Abstract: This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.
Abstract: In this work we present a family of new convergent
type methods splitting high order no negative steps feature that
allows your application to irreversible problems. Performing affine
combinations consist of results obtained with Trotter Lie integrators
of different steps. Some examples where applied symplectic
compared with methods, in particular a pair of differential equations
semilinear. The number of basic integrations required is comparable
with integrators symplectic, but this technique allows the ability
to do the math in parallel thus reducing the times of which
exemplify exhibiting some implementations with simple schemes for
its modularity and scalability process.
Abstract: Torrefaction of biomass pellets is considered as a
useful pretreatment technology in order to convert them into a high
quality solid biofuel that is more suitable for pyrolysis, gasification,
combustion, and co-firing applications. In the course of torrefaction,
the temperature varies across the pellet, and therefore chemical
reactions proceed unevenly within the pellet. However, the
uniformity of the thermal distribution along the pellet is generally
assumed. The torrefaction process of a single cylindrical pellet is
modeled here, accounting for heat transfer coupled with chemical
kinetics. The drying sub-model was also introduced. The nonstationary
process of wood pellet decomposition is described by the
system of non-linear partial differential equations over the
temperature and mass. The model captures well the main features of
the experimental data.
Abstract: In the present study we have investigated axial
buckling characteristics of nanocomposite beams reinforced by
single-walled carbon nanotubes (SWCNTs). Various types of beam
theories including Euler-Bernoulli beam theory, Timoshenko beam
theory and Reddy beam theory were used to analyze the buckling
behavior of carbon nanotube-reinforced composite beams.
Generalized differential quadrature (GDQ) method was utilized to
discretize the governing differential equations along with four
commonly used boundary conditions. The material properties of the
nanocomposite beams were obtained using molecular dynamic (MD)
simulation corresponding to both short-(10,10) SWCNT and long-
(10,10) SWCNT composites which were embedded by amorphous
polyethylene matrix. Then the results obtained directly from MD
simulations were matched with those calculated by the mixture rule
to extract appropriate values of carbon nanotube efficiency
parameters accounting for the scale-dependent material properties.
The selected numerical results were presented to indicate the
influences of nanotube volume fractions and end supports on the
critical axial buckling loads of nanocomposite beams relevant to
long- and short-nanotube composites.
Abstract: MHD chemically reacting viscous fluid flow towards
a vertical surface with slip and convective boundary conditions has
been conducted. The temperature and the chemical species
concentration of the surface and the velocity of the external flow are
assumed to vary linearly with the distance from the vertical surface.
The governing differential equations are modeled and transformed
into systems of ordinary differential equations, which are then solved
numerically by a shooting method. The effects of various parameters
on the heat and mass transfer characteristics are discussed. Graphical
results are presented for the velocity, temperature, and concentration
profiles whilst the skin-friction coefficient and the rate of heat and
mass transfers near the surface are presented in tables and discussed.
The results revealed that increasing the strength of the magnetic field
increases the skin-friction coefficient and the rate of heat and mass
transfers toward the surface. The velocity profiles are increased
towards the surface due to the presence of the Lorenz force, which
attracts the fluid particles near the surface. The rate of chemical
reaction is seen to decrease the concentration boundary layer near the
surface due to the destructive chemical reaction occurring near the
surface.
Abstract: This paper deals with nonlinear vibration analysis
using finite element method for frame structures consisting of elastic
and viscoelastic damping layers supported by multiple nonlinear
concentrated springs with hysteresis damping. The frame is supported
by four nonlinear concentrated springs near the four corners. The
restoring forces of the springs have cubic non-linearity and linear
component of the nonlinear springs has complex quantity to represent
linear hysteresis damping. The damping layer of the frame structures
has complex modulus of elasticity. Further, the discretized equations in
physical coordinate are transformed into the nonlinear ordinary
coupled differential equations using normal coordinate corresponding
to linear natural modes. Comparing shares of strain energy of the
elastic frame, the damping layer and the springs, we evaluate the
influences of the damping couplings on the linear and nonlinear impact
responses. We also investigate influences of damping changed by
stiffness of the elastic frame on the nonlinear coupling in the damped
impact responses.
Abstract: In this study, one dimensional phase change problem
(a Stefan problem) is considered and a numerical solution of this
problem is discussed. First, we use similarity transformation to
convert the governing equations into ordinary differential equations
with its boundary conditions. The solutions of ordinary differential
equation with the associated boundary conditions and interface
condition (Stefan condition) are obtained by using a numerical
approach based on operational matrix of differentiation of shifted
second kind Chebyshev wavelets. The obtained results are compared
with existing exact solution which is sufficiently accurate.
Abstract: Bringing forth a survey on recent higher order spline
techniques for solving boundary value problems in ordinary
differential equations. Here we have discussed the summary of the
articles since 2000 till date based on higher order splines like Septic,
Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree
splines. Comparisons of methods with own critical comments as
remarks have been included.
Abstract: This paper deals with the study of reflection and
transmission characteristics of acoustic waves at the interface of a
semiconductor half-space and elastic solid. The amplitude ratios
(reflection and transmission coefficients) of reflected and transmitted
waves to that of incident wave varying with the incident angles have
been examined for the case of quasi-longitudinal wave. The special
cases of normal and grazing incidence have also been derived with
the help of Gauss elimination method. The mathematical model
consisting of governing partial differential equations of motion and
charge carriers’ diffusion of n-type semiconductors and elastic solid
has been solved both analytically and numerically in the study. The
numerical computations of reflection and transmission coefficients
has been carried out by using MATLAB programming software for
silicon (Si) semiconductor and copper elastic solid. The computer
simulated results have been plotted graphically for Si
semiconductors. The study may be useful in semiconductors,
geology, and seismology in addition to surface acoustic wave (SAW)
devices.
Abstract: In this study, out-of-plane free vibrations of a circular
rods is investigated theoretically. The governing equations for
naturally twisted and curved spatial rods are obtained using
Timoshenko beam theory and rewritten for circular rods. Effects of
the axial and shear deformations are considered in the formulations.
Ordinary differential equations in scalar form are solved analytically
by using transfer matrix method. The circular rods of the mass matrix
are obtained by using straight rod of consistent mass matrix. Free
vibrations frequencies obtained by solving eigenvalue problem. A
computer program coded in MATHEMATICA language is prepared.
Circular beams are analyzed through various examples for free
vibrations analysis. Results are compared with ANSYS results based
on finite element method and available in the literature.
Abstract: In this paper, the problem of steady laminar boundary
layer flow and heat transfer over a permeable exponentially
stretching/shrinking sheet with generalized slip velocity is
considered. The similarity transformations are used to transform the
governing nonlinear partial differential equations to a system of
nonlinear ordinary differential equations. The transformed equations
are then solved numerically using the bvp4c function in MATLAB.
Dual solutions are found for a certain range of the suction and
stretching/shrinking parameters. The effects of the suction parameter,
stretching/shrinking parameter, velocity slip parameter, critical shear
rate and Prandtl number on the skin friction and heat transfer
coefficients as well as the velocity and temperature profiles are
presented and discussed.
Abstract: An analysis is carried out to investigate the effect of
magnetic field and heat source on the steady boundary layer flow and
heat transfer of a Casson nanofluid over a vertical cylinder stretching
exponentially along its radial direction. Using a similarity
transformation, the governing mathematical equations, with the
boundary conditions are reduced to a system of coupled, non –linear
ordinary differential equations. The resulting system is solved
numerically by the fourth order Runge – Kutta scheme with shooting
technique. The influence of various physical parameters such as
Reynolds number, Prandtl number, magnetic field, Brownian motion
parameter, thermophoresis parameter, Lewis number and the natural
convection parameter are presented graphically and discussed for non
– dimensional velocity, temperature and nanoparticle volume
fraction. Numerical data for the skin – friction coefficient, local
Nusselt number and the local Sherwood number have been tabulated
for various parametric conditions. It is found that the local Nusselt
number is a decreasing function of Brownian motion parameter Nb
and the thermophoresis parameter Nt.
Abstract: We have developed a new computer program in
Fortran 90, in order to obtain numerical solutions of a system
of Relativistic Magnetohydrodynamics partial differential equations
with predetermined gravitation (GRMHD), capable of simulating
the formation of relativistic jets from the accretion disk of matter
up to his ejection. Initially we carried out a study on numerical
methods of unidimensional Finite Volume, namely Lax-Friedrichs,
Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods
dependent on Riemann problems, applied to equations Euler in
order to verify their main features and make comparisons among
those methods. It was then implemented the method of Finite
Volume Centered of Nessyahu-Tadmor, a numerical schemes that
has a formulation free and without dimensional separation of
Riemann problem solvers, even in two or more spatial dimensions,
at this point, already applied in equations GRMHD. Finally, the
Nessyahu-Tadmor method was possible to obtain stable numerical
solutions - without spurious oscillations or excessive dissipation -
from the magnetized accretion disk process in rotation with respect
to a central black hole (BH) Schwarzschild and immersed in a
magnetosphere, for the ejection of matter in the form of jet over a
distance of fourteen times the radius of the BH, a record in terms
of astrophysical simulation of this kind. Also in our simulations,
we managed to get substructures jets. A great advantage obtained
was that, with the our code, we got simulate GRMHD equations in
a simple personal computer.
Abstract: Laplace transformations have wide applications in
engineering and sciences. All previous studies of modified Laplace
transformations depend on differential equation with initial
conditions. The purpose of our paper is to solve the linear differential
equations (not initial value problem) and then find the general
solution (not particular) via the Laplace transformations without
needed any initial condition. The study involves both types of
differential equations, ordinary and partial.
Abstract: Taro Scarab beetles (Papuana uninodis, Coleoptera:
Scarabaeidae) inflict severe damage on important root crops and
plants such as Taro or Cocoyam, yam, sweet potatoes, oil palm and
coffee tea plants across Africa and Asia resulting in economic
hardship and starvation in some nations. Scoliid wasps and
Metarhizium anisopliae fungus - bio-control agents; are shown to be
able to control the population of Scarab beetle adults and larvae using
a newly created simulation model based on non-linear ordinary
differential equations that track the populations of the beetle life
cycle stages: egg, larva, pupa, adult and the population of the scoliid
parasitoid wasps, which attack beetle larvae. In spite of the challenge
driven by the longevity of the scarab beetles, the combined effect of
the larval wasps and the fungal bio-control agent is able to control
and drive down the population of both the adult and the beetle eggs
below the environmental carrying capacity within an interval of 120
days, offering the long term prospect of a stable and eco-friendly
environment; where the population of scarab beetles is: regulated by
parasitoid wasps and beneficial soil saprophytes.
Abstract: This study proposes the transformation of nonlinear
Magnetic Levitation System into linear one, via state and feedback
transformations using explicit algorithm. This algorithm allows
computing explicitly the linearizing state coordinates and feedback
for any nonlinear control system, which is feedback linearizable,
without solving the Partial Differential Equations. The algorithm is
performed using a maximum of N-1 steps where N being the
dimension of the system.
Abstract: A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.
Abstract: The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.
Abstract: In this paper, we apply the Exp-function method to
Rosenau-Kawahara and Rosenau-KdV equations. Rosenau-Kawahara
equation is the combination of the Rosenau and standard Kawahara
equations and Rosenau-KdV equation is the combination of the
Rosenau and standard KdV equations. These equations are nonlinear
partial differential equations (NPDE) which play an important role
in mathematical physics. Exp-function method is easy, succinct and
powerful to implement to nonlinear partial differential equations
arising in mathematical physics. We mainly try to present an
application of Exp-function method and offer solutions for common
errors wich occur during some of the recent works.
Abstract: The coefficient diagram method is primarily an algebraic control design method whose objective is to easily obtain
a good controller with minimum user effort. As a matter of fact, if a
system model, in the form of linear differential equations, is known,
the user only need to define a time-constant and the controller order.
The later can be established regarding the expected disturbance type
via a lookup table first published by Koksal and Hamamci in 2004.
However an inaccuracy in this table was detected and pointed-out in
the present work. Moreover the above mentioned table was expanded
in order to enclose any k order type disturbance.