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 paper, a probabilistic framework based on
Fokker-Planck-Kolmogorov (FPK) approach has been applied to
simulate triaxial cyclic constitutive behavior of uncertain soils. The
framework builds upon previous work of the writers, and it has
been extended for cyclic probabilistic simulation of triaxial undrained
behavior of soils. von Mises elastic-perfectly plastic material model is
considered. It is shown that by using probabilistic framework, some of
the most important aspects of soil behavior under cyclic loading can
be captured even with a simple elastic-perfectly plastic constitutive
model.
Abstract: The problem of conjugate free convection in a square
cavity filled with nanofluid and heated from below by spatial wall
temperature is studied numerically using the finite difference method.
Water-based nanofluid with copper nanoparticles are chosen for the
investigation. Governing equations are solved over a wide range
of nanoparticle volume fraction (0 ≤ φ ≤ 0.2), wave number
((0 ≤ λ ≤ 4) and thermal conductivity ratio (0.44 ≤ Kr ≤ 6). The
results presented for values of the governing parameters in terms of
streamlines, isotherms and average Nusselt number. It is found that
the flow behavior and the heat distribution are clearly enhanced with
the increment of the non-uniform heating.
Abstract: A thermosyphon system is a heat transfer loop which
operates on the basis of gravity and buoyancy forces. It guarantees a
good reliability and low maintenance cost as it does not involve any
mechanical pump. Therefore, it can be used in many industrial
applications such as refrigeration and air conditioning, electronic
cooling, nuclear reactors, geothermal heat extraction, etc. But flow
instabilities and loop configuration are the major problems in this
system. Several previous researchers studied that stabilities can be
suppressed by using nanofluids as loop fluid. In the present study a
rectangular thermosyphon loop with end heat exchangers are
considered for the study. This configuration is more appropriate for
many practical applications such as solar water heater, geothermal
heat extraction, etc. In the present work, steady-state analysis is
carried out on thermosyphon loop with parallel flow coaxial heat
exchangers at heat source and heat sink. In this loop nanofluid is
considered as the loop fluid and water is considered as the external
fluid in both hot and cold heat exchangers. For this analysis onedimensional
homogeneous model is developed. In this model,
conservation equations like conservation of mass, momentum, energy
are discretized using finite difference method. A computer code is
written in MATLAB to simulate the flow in thermosyphon loop. A
comparison in terms of heat transfer is made between water and
nanofluid as working fluids in the loop.
Abstract: This work deals with heat and mass transfer by steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate with variable surface heat flux embedded in a fluid saturated porous medium in the presence of thermophoresis particle deposition effect. The governing partial differential equations are transformed into no-similar form by using special transformation and solved numerically by using an implicit finite difference method. Many results are obtained and a representative set is displaced graphically to illustrate the influence of the various physical parameters on the wall thermophoresis deposition velocity and concentration profiles. It is found that the increasing of thermophoresis constant or temperature differences enhances heat transfer rates from vertical surfaces and increase wall thermophoresis velocities; this is due to favorable temperature gradients or buoyancy forces. It is also found that the effect of thermophoresis phenomena is more pronounced near pure natural convection heat transfer limit; because this phenomenon is directly a temperature gradient or buoyancy forces dependent. Comparisons with previously published work in the limits are performed and the results are found to be in excellent agreement.
Abstract: A numerical investigation of the fin efficiency and temperature distribution of an annular fin under dehumidification has been presented in this paper. The non-homogeneous second order differential equation that describes the temperature distribution from the fin base to the fin tip has been solved using the central finite difference method. The effects of variations in parameters including relative humidity, air temperature, air face velocity on temperature distribution and fin efficiency are investigated and compared with those under fully dry fin conditions. Also, the effect of fin pitch on the dimensionless temperature has been studied.
Abstract: A theoretical investigation on the effects of both
steady-state and dynamic deformations of the foils on the dynamic
performance characteristics of a self-acting air foil journal bearing
operating under small harmonic vibrations is proposed. To take into
account the dynamic deformations of foils, the perturbation method is
used for determining the gas-film stiffness and damping coefficients
for given values of excitation frequency, compressibility number, and
compliance factor of the bump foil. The nonlinear stationary
Reynolds’ equation is solved by means of the Galerkins’ finite
element formulation while the finite differences method are used to
solve the first order complex dynamic equations resulting from the
perturbation of the nonlinear transient compressible Reynolds’
equation. The stiffness of a bump is uniformly distributed throughout
the bearing surface (generation I bearing). It was found that the
dynamic properties of the compliant finite length journal bearing are
significantly affected by the compliance of foils especially whenthe
dynamic deformation of foils is considered in addition to the static
one by applying the principle of superposition.
Abstract: The migration of a deformable drop in simple shear
flow at finite Reynolds numbers is investigated numerically by
solving the full Navier-Stokes equations using a finite
difference/front tracking method. The objectives of this study are to
examine the effectiveness of the present approach to predict the
migration of a drop in a shear flow and to investigate the behavior of
the drop migration with different drop sizes and non-unity viscosity
ratios. It is shown that the drop deformation depends strongly on the
capillary number, so that; the proper non-dimensional number for the
interfacial tension is the capillary number. The rate of migration
increased with increasing the drop radius. In other words, the
required time for drop migration to the centreline decreases. As the
viscosity ratio increases, the drop rotates more slowly and the
lubrication force becomes stronger. The increased lubrication force
makes it easier for the drop to migrate to the centre of the channel.
The migration velocity of the drop vanishes as the drop reaches the
centreline under viscosity ratio of one and non-unity viscosity ratios.
To validate the present calculations, some typical results are
compared with available experimental and theoretical data.
Abstract: In this paper, fully developed flow and heat transfer of
viscoelastic materials in curved ducts with square cross section under
constant heat flux have been investigated. Here, staggered mesh is
used as computational grids and flow and heat transfer parameters
have been allocated in this mesh with marker and cell method.
Numerical solution of governing equations has being performed with
FTCS finite difference method. Furthermore, Criminale-Eriksen-
Filbey (CEF) constitutive equation has being used as viscoelastic
model. CEF constitutive equation is a suitable model for studying
steady shear flow of viscoelastic materials which is able to model
both effects of the first and second normal stress differences. Here, it
is shown that the first and second normal stresses differences have
noticeable and inverse effect on secondary flows intensity and mean
Nusselt number which is the main novelty of current research.
Abstract: The spectral action balance equation is an equation that
used to simulate short-crested wind-generated waves in shallow water
areas such as coastal regions and inland waters. This equation consists
of two spatial dimensions, wave direction, and wave frequency which
can be solved by finite difference method. When this equation with
dominating convection term are discretized using central differences,
stability problems occur when the grid spacing is chosen too coarse.
In this paper, we introduce the splitting upwind schemes for avoiding
stability problems and prove that it is consistent to the upwind scheme
with same accuracy. The splitting upwind schemes was adopted
to split the wave spectral action balance equation into four onedimensional
problems, which for each small problem obtains the
independently tridiagonal linear systems. For each smaller system
can be solved by direct or iterative methods at the same time which
is very fast when performed by a multi-processor computer.
Abstract: Smoke discharging is a main reason of air pollution
problem from industrial plants. The obstacle of a building has an
affect with the air pollutant discharge. In this research, a mathematical
model of the smoke dispersion from two sources and one source with
a structural obstacle is considered. The governing equation of the
model is an isothermal mass transfer model in a viscous fluid. The
finite element method is used to approximate the solutions of the
model. The triangular linear elements have been used for discretising
the domain, and time integration has been carried out by semi-implicit
finite difference method. The simulations of smoke dispersion in
cases of one chimney and two chimneys are presented. The maximum
calculated smoke concentration of both cases are compared. It is then
used to make the decision for smoke discharging and air pollutant
control problems on industrial area.
Abstract: The aim of this paper is to study the internal
stabilization of the Bernoulli-Euler equation numerically. For this,
we consider a square plate subjected to a feedback/damping force
distributed only in a subdomain. An algorithm for obtaining an
approximate solution to this problem was proposed and implemented.
The numerical method used was the Finite Difference Method.
Numerical simulations were performed and showed the behavior of
the solution, confirming the theoretical results that have already been
proved in the literature. In addition, we studied the validation of the
numerical scheme proposed, followed by an analysis of the numerical
error; and we conducted a study on the decay of the energy associated.
Abstract: This paper adopted the hybrid differential transform approach for studying heat transfer problems in a gold/chromium thin film with an ultra-short-pulsed laser beam projecting on the gold side. The physical system, formulated based on the hyperbolic two-step heat transfer model, covers three characteristics: (i) coupling effects between the electron/lattice systems, (ii) thermal wave propagation in metals, and (iii) radiation effects along the interface. The differential transform method is used to transfer the governing equations in the time domain into the spectrum equations, which is further discretized in the space domain by the finite difference method. The results, obtained through a recursive process, show that the electron temperature in the gold film can rise up to several thousand degrees before its electron/lattice systems reach equilibrium at only several hundred degrees. The electron and lattice temperatures in the chromium film are much lower than those in the gold film.
Abstract: The spectral action balance equation is an equation that
used to simulate short-crested wind-generated waves in shallow water
areas such as coastal regions and inland waters. This equation consists
of two spatial dimensions, wave direction, and wave frequency which
can be solved by finite difference method. When this equation with
dominating propagation velocity terms are discretized using central
differences, stability problems occur when the grid spacing is chosen
too coarse. In this paper, we introduce the splitting modified donorcell
scheme for avoiding stability problems and prove that it is
consistent to the modified donor-cell scheme with same accuracy. The
splitting modified donor-cell scheme was adopted to split the wave
spectral action balance equation into four one-dimensional problems,
which for each small problem obtains the independently tridiagonal
linear systems. For each smaller system can be solved by direct or
iterative methods at the same time which is very fast when performed
by a multi-cores computer.
Abstract: A numerical study on the heat transfer in the thermal
barrier coatings and the substrates of a parallel-plate enclosure is
carried out. Some of the thermal barrier coatings, such as ceramics, are
semitransparent and are of interest for high-temperature applications
where radiation effects are significant. The radiative transfer equations
and the energy equations are solved by using the discrete ordinates
method and the finite difference method. Illustrative results are
presented for temperature distributions in the coatings and the opaque
walls under various heating conditions. The results show that the
temperature distribution is more uniform in the interior portion of each
coating away from its boundary for the case with a larger average of
varying refractive index and a positive gradient of refractive index
enhances radiative transfer to the substrates.
Abstract: Based on Rayleigh beam theory, the sub-impacts of a
free-free beam struck horizontally by a round-nosed rigid mass is
simulated by the finite difference method and the impact-separation
conditions. In order to obtain the sub-impact force, a uniaxial
compression elastic-plastic contact model is employed to analyze the
local deformation field on contact zone. It is found that the horizontal
impact is a complicated process including the elastic plastic
sub-impacts in sequence. There are two sub-zones of sub-impact. In
addition, it found that the elastic energy of the free-free beam is more
suitable for the Poisson collision hypothesis to explain compression
and recovery processes.
Abstract: This paper deals with a numerical analysis of the
transient response of composite beams with strain rate dependent
mechanical properties by use of a finite difference method. The
equations of motion based on Timoshenko beam theory are derived.
The geometric nonlinearity effects are taken into account with von
Kármán large deflection theory. The finite difference method in
conjunction with Newmark average acceleration method is applied to
solve the differential equations. A modified progressive damage
model which accounts for strain rate effects is developed based on
the material property degradation rules and modified Hashin-type
failure criteria and added to the finite difference model. The
components of the model are implemented into a computer code in
Mathematica 6. Glass/epoxy laminated composite beams with
constant and strain rate dependent mechanical properties under
dynamic load are analyzed. Effects of strain rate on dynamic
response of the beam for various stacking sequences, load and
boundary conditions are investigated.