Abstract: The reliable results of an insulated oval duct
considering heat radiation are obtained basing on accurate oval
perimeter obtained by integral method as well as one-dimensional
Plane Wedge Thermal Resistance (PWTR) model. This is an extension
study of former paper of insulated oval duct neglecting heat radiation.
It is found that in the practical situations with long-short-axes ratio a/b
4.5% while t/R2
Abstract: The objective of this research is to examine the shear thinning behaviour of mixing flow of non-Newtonian fluid like toothpaste in the dissolution container with rotating stirrer. The problem under investigation is related to the chemical industry. Mixing of fluid is performed in a cylindrical container with rotating stirrer, where stirrer is eccentrically placed on the lid of the container. For the simulation purpose the associated motion of the fluid is considered as revolving of the container, with stick stirrer. For numerical prediction, a time-stepping finite element algorithm in a cylindrical polar coordinate system is adopted based on semi-implicit Taylor-Galerkin/pressure-correction scheme. Numerical solutions are obtained for non-Newtonian fluids employing power law model. Variations with power law index have been analysed, with respect to the flow structure and pressure drop.
Abstract: Flow movement in unsaturated soil can be expressed
by a partial differential equation, named Richards equation. The
objective of this study is the finding of an appropriate implicit
numerical solution for head based Richards equation. Some of the
well known finite difference schemes (fully implicit, Crank Nicolson
and Runge-Kutta) have been utilized in this study. In addition, the
effects of different approximations of moisture capacity function,
convergence criteria and time stepping methods were evaluated. Two
different infiltration problems were solved to investigate the
performance of different schemes. These problems include of vertical
water flow in a wet and very dry soils. The numerical solutions of
two problems were compared using four evaluation criteria and the
results of comparisons showed that fully implicit scheme is better
than the other schemes. In addition, utilizing of standard chord slope
method for approximation of moisture capacity function, automatic
time stepping method and difference between two successive
iterations as convergence criterion in the fully implicit scheme can
lead to better and more reliable results for simulation of fluid
movement in different unsaturated soils.
Abstract: In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.
Abstract: In this work we adopt a combination of Laplace
transform and the decomposition method to find numerical solutions
of a system of multi-pantograph equations. The procedure leads to a
rapid convergence of the series to the exact solution after computing a
few terms. The effectiveness of the method is demonstrated in some
examples by obtaining the exact solution and in others by computing
the absolute error which decreases as the number of terms of the series
increases.
Abstract: In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.
Abstract: In this paper, we have applied the homotopy perturbation
method (HPM) for obtaining the analytical solution of unsteady
flow of gas through a porous medium and we have also compared the
findings of this research with some other analytical results. Results
showed a very good agreement between results of HPM and the
numerical solutions of the problem rather than other analytical solutions
which have previously been applied. The results of homotopy
perturbation method are of high accuracy and the method is very
effective and succinct.
Abstract: Unsteady magnetohydrodynamics (MHD) boundary
layer flow and heat transfer over a continuously stretching surface in
the presence of radiation is examined. By similarity transformation,
the governing partial differential equations are transformed to a set of
ordinary differential equations. Numerical solutions are obtained by
employing the Runge-Kutta-Fehlberg method scheme with shooting
technique in Maple software environment. The effects of
unsteadiness parameter, radiation parameter, magnetic parameter and
Prandtl number on the heat transfer characteristics are obtained and
discussed. It is found that the heat transfer rate at the surface
increases as the Prandtl number and unsteadiness parameter increase
but decreases with magnetic and radiation parameter.
Abstract: A conjugate heat transfer for steady two-dimensional
mixed convection with magnetic hydrodynamic (MHD) flow of an
incompressible quiescent fluid over an unsteady thermal forming
stretching sheet has been studied. A parameter, M, which is used to
represent the dominance of the magnetic effect has been presented in
governing equations. The similar transformation and an implicit
finite-difference method have been used to analyze the present
problem. The numerical solutions of the flow velocity distributions,
temperature profiles, the wall unknown values of f''(0) and '(θ (0) for
calculating the heat transfer of the similar boundary-layer flow are
carried out as functions of the unsteadiness parameter (S), the Prandtl
number (Pr), the space-dependent parameter (A) and
temperature-dependent parameter (B) for heat source/sink and the
magnetic parameter (M). The effects of these parameters have also
discussed. At the results, it will produce greater heat transfer effect
with a larger Pr and M, S, A, B will reduce heat transfer effects. At
last, conjugate heat transfer for the free convection with a larger G has
a good heat transfer effect better than a smaller G=0.
Abstract: This paper proposes a simple model of economic geography within the Dixit-Stiglitz-Iceberg framework that may be used to analyze migration patterns among three cities. The cost–benefit tradeoffs affecting incentives for three types of migration, including echelon migration, are discussed. This paper develops a tractable, heterogeneous-agent, general equilibrium model, where agents share constant human capital, and explores the relationship between the benefits of echelon migration and gross human capital. Using Chinese numerical solutions, we study the manifestation of echelon migration and how it responds to changes in transportation cost and elasticity of substitution. Numerical results demonstrate that (i) there are positive relationships between a migration-s benefit-and-wage ratio, (ii) there are positive relationships between gross human capital ratios and wage ratios as to origin and destination, and (iii) we identify 13 varieties of human capital convergence among cities. In particular, this model predicts population shock resulting from the processes of migration choice and echelon migration.
Abstract: This is the second part of the paper. It, aside from the
core subroutine test reported previously, focuses on the simulation of
turbulence governed by the full STF Navier-Stokes equations on a
large scale. Law of the wall is found plausible in this study as a model
of the boundary layer dynamics. Model validations proceed to
include velocity profiles of a stationary turbulent Couette flow, pure
sloshing flow simulations, and the identification of water-surface
inclination due to fluid accelerations. Errors resulting from the
irrotational and hydrostatic assumptions are explored when studying
a wind-driven water circulation with no shakings. Illustrative
examples show that this numerical strategy works for the simulation
of sloshing-shear mixed flow in a 3-D rigid rectangular base tank.
Abstract: In this paper, the local grid refinement is focused by
using a nested grid technique. The Cartesian grid numerical method is
developed for simulating unsteady, viscous, incompressible flows
with complex immersed boundaries. A finite volume method is used in
conjunction with a two-step fractional-step procedure. The key aspects
that need to be considered in developing such a nested grid solver are
imposition of interface conditions on the inter-block and accurate
discretization of the governing equation in cells that are with the
inter-block as a control surface. A new interpolation procedure is
presented which allows systematic development of a spatial
discretization scheme that preserves the spatial accuracy of the
underlying solver. The present nested grid method has been tested by
two numerical examples to examine its performance in the two
dimensional problems. The numerical examples include flow past a
circular cylinder symmetrically installed in a Channel and flow past
two circular cylinders with different diameters. From the numerical
experiments, the ability of the solver to simulate flows with
complicated immersed boundaries is demonstrated and the nested grid
approach can efficiently speed up the numerical solutions.
Abstract: Today, numerical simulation is a powerful tool to
solve various hydraulic engineering problems. The aim of this
research is numerical solutions of shallow water equations using
finite volume method for Simulations of dam break over wet and dry
bed. In order to solve Riemann problem, Roe-s approximate solver is
used. To evaluate numerical model, simulation was done in 1D and
2D states. In 1D state, two dam break test over dry bed (with and
without friction) were studied. The results showed that Structural
failure around the dam and damage to the downstream constructions
in bed without friction is more than friction bed. In 2D state, two
tests for wet and dry beds were done. Generally in wet bed case,
waves are propagated to canal sides but in dry bed it is not
significant. Therefore, damage to the storage facilities and
agricultural lands in wet bed case is more than in dry bed.
Abstract: An unstructured finite volume numerical model is
presented here for simulating shallow-water flows with wetting and
drying fronts. The model is based on the Green-s theorem in
combination with Chorin-s projection method. A 2nd-order upwind
scheme coupled with a Least Square technique is used to handle
convection terms. An Wetting and drying treatment is used in the
present model to ensures the total mass conservation. To test it-s
capacity and reliability, the present model is used to solve the
Parabolic Bowl problem. We compare our numerical solutions with
the corresponding analytical and existing standard numerical results.
Excellent agreements are found in all the cases.
Abstract: The optimal control problem for the viscoelastic melt
spinning process has not been reported yet in the literature. In this
study, an optimal control problem for a mathematical model of a
viscoelastic melt spinning process is considered. Maxwell-Oldroyd
model is used to describe the rheology of the polymeric material, the
fiber is made of. The extrusion velocity of the polymer at the spinneret
as well as the velocity and the temperature of the quench air and the
fiber length serve as control variables. A constrained optimization
problem is derived and the first–order optimality system is set up
to obtain the adjoint equations. Numerical solutions are carried out
using a steepest descent algorithm. A computer program in MATLAB
is developed for simulations.
Abstract: Based on the standard finite element method, a new
finite element method which is known as nonlocal finite element
method (NL-FEM) is numerically implemented in this article to
study the nonlocal effects for solving 1D nonlocal elastic problem.
An Eringen-type nonlocal elastic model is considered. In this model,
the constitutive stress-strain law is expressed interms of integral
equation which governs the nonlocal material behavior. The new
NL-FEM is adopted in such a way that the postulated nonlocal elastic
behavior of material is captured by a finite element endowed with a
set of (cross-stiffness) element itself by the other elements in mesh.
An example with their analytical solutions and the relevant numerical
findings for various load and boundary conditions are presented and
discussed in details. It is observed from the numerical solutions that
the torsional deformation angle decreases with increasing nonlocal
nanoscale parameter. It is also noted that the analytical solution fails
to capture the nonlocal effect in some cases where numerical
solutions handle those situation effectively which prove the
reliability and effectiveness of numerical techniques.
Abstract: The present work deals with analyses of the effects
of bearing curvature and non-Newtonian characteristics on the load capacity of an exponential rectangular squeeze film bearing using
Bingham fluids as lubricants. Bingham fluids are characterized by an
yield value and hence the formation of a “rigid" core in the region
between the plates is justified. The flow is confined to the region
between the core and the plates. The shape of the core has been
identified through numerical means. Further, numerical solutions for
the pressure distribution and load carrying capacity of the bearing
for various values of Bingham number and curvature parameter have
been obtained. The effects of bearing curvature and non-Newtonian
characteristics of the lubricant on the bearing performances have been
discussed.
Abstract: In this article two algorithms, one based on variation iteration method and the other on Adomian's decomposition method, are developed to find the numerical solution of an initial value problem involving the non linear integro differantial equation where R is a nonlinear operator that contains partial derivatives with respect to x. Special cases of the integro-differential equation are solved using the algorithms. The numerical solutions are compared with analytical solutions. The results show that these two methods are efficient and accurate with only two or three iterations
Abstract: The aim of this paper is to study the oblique
stagnation point flow on vertical plate with uniform surface heat flux
in presence of magnetic field. Using Stream function, partial
differential equations corresponding to the momentum and energy
equations are converted into non-linear ordinary differential
equations. Numerical solutions of these equations are obtained using
Runge-Kutta Fehlberg method with the help of shooting technique.
In the present work the effects of striking angle, magnetic field
parameter, Grashoff number, the Prandtl number on velocity and heat
transfer characteristics have been discussed. Effect of above
mentioned parameter on the position of stagnation point are also
studied.
Abstract: The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.