Abstract: Mathematical and computational modeling of calcium
signalling in nerve cells has produced considerable insights into how
the cells contracts with other cells under the variation of biophysical
and physiological parameters. The modeling of calcium signaling in
astrocytes has become more sophisticated. The modeling effort has
provided insight to understand the cell contraction. Main objective
of this work is to study the effect of voltage gated (Operated)
calcium channel (VOC) on calcium profile in the form of advection
diffusion equation. A mathematical model is developed in the form
of advection diffusion equation for the calcium profile. The model
incorporates the important physiological parameter like diffusion
coefficient etc. Appropriate boundary conditions have been framed.
Finite volume method is employed to solve the problem. A program
has been developed using in MATLAB 7.5 for the entire problem
and simulated on an AMD-Turion 32-bite machine to compute the
numerical results.
Abstract: The paper deals with a mathematical model for fluid dynamic flows on road networks which is based on conservation laws. This nonlinear framework is based on the conservation of cars. We focus on traffic circle, which is a finite number of roads that meet at some junctions. The traffic circle with junctions having either one incoming and two outgoing or two incoming and one outgoing roads. We describe the numerical schemes with the particular boundary conditions used to produce approximated solutions of the problem.
Abstract: The Spalart and Allmaras turbulence model has been
implemented in a numerical code to study the compressible turbulent
flows, which the system of governing equations is solved with a
finite volume approach using a structured grid. The AUSM+ scheme
is used to calculate the inviscid fluxes. Different benchmark
problems have been computed to validate the implementation and
numerical results are shown. A special Attention is paid to wall jet
applications. In this study, the jet is submitted to various wall
boundary conditions (adiabatic or uniform heat flux) in forced
convection regime and both two-dimensional and axisymmetric wall
jets are considered. The comparison between the numerical results
and experimental data has given the validity of this turbulence model
to study the turbulent wall jets especially in engineering applications.
Abstract: To achieve accurate and precise results of finite
element analysis (FEA) of bones, it is important to represent the
load/boundary conditions as identical as possible to the human body
such as the bone properties, the type and force of the muscles, the
contact force of the joints, and the location of the muscle attachment.
In this study, the difference in the Von-Mises stress and the total
deformation was compared by classifying them into Case 1, which
shows the actual anatomical form of the muscle attached to the femur
when the same muscle force was applied, and Case 2, which gives a
simplified representation of the attached location. An inverse
dynamical musculoskeletal model was simulated using data from an
actual walking experiment to complement the accuracy of the
muscular force, the input value of FEA. The FEA method using the
results of the muscular force that were calculated through the
simulation showed that the maximum Von-Mises stress and the
maximum total deformation in Case 2 were underestimated by 8.42%
and 6.29%, respectively, compared to Case 1. The torsion energy and
bending moment at each location of the femur occurred via the stress
ingredient. Due to the geometrical/morphological feature of the femur
of having a long bone shape when the stress distribution is wide, as
shown in Case 1, a greater Von-Mises stress and total deformation are
expected from the sum of the stress ingredients. More accurate results
can be achieved only when the muscular strength and the attachment
location in the FEA of the bones and the attachment form are the same
as those in the actual anatomical condition under the various moving
conditions of the human body.
Abstract: This paper is concerned with propagation of thermoelastic longitudinal vibrations of an infinite circular cylinder, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equation, by using the traction free boundary conditions, is given in the form of a determinant involving Bessel functions. The roots of the frequency equation give the value of the characteristic circular frequency as function of the wave number. These roots, which correspond to various modes, are numerically computed and presented graphically for different values of the thermal relaxation times. It is found that the influences of the thermal relaxation times on the amplitudes of the elastic and thermal waves are remarkable. Also, it is shown in this study that the propagation of thermoelastic longitudinal vibrations based on the generalized thermoelasticity can differ significantly compared with the results under the classical formulation. A comparison of the results for the case with no thermal effects shows well agreement with some of the corresponding earlier results.
Abstract: In this study the mixed convection heat transfer in a
coil-in-shell heat exchanger for various Reynolds numbers and
various dimensionless coil pitch was experimentally investigated.
The experiments were conducted for both laminar and turbulent flow
inside coil and the effects of coil pitch on shell-side heat transfer
coefficient of the heat exchanger were studied. The particular
difference in this study in comparison with the other similar studies
was the boundary conditions for the helical coils. The results indicate
that with the increase of coil pitch, shell-side heat transfer coefficient
is increased.
Abstract: A method based on the power series solution is proposed to solve the natural frequency of flapping vibration for the rotating inclined Euler beam with constant angular velocity. The vibration of the rotating beam is measured from the position of the corresponding steady state axial deformation. In this paper the governing equations for linear vibration of a rotating Euler beam are derived by the d'Alembert principle, the virtual work principle and the consistent linearization of the fully geometrically nonlinear beam theory in a rotating coordinate system. The governing equation for flapping vibration of the rotating inclined Euler beam is linear ordinary differential equation with variable coefficients and is solved by a power series with four independent coefficients. Substituting the power series solution into the corresponding boundary conditions at two end nodes of the rotating beam, a set of homogeneous equations can be obtained. The natural frequencies may be determined by solving the homogeneous equations using the bisection method. Numerical examples are studied to investigate the effect of inclination angle on the natural frequency of flapping vibration for rotating inclined Euler beams with different angular velocity and slenderness ratio.
Abstract: Direct numerical simulation (DNS) is used to study the evolution of a boundary layer that was laminar initially followed by separation and then reattachment owing to generation of turbulence. This creates a closed region of recirculation, known as the laminar-separation bubble. The present simulation emulates the flow environment encountered in a modern LP turbine blade, where a laminar separation bubble may occur on the suction surface. The unsteady, incompressible three-dimensional (3-D) Navier-Stokes (NS) equations have been solved over a flat plate in the Cartesian coordinates. The adverse pressure gradient, which causes the flow to separate, is created by a boundary condition. The separated shear layer undergoes transition through appearance of ╬ø vortices, stretching of these create longitudinal streaks. Breakdown of the streaks into small and irregular structures makes the flow turbulent downstream.
Abstract: The hydrodynamics behavior of fluid flow in microconverging
plates is investigated analytically. Effects of Knudsen number () on the microchannel hydrodynamics behavior and the
coefficient of friction are investigated. It is found that as increases the slip in the hydrodynamic boundary condition increases.
Also, the coefficient of friction decreases as increases.
Abstract: Organ motion, especially respiratory motion, is a technical challenge to radiation therapy planning and dosimetry. This motion induces displacements and deformation of the organ tissues within the irradiated region which need to be taken into account when simulating dose distribution during treatment. Finite element modeling (FEM) can provide a great insight into the mechanical behavior of the organs, since they are based on the biomechanical material properties, complex geometry of organs, and anatomical boundary conditions. In this paper we present an original approach that offers the possibility to combine image-based biomechanical models with particle transport simulations. We propose a new method to map material density information issued from CT images to deformable tetrahedral meshes. Based on the principle of mass conservation our method can correlate density variation of organ tissues with geometrical deformations during the different phases of the respiratory cycle. The first results are particularly encouraging, as local error quantification of density mapping on organ geometry and density variation with organ motion are performed to evaluate and validate our approach.
Abstract: The Stokes equation connected with the fluid flow
over the axisymmetric bodies in a cylindrical area is considered. The
equation is studied in a moving coordinate system with the
appropriate boundary conditions. Effective formulas for the velocity
components are obtained. The graphs of the velocity components and
velocity profile are plotted.
Abstract: Different techniques for estimating seasonal water
use from soil profile water depletion frequently do not account for
flux below the root zone. Shallow water table contribution to supply
crop water use may be important in arid and semi-arid regions.
Development of predictive root uptake models, under influence of
shallow water table makes it possible for planners to incorporate
interaction between water table and root zone into design of irrigation
projects. A model for obtaining soil moisture depletion from root
zone and water movement below it is discussed with the objective to
determine impact of shallow water table on seasonal moisture
depletion patterns under water table depth variation, up to the bottom
of root zone. The role of different boundary conditions has also been
considered. Three crops: Wheat (Triticum aestivum), Corn (Zea
mays) and Potato (Solanum tuberosum), common in arid & semi-arid
regions, are chosen for the study. Using experimentally obtained soil
moisture depletion values for potential soil moisture conditions,
moisture depletion patterns using a non linear root uptake model have
been obtained for different water table depths. Comparative analysis
of the moisture depletion patterns under these conditions show a wide
difference in percent depletion from different layers of root zone
particularly top and bottom layers with middle layers showing
insignificant variation in moisture depletion values. Moisture
depletion in top layer, when the water table rises to root zone
increases by 19.7%, 22.9% & 28.2%, whereas decrease in bottom
layer is 68.8%, 61.6% & 64.9% in case of wheat, corn & potato
respectively. The paper also discusses the causes and consequences
of increase in moisture depletion from top layers and exceptionally
high reduction in bottom layer, and the possible remedies for the
same. The numerical model developed for the study can be used to
help formulating irrigation strategies for areas where shallow
groundwater of questionable quality is an option for crop production.
Abstract: In this paper, linear multistep technique using power
series as the basis function is used to develop the block methods
which are suitable for generating direct solution of the special second
order ordinary differential equations with associated initial or
boundary conditions. The continuous hybrid formulations enable us
to differentiate and evaluate at some grids and off – grid points to
obtain two different four discrete schemes, each of order (5,5,5,5)T,
which were used in block form for parallel or sequential solutions of
the problems. The computational burden and computer time wastage
involved in the usual reduction of second order problem into system
of first order equations are avoided by this approach. Furthermore, a
stability analysis and efficiency of the block methods are tested on
linear and non-linear ordinary differential equations and the results
obtained compared favorably with the exact solution.
Abstract: An attempt has been made to develop a
seminumerical model to study temperature variations in dermal
layers of human limbs. The model has been developed for two
dimensional steady state case. The human limb has been assumed to
have elliptical cross section. The dermal region has been divided
into three natural layers namely epidermis, dermis and subdermal
tissues. The model incorporates the effect of important physiological
parameters like blood mass flow rate, metabolic heat generation, and
thermal conductivity of the tissues. The outer surface of the limb is
exposed to the environment and it is assumed that heat loss takes
place at the outer surface by conduction, convection, radiation, and
evaporation. The temperature of inner core of the limb also varies at
the lower atmospheric temperature. Appropriate boundary conditions
have been framed based on the physical conditions of the problem.
Cubic splines approach has been employed along radial direction and
Fourier series along angular direction to obtain the solution. The
numerical results have been computed for different values of
eccentricity resembling with the elliptic cross section of the human
limbs. The numerical results have been used to obtain the
temperature profile and to study the relationships among the various
physiological parameters.
Abstract: An efficient transient flow simulation for gas
pipelines and networks is presented. The proposed transient flow
simulation is based on the transfer function models and MATLABSimulink.
The equivalent transfer functions of the nonlinear
governing equations are derived for different types of the boundary
conditions. Next, a MATLAB-Simulink library is developed and
proposed considering any boundary condition type. To verify the
accuracy and the computational efficiency of the proposed
simulation, the results obtained are compared with those of the
conventional finite difference schemes (such as TVD, method of
lines, and other finite difference implicit and explicit schemes). The
effects of the flow inertia and the pipeline inclination are
incorporated in this simulation. It is shown that the proposed
simulation has a sufficient accuracy and it is computationally more
efficient than the other methods.
Abstract: Since polymerase chain reaction (PCR) has been
invented, it has emerged as a powerful tool in genetic analysis. The
PCR products are closely linked with thermal cycles. Therefore, to
reduce the reaction time and make temperature distribution uniform in
the reaction chamber, a novel oscillatory thermal cycler is designed.
The sample is placed in a fixed chamber, and three constant isothermal
zones are established and lined in the system. The sample is oscillated
and contacted with three different isothermal zones to complete
thermal cycles. This study presents the design of the geometric
characteristics of the chamber. The commercial software
CFD-ACE+TM is utilized to investigate the influences of various
materials, heating times, chamber volumes, and moving speed of the
chamber on the temperature distributions inside the chamber. The
chamber moves at a specific velocity and the boundary conditions
with time variations are related to the moving speed. Whereas the
chamber moves, the boundary is specified at the conditions of the
convection or the uniform temperature. The user subroutines compiled
by the FORTRAN language are used to make the numerical results
realistically. Results show that the reaction chamber with a rectangular
prism is heated on six faces; the effects of various moving speeds of
the chamber on the temperature distributions are examined. Regarding
to the temperature profiles and the standard deviation of the
temperature at the Y-cut cross section, the non-uniform temperature
inside chamber is found as the moving speed is larger than 0.01 m/s.
By reducing the heating faces to four, the standard deviation of the
temperature of the reaction chamber is under 1.4×10-3K with the range
of velocities between 0.0001 m/s and 1 m/s. The nature convective
boundary conditions are set at all boundaries while the chamber moves
between two heaters, the effects of various moving velocities of the
chamber on the temperature distributions are negligible at the assigned
time duration.
Abstract: Study of the vibration cylindrical shells made of
a functionally gradient material (FGM) composed of stainless
steel and nickel is important. Material properties are graded in
the thickness direction of the shell according to volume
fraction power law distribution. The objective is to study the
natural frequencies, the influence of constituent volume
fractions and the effects of boundary conditions on the natural
frequencies of the FG cylindrical shell. The study is carried
out using third order shear deformation shell theory. The
governing equations of motion of FG cylindrical shells are
derived based on shear deformation theory. Results are
presented on the frequency characteristics, influence of
constituent volume fractions and the effects of clampedclamped
boundary conditions.
Abstract: In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of clamped-free boundary conditions
Abstract: In mechanical and environmental engineering, mixed
convection is a frequently encountered thermal fluid phenomenon
which exists in atmospheric environment, urban canopy flows, ocean
currents, gas turbines, heat exchangers, and computer chip cooling
systems etc... . This paper deals with a numerical investigation of
mixed convection in a vertical heated channel. This flow results from
the mixing of the up-going fluid along walls of the channel with the
one issued from a flat nozzle located in its entry section. The fluiddynamic
and heat-transfer characteristics of vented vertical channels
are investigated for constant heat-flux boundary conditions, a
Rayleigh number equal to 2.57 1010, for two jet Reynolds number
Re=3 103 and 2104 and the aspect ratio in the 8-20 range. The system
of governing equations is solved with a finite volumes method and an
implicit scheme. The obtained results show that the turbulence and
the jet-wall interaction activate the heat transfer, as does the drive of
ambient air by the jet. For low Reynolds number Re=3 103, the
increase of the aspect Ratio enhances the heat transfer of about 3%,
however; for Re=2 104, the heat transfer enhancement is of about
12%. The numerical velocity, pressure and temperature fields are
post-processed to compute the quantities of engineering interest such
as the induced mass flow rate, and average Nusselt number, in terms
of Rayleigh, Reynolds numbers and dimensionless geometric
parameters are presented.
Abstract: In this paper we investigate numerically positive solutions of the equation -Δu = λuq+up with Dirichlet boundary condition in a boundary domain ╬® for λ > 0 and 0 < q < 1 < p < 2*, we will compute and visualize the range of λ, this problem achieves a numerical solution.