A study on mhd boundary layer flow over a nonlinear stretching sheet using im...eSAT Journals
Abstract
The problem of the MHD boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is discussed.
Using similarity transformation governing equations are transformed in to nonlinear ordinary differential equation. The Implicit finite
difference Keller box method is applied to find the numerical solution of nonlinear differential equation. Graphical results of fluid
velocity have been presented and discussed for the related parameters.
Keywords: MHD, boundary layer, nonlinear differential equations, and Keller box method
Numerical simulation on laminar free convection flow and heat transfer over a...eSAT Journals
Abstract
In the present numerical study, laminar free-convection flow and heat transfer over an isothermal vertical plate is presented. By
means of similarity transformation, the original nonlinear coupled partial differential equations of flow are transformed to a pair
of simultaneous nonlinear ordinary differential equations. Then, they are reduced to first order system. Finally, NewtonRaphson
method and adaptive Runge-Kutta method are used for their integration. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity and temperature profiles for various Prandtl number are illustrated graphically. Flow
and heat transfer parameters are derived as functions of Prandtl number alone. The results of the present simulation are then
compared with experimental data published in literature and find a good agreement.
Keywords: Free Convection, Heat Transfer, Matlab, Numerical Simulation, Vertical Plate.
A study on mhd boundary layer flow over a nonlinear stretching sheet using im...eSAT Journals
Abstract
The problem of the MHD boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is discussed.
Using similarity transformation governing equations are transformed in to nonlinear ordinary differential equation. The Implicit finite
difference Keller box method is applied to find the numerical solution of nonlinear differential equation. Graphical results of fluid
velocity have been presented and discussed for the related parameters.
Keywords: MHD, boundary layer, nonlinear differential equations, and Keller box method
Numerical simulation on laminar free convection flow and heat transfer over a...eSAT Journals
Abstract
In the present numerical study, laminar free-convection flow and heat transfer over an isothermal vertical plate is presented. By
means of similarity transformation, the original nonlinear coupled partial differential equations of flow are transformed to a pair
of simultaneous nonlinear ordinary differential equations. Then, they are reduced to first order system. Finally, NewtonRaphson
method and adaptive Runge-Kutta method are used for their integration. The computer codes are developed for this numerical
analysis in Matlab environment. Velocity and temperature profiles for various Prandtl number are illustrated graphically. Flow
and heat transfer parameters are derived as functions of Prandtl number alone. The results of the present simulation are then
compared with experimental data published in literature and find a good agreement.
Keywords: Free Convection, Heat Transfer, Matlab, Numerical Simulation, Vertical Plate.
Split Second Analysis Covering High Pressure Gas Flow Dynamics At Pipe Outlet...AEIJjournal2
A detailed investigation covering piped gas flow characteristics in high pressure flow conditions. Such flow
analysis can be resolved using established mathematical equations known as the Fanno condition, which
usually cover steady state, or final flow conditions. However, in real life, such flow conditions are
transient, varying with time. This paper uses CFD analysis providing a split second “snapshot” at what
happens at the pipe outlet, and therefore, a closer understanding at what happens at the pipe’s outlet in
high pressure gas flow condition.
In this example air was selected for simulation purposes. In HVAC applications, such gas flow conditions
can occur in typical applications such as; air compressors releasing high pressure air through a pipe, or
compressor over pressure refrigerant gas being released into the atmosphere via a discharge pipe.
Investigation has shown that rather than a steady mass flow rate condition occurring at the pipe outlet,
calculated by the Fanno flow condition, a spiked increase in flow rate occurs at the beginning,and then
stabilizing after a few seconds, with relatively minor ripples in flow rate. Other observations were also
made and commented.
CFD results in mass flow rate were compared with the mathematically derived results, differences were
recorded. The CFD analysis showed how the k-omega turbulence model performed well, with the processor
stabilizing at an early stage.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
SPLIT SECOND ANALYSIS COVERING HIGH PRESSURE GAS FLOW DYNAMICS AT PIPE OUTLET...AEIJjournal2
A detailed investigation covering piped gas flow characteristics in high pressure flow conditions. Such flow analysis can be resolved using established mathematical equations known as the Fanno condition, which usually cover steady state, or final flow conditions. However, in real life, such flow conditions are
transient, varying with time. This paper uses CFD analysis providing a split second “snapshot” at what happens at the pipe outlet, and therefore, a closer understanding at what happens at the pipe’s outlet in high pressure gas flow condition
Anomalous Diffusion Through Homopolar Membrane: One-Dimensional Model by Guilherme Garcia Gimenez and Adélcio C Oliveira* in Evolutions in Mechanical Engineering
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Split Second Analysis Covering High Pressure Gas Flow Dynamics At Pipe Outlet...AEIJjournal2
A detailed investigation covering piped gas flow characteristics in high pressure flow conditions. Such flow
analysis can be resolved using established mathematical equations known as the Fanno condition, which
usually cover steady state, or final flow conditions. However, in real life, such flow conditions are
transient, varying with time. This paper uses CFD analysis providing a split second “snapshot” at what
happens at the pipe outlet, and therefore, a closer understanding at what happens at the pipe’s outlet in
high pressure gas flow condition.
In this example air was selected for simulation purposes. In HVAC applications, such gas flow conditions
can occur in typical applications such as; air compressors releasing high pressure air through a pipe, or
compressor over pressure refrigerant gas being released into the atmosphere via a discharge pipe.
Investigation has shown that rather than a steady mass flow rate condition occurring at the pipe outlet,
calculated by the Fanno flow condition, a spiked increase in flow rate occurs at the beginning,and then
stabilizing after a few seconds, with relatively minor ripples in flow rate. Other observations were also
made and commented.
CFD results in mass flow rate were compared with the mathematically derived results, differences were
recorded. The CFD analysis showed how the k-omega turbulence model performed well, with the processor
stabilizing at an early stage.
EXACT SOLUTIONS OF A FAMILY OF HIGHER-DIMENSIONAL SPACE-TIME FRACTIONAL KDV-T...cscpconf
In this paper, based on the definition of conformable fractional derivative, the functional
variable method (FVM) is proposed to seek the exact traveling wave solutions of two higherdimensional
space-time fractional KdV-type equations in mathematical physics, namely the
(3+1)-dimensional space–time fractional Zakharov-Kuznetsov (ZK) equation and the (2+1)-
dimensional space–time fractional Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony
(GZK-BBM) equation. Some new solutions are procured and depicted. These solutions, which
contain kink-shaped, singular kink, bell-shaped soliton, singular soliton and periodic wave
solutions, have many potential applications in mathematical physics and engineering. The
simplicity and reliability of the proposed method is verified.
SPLIT SECOND ANALYSIS COVERING HIGH PRESSURE GAS FLOW DYNAMICS AT PIPE OUTLET...AEIJjournal2
A detailed investigation covering piped gas flow characteristics in high pressure flow conditions. Such flow analysis can be resolved using established mathematical equations known as the Fanno condition, which usually cover steady state, or final flow conditions. However, in real life, such flow conditions are
transient, varying with time. This paper uses CFD analysis providing a split second “snapshot” at what happens at the pipe outlet, and therefore, a closer understanding at what happens at the pipe’s outlet in high pressure gas flow condition
Anomalous Diffusion Through Homopolar Membrane: One-Dimensional Model by Guilherme Garcia Gimenez and Adélcio C Oliveira* in Evolutions in Mechanical Engineering
Similar to Generalized couette flow by assume solution (10)
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2. 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 2
3. ----- (1)
And the boundary are
5/1/2018 3
22
0
2
1 Bu u p
u u
t y x k
0
(0, ) 0
( , )
u t
u h t U
6. Put all these dimensional less
values in equation(1) we get
After simplification we get
5/1/2018 6
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
7. To make it more simplify we Drop
the sign of * we get
---------------(2)
5/1/2018 7
2
2
u u p
Hu
t y x
8. Assume solution for this
phenomena is
---------(3)
5/1/2018 8
( , ) Re{ ( ) }iwt
U y t F y e
iwtp
e
x
9. Put all these values in equation(2)
we get
After applying derivative we get
5/1/2018 9
2
2
Re [Re{ ( ) }] [Re{ ( ) }] [Re{ ( ) }]iwt iwt iwt iwt
F y e F y e e M F y e
t y
2
2
{ ( )} [Re ]( ( ))
d
F y iw M F y
dy
10. After the arranging of above
equation we have
(4)
5/1/2018 10
2
2
{ ( )} [Re ]( ( ))
d
F y iw M F y
dy
11. And the transform boundary
conditions are:
5/1/2018 11
0
(0) 0
(1)
f
f U
12. The auxiliary equation of (4) is
The solution is
5/1/2018 12
2
(Re ) 0m iw M
1 2cosh Re sinh Recy c iw My c iw My
14. Put these values in equation(4) we get
5/1/2018 14
0 [Re ]
[Re ]
iw M A
A
iw M
15. The general solution is
Apply the boundary conditions in above
equation we get
5/1/2018 15
1 2cosh Re sinh Re
[Re ]
y c iw My c iw My
iw M
1
0
2
Re
cosh Re
Re Re
sinh Re
c
iw M
U iw M
iw M iw Mc
iw M
16. Repalce and
5/1/2018 16
2c1c
0
cosh Re
Re
cosh Re
Re Re sinh Re
sinh Re
[Re ]
y iw My
iw M
U iw M
iw M iw M iw My
iw M
iw M