergence and decreasing computational time. Hereby, we obtained numerical solution of Helmholtz type partial differential
equation.
Key Words: Helmholtz equation, Two-dimensional differential transformation, Multivariate Padé approximation,
power series
Exact Solutions for MHD Flow of a Viscoelastic Fluid with the Fractional Bur...IJMER
This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a
generalized Burgers’ fluid in an annular pipe. Closed from solutions for velocity is obtained by using finite
Hankel transform and discrete Laplace transform of the sequential fractional derivatives. Finally, the
figures are plotted to show the effects of different parameters on the velocity profile.
Have you ever wondered how search works while visiting an e-commerce site, internal website, or searching through other types of online resources? Look no further than this informative session on the ways that taxonomies help end-users navigate the internet! Hear from taxonomists and other information professionals who have first-hand experience creating and working with taxonomies that aid in navigation, search, and discovery across a range of disciplines.
This presentation, created by Syed Faiz ul Hassan, explores the profound influence of media on public perception and behavior. It delves into the evolution of media from oral traditions to modern digital and social media platforms. Key topics include the role of media in information propagation, socialization, crisis awareness, globalization, and education. The presentation also examines media influence through agenda setting, propaganda, and manipulative techniques used by advertisers and marketers. Furthermore, it highlights the impact of surveillance enabled by media technologies on personal behavior and preferences. Through this comprehensive overview, the presentation aims to shed light on how media shapes collective consciousness and public opinion.
This presentation by Morris Kleiner (University of Minnesota), was made during the discussion “Competition and Regulation in Professions and Occupations” held at the Working Party No. 2 on Competition and Regulation on 10 June 2024. More papers and presentations on the topic can be found out at oe.cd/crps.
This presentation was uploaded with the author’s consent.
0x01 - Newton's Third Law: Static vs. Dynamic AbusersOWASP Beja
f you offer a service on the web, odds are that someone will abuse it. Be it an API, a SaaS, a PaaS, or even a static website, someone somewhere will try to figure out a way to use it to their own needs. In this talk we'll compare measures that are effective against static attackers and how to battle a dynamic attacker who adapts to your counter-measures.
About the Speaker
===============
Diogo Sousa, Engineering Manager @ Canonical
An opinionated individual with an interest in cryptography and its intersection with secure software development.
Acorn Recovery: Restore IT infra within minutesIP ServerOne
Introducing Acorn Recovery as a Service, a simple, fast, and secure managed disaster recovery (DRaaS) by IP ServerOne. A DR solution that helps restore your IT infra within minutes.
Sharpen existing tools or get a new toolbox? Contemporary cluster initiatives...Orkestra
UIIN Conference, Madrid, 27-29 May 2024
James Wilson, Orkestra and Deusto Business School
Emily Wise, Lund University
Madeline Smith, The Glasgow School of Art
2. GROUP MEMBERS
• Abbas Ali
• Haris Anwar
• Manzoor Ahmed
• Sehrish Amin
• Syed Wasim Shah
• Usman Khan
• Waqas Noman
2
3. • On the Unsteady unidirectional
flows generated by impulsive
motion of a boundary or sudden
application of a pressure gradient
in the presence of MHD and
porous medium .
M. Emin Erdogan
3
TOPIC OF PRESENTATION
4. INTRODUCTION
The governing equation for fluid mechanics are
the Navier-Stokes Equation. Exact solutions are
very important for many reasons. They provide a
standard for checking the accuracies of many
approximate methods. An exact solution is
defined as a solution of the Navier-Stokes
equations and the continuity equation. Most of
the exact solutions for unsteady flows are in
series form.
4
5. CONTINUED
In this paper, unsteady flows considered are
Stoke’s first problem, unsteady couette flow,
unsteady Poiseuille flow and unsteady
generalized Couette flow.
The solutions for these flows are in the form of
series.
5
7. The flow over a plane wall which is initially at
rest and is suddenly moved in its own plane with
a constant velocity is termed Stoke’s first
problem. The fluid stays in the region y≥0 and
the x-axis is chosen as the plane wall, in the
presence of MHD and porous media.
7
MATHEMATICAL FORMULATION
8. The governing equation is:
• Where
• Magnetic parameter
• porousity parameter
8
22
0
2
(1)
u u
u u
t y K
2
0
K
9. • The dimensionless variable are
• , ,
9
0u
u
u
uuu
0
ou
y y
2
ou
t t
0
y
y
u
2
0
t
t
u
10. • From (1)
10
2 2
0 0 0 0
0
2
2
0 0
3 3 22
0 0 0 0
02 2
3 3 22
0 0 0 0
02
( )
( )
( ) ( )
( )
( ) ( )
( )
( ) ( )
u u u u u u
u u
y Kt y
u u
u u u uu u
u u
t y K
u u u uu u
u u
t y K
11. • Multiplying by we get
11
u
K
Mu
y
u
t
u 1
2
2
3
0u
22
0
2 2 2
0 0
( )
uu u
u
t y u K u
12. • Let
• And
• For easy writing we use “u” instead of
12
u
2
0
2
0
2
2
0
(dim )
1
u
M ensionles
u
ku k
22. Let
Formula
22
24
2
2 Hy
a
Hy
a
)()(
4 22
2
2
2
2
r
a
rerfce
r
a
rerfcedze aa
t
y
z
a
z
)
2
2
()
2
2
(
2
1
),(
2
2
22
2
2
t
yt
y
erfce
t
yt
y
erfcetyu
Hy
Hy
Hy
Hy
23. Now we check the condition
23
)
2
()
2
(
2
1
),( Ht
t
y
erfceHt
t
y
erfcetyu
yy
HH
25. • Satisfy all the condition so our solution is ok
25
0),(
)()(
2
1
),(
tu
erfceerfcetu
26. • Porosity term in dimensionless
• And M is also Dimensionless
26
1
)( 24
24
212
24
2
0
2
TL
TL
LTL
TL
ku
2 2 1 2 1 2 1 3 3 2
0
2 3 2 2
0
( ) ( )L T MT A M L T A
u ML L T
27. 27
2
2 1 2 4 2 1 3 3 2 1 3 2 20
2
0
2
2 1 1 3 3 2 2 1 4 3 20
2
0
2
0 0 00
2
0
1
L L M T A M L T A M L L T
u
M L T
u
M L T
u
29. COUETTE FLOW
If the flow is in between two
infinite parallel plates and one
of them is moving relative to
the other plate, then this kind
of flow is called couette flow.
5/1/2018 29
CITY UNIVERSITY OF SCIENCE AND
INFORMATION TECHNOLOGY
30. MATHEMATICAL FORMULATION
Suppose that the incompressible newtonian
viscous fluid is bounded between two rigid
boundaries at y=0 and y=h. Initially the fluid is at
rest. The fluid start motion due to the
disturbance of upper plate, and the lower plate
is held stationary. Also, in the presence of MHD
and porous medium.
5/1/2018 30
34. M is the MHD
1/k is the porous media
5/1/2018 34
2
0
2
0
2
2
0
,
1
,
1
,
B
M
u
k ku
H M
k
35. Put all these dimensional less
values in equation(1)
And After simplification we get
5/1/2018 35
* 2 *
*
* 2 *
u u
Hu
t y
36. To make it more simplify we Drop
the sign of * we get
---------------(2)
5/1/2018 36
2
2
u u
Hu
t y
37. For steady flow the
Then we get
5/1/2018 37
0
u
t
1 2
2 2
1 1
2 2
c y c
u
H H
y y
38. put y(0)=0 and y(1)=1 then it
become
Put all these value in above equation
we get
5/1/2018 38
2
1
0
1
2
c
H
c
39. Which is the solution for the case of
steady part.
For unsteady we get an equation of
the form
5/1/2018 39
(4)
2
1
2
1
2
H
y
u
H
y
40. Where f(y,t) satisfies the following differential equation:
5/1/2018 40
2
1
2
( , )
1
2
H
y
u f y t
H
y
2
2
(1, ) 0,
(0, ) 0
f f
Hf
t y
f t
f t
41. As we known that
5/1/2018 41
'
'
2
''
2
( , ) ( ) ( )
( ) ( )
( ) ( )
( ) ( )
f y t Y y T t
f
Y y T t
t
f
Y y T t
y
f
Y y T t
y
42. Now the above equation become
5/1/2018 42
' ''
' ''
' ''
( ) ( ) ( ) ( ) ( ) ( )
( )
( )
Y y T t Y y T t HY y T t
YT T Y HY
T Y HY
T Y
43. Let suppose that
The equation become
5/1/2018 43
' ''
T Y
H
T Y
'
''
T
T
Y
H
Y
45. Put the initial conditions we get
5/1/2018 45
2
1 2
( ) 0
( ) cos sin
D H
D i H
Y y A H y A H y
1
2
2
0
(1) sin
sin 0
A
and
y A H
A H
49. Hence
Thus
5/1/2018 49
2 2
2
( )
1
( , ) sin
n
H t
h
n n
n
f y t A e n y
2 2
( )
1
2 ( 1)
sin
n
n H t
n
u Y e n y
n
51. POISEUILLE FLOW
If the flow is in between two
infinite parallel plates and the
flow is induced due to the
sudden application of pressure
gradient.
5/1/2018 51
CITY UNIVERSITY OF SCIENCE AND
INFORMATION TECHNOLOGY
52. MATHEMATICAL FORMULATION
Suppose that the incompressible newtonian
viscous fluid is bounded between two parallel
plates at y = -b and y = b, and it is initially at rest
and the fluid starts suddenly due to a constant
pressure gradient. In the presence of MHD and
porous media.
5/1/2018 52
54. Mathematical modeling
And the boundary are
5/1/2018 54
22
0
2
1 Bu u p
u u
t y x k
(1)
( , ) 0
( , ) 0
u b t
u b t
56. M is the MHD
1/k is the porous media
5/1/2018 56
2
0
2
0
2
2
0
,
1
,
1
,
B
M
u
k ku
H M
k
57. Put all these dimensional less
values in equation(1) we get
After simplification we get
5/1/2018 57
* 2 * *
*
* 2 * *
u u p
Hu
t y x
58. To make it more simplify we Drop
the sign of * we get
---------------(2)
5/1/2018 58
2
2
u u p
Hu
t y x
59. For steady flow the
Then we get
5/1/2018 59
0
u
t
2
1 2
2 22
1 12 1
2 22
c y cp y
u
Hy Hyx Hy
60. put y(1)=0 and y(-1)=0 then it
become
Put all these value in above equation
we get
5/1/2018 60
2
2
1
2
0
p b
c
x
c
61. 5/1/2018 61
(4)
Which is the
solution for the
case of study
part.
For unsteady we
get an equation
of the form
2
2
1
1
2 1
2
p
u y
x Hy
62. Where we have
5/1/2018 62
2
2
( , )
(1, ) 0,
( 1, ) 0
f f
Hf y t
t y
f t
f t
2
2
1
1 ( , )
2 1
2
p
u y f y t
x Hy
63. As we known that
5/1/2018 63
'
'
2
''
2
( , ) ( ) ( )
( ) ( )
( ) ( )
( ) ( )
f y t Y y T t
f
Y y T t
t
f
Y y T t
y
f
Y y T t
y
64. Now the above equation become
5/1/2018 64
' ''
' ''
''
'
( ) ( ) ( ) ( ) ( ) ( )
( )
( )
Y y T t Y y T t HY y T t
YT T Y HY
Y HY
T T
Y
65. Let suppose that
The equation become
5/1/2018 65
' ''
T Y
H
T Y
'
''
T
T
Y
H
Y
67. Put the initial conditions we get
5/1/2018 67
2
1 2
( ) 0
( ) cos sin
D H
D i H
Y y A H y A H y
2
1
1
0
(1) cos
cos 0
A
and
y A H
A H
73. It is the special case of flow because it is
formed from couette and poiseuille flow.
The flow in bounded in between two
parallel plates at y=0 and y=h and it is
initially at rest. The fluid is also magnetically
conducted and pass through porous media.
The flow is due to pressure gradient as well
as of motion of upper plate. The governing
equation for this flow is given as
5/1/2018 73
75. Mathematical modeling
And the boundary are
5/1/2018 75
22
0
2
1 Bu u p
u u
t y x k
0
(0, ) 0
( , )
u t
u h t U
(1)
78. Put all these dimensional less
values in equation(1) we get
After simplification we get
5/1/2018 78
2 0* 2 * *
* *0 0 0 0 0
* 2 2 * 2 *
U U U U Uu u p
u u
d t d y d x k
* 2 * *
*
* 2 * *
u u p
Hu
t y x
79. To make it more simplify we Drop
the sign of * we get
---------------(2)
5/1/2018 79
2
2
u u p
Hu
t y x
80. For steady flow the
Then we get
5/1/2018 80
0
u
t
2 2
1 2
1
2
p
u y HUy c y c
y
81. put y(0)=0 and y(1)=1 then it
become
Put all these value in above equation
we get
5/1/2018 81
2
1
0
2
c
p
c U HU
x
82. After simplification we get
5/1/2018 82
(4)
2 2
[ ]
2 2
p p
u y HUy U HU y
x x
83. Which is the solution for the case of
study part.
For unsteady we get an equation of
the form
5/1/2018 83
2
[ ] [ ]
2 2
p p
u HU y U HU y
x x
84. Where we have
5/1/2018 84
2
[ ] [ ] ( , )
2 2
p p
u HU y U HU y f y t
x x
2
2
( , )
(1, ) 0,
(0, ) 0
f f
Hf y t
t y
f t
f t
85. As we known that
5/1/2018 85
'
'
2
''
2
( , ) ( ) ( )
( ) ( )
( ) ( )
( ) ( )
f y t Y y T t
f
Y y T t
t
f
Y y T t
y
f
Y y T t
y
86. Now the above equation become
5/1/2018 86
' ''
' ''
''
'
( ) ( ) ( ) ( ) ( ) ( )
( )
( )
Y y T t Y y T t HY y T t
YT T Y HY
Y HY
T T
Y
87. Let suppose that
The equation become
5/1/2018 87
' ''
T Y
H
T Y
'
''
T
T
Y
H
Y
89. Put the initial conditions we get
5/1/2018 89
2
1 2
( ) 0
( ) cos sin
D H
D i H
Y y A H y A H y
1
2
2
0
( ) sin
sin 0
A
and
y h A H
A H
93. Hence
Thus
5/1/2018 93
2 2
( )
1
( , ) sinn H t
n n
n
f y t A e n y
2 2
2 ( )
1
2 ( 1)
[ ] [ ] sin
2 2
n
n H t
n
p p
u HU y U HU y e n y
x x n