Abstract: Fluid flow and heat transfer of vertical full cone
embedded in porous media is studied in this paper. Nonlinear
differential equation arising from similarity solution of inverted cone
(subjected to wall temperature boundary conditions) embedded in
porous medium is solved using a hybrid neural network- particle
swarm optimization method.
To aim this purpose, a trial solution of the differential equation is
defined as sum of two parts. The first part satisfies the initial/
boundary conditions and does contain an adjustable parameter and
the second part which is constructed so as not to affect the
initial/boundary conditions and involves adjustable parameters (the
weights and biases) for a multi-layer perceptron neural network.
Particle swarm optimization (PSO) is applied to find adjustable
parameters of trial solution (in first and second part). The obtained
solution in comparison with the numerical ones represents a
remarkable accuracy.
Abstract: In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. The coupled equations are simultaneously solved by imposing the vorticity definition at boundary without requiring the explicit specification of the vorticity boundary conditions. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields. Thus, it is convinced that the present formulation is capable of solving coupled Navier-Stokes equations effectively and accurately.
Abstract: This paper describes a one-dimensional numerical model for natural gas production from the dissociation of methane hydrate in hydrate-capped gas reservoir under depressurization and thermal stimulation. Some of the hydrate reservoirs discovered are overlying a free-gas layer, known as hydrate-capped gas reservoirs. These reservoirs are thought to be easiest and probably the first type of hydrate reservoirs to be produced. The mathematical equations that can be described this type of reservoir include mass balance, heat balance and kinetics of hydrate decomposition. These non-linear partial differential equations are solved using finite-difference fully implicit scheme. In the model, the effect of convection and conduction heat transfer, variation change of formation porosity, the effect of using different equations of state such as PR and ER and steam or hot water injection are considered. In addition distributions of pressure, temperature, saturation of gas, hydrate and water in the reservoir are evaluated. It is shown that the gas production rate is a sensitive function of well pressure.
Abstract: The present contribution deals with the
thermophoretic deposition of nanoparticles over a rapidly rotating
permeable disk in the presence of partial slip, magnetic field, thermal
radiation, thermal-diffusion, and diffusion-thermo effects. The
governing nonlinear partial differential equations such as continuity,
momentum, energy and concentration are transformed into nonlinear
ordinary differential equations using similarity analysis, and the
solutions are obtained through the very efficient computer algebra
software MATLAB. Graphical results for non-dimensional
concentration and temperature profiles including thermophoretic
deposition velocity and Stanton number (thermophoretic deposition
flux) in tabular forms are presented for a range of values of the
parameters characterizing the flow field. It is observed that slip
mechanism, thermal-diffusion, diffusion-thermo, magnetic field and
radiation significantly control the thermophoretic particles deposition
rate. The obtained results may be useful to many industrial and
engineering applications.
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: This paper aims to perform the second law analysis of
thermodynamics on the laminar film condensation of pure saturated
vapor flowing in the direction of gravity on an ellipsoid with variable
wall temperature. The analysis provides us understanding how the
geometric parameter- ellipticity and non-isothermal wall temperature
variation amplitude “A." affect entropy generation during film-wise
condensation heat transfer process. To understand of which
irreversibility involved in this condensation process, we derived an
expression for the entropy generation number in terms of ellipticity
and A. The result indicates that entropy generation increases with
ellipticity. Furthermore, the irreversibility due to finite temperature
difference heat transfer dominates over that due to condensate film
flow friction and the local entropy generation rate decreases with
increasing A in the upper half of ellipsoid. Meanwhile, the local
entropy generation rate enhances with A around the rear lower half of
ellipsoid.
Abstract: The transient hydrodynamics and thermal behaviors of
fluid flow in open-ended vertical parallel-plate porous microchannel are investigated semi-analytically under the effect of the hyperbolic
heat conduction model. The model that combines both the continuum approach and the possibility of slip at the boundary is adopted in the
study. The Effects of Knudsen number , Darcy number , and thermal relaxation time on the microchannel hydrodynamics and thermal behaviors are investigated using the hyperbolic heat
conduction models. It is found that as increases the slip in the hydrodynamic and thermal boundary condition increases. This slip in
the hydrodynamic boundary condition increases as increases. Also, the slip in the thermal boundary condition increases as
decreases especially the early stage of time.
Abstract: In research on natural ventilation, and passive cooling
with forced convection, is essential to know how heat flows in a solid
object and the pattern of temperature distribution on their surfaces,
and eventually how air flows through and convects heat from the
surfaces of steel under roof. This paper presents some results from
running the computational fluid dynamic program (CFD) by
comparison between natural ventilation and forced convection within
roof attic that is received directly from solar radiation. The CFD
program for modeling air flow inside roof attic has been modified to
allow as two cases. First case, the analysis under natural ventilation,
is closed area in roof attic and second case, the analysis under forced
convection, is opened area in roof attic. These extend of all cases to
available predictions of variations such as temperature, pressure, and
mass flow rate distributions in each case within roof attic. The
comparison shows that this CFD program is an effective model for
predicting air flow of temperature and heat transfer coefficient
distribution within roof attic. The result shows that forced convection
can help to reduce heat transfer through roof attic and an around area
of steel core has temperature inner zone lower than natural
ventilation type. The different temperature on the steel core of roof
attic of two cases was 10-15 oK.
Abstract: The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy-s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-order nonlinear differential equation. In this paper, an approximate method for solving higher-order ordinary differential equations is proposed. The approach is based on a rational Chebyshev Tau (RCT) method. The operational matrices of the derivative and product of rational Chebyshev (RC) functions are presented. These matrices together with the Tau method are utilized to reduce the solution of the higher-order ordinary differential equations to the solution of a system of algebraic equations. We also present the comparison of this work with others and show that the present method is applicable.
Abstract: A numerical study on the influence of electroosmotic flow on analyte preconcentration by isotachophoresis ( ITP) is made. We consider that the double layer induced electroosmotic flow ( EOF) counterbalance the electrophoretic velocity and a stationary ITP stacked zones results. We solve the Navier-Stokes equations coupled with the Nernst-Planck equations to determine the local convective velocity and the preconcentration dynamics of ions. Our numerical algorithm is based on a finite volume method along with a secondorder upwind scheme. The present numerical algorithm can capture the the sharp boundaries of step-changes ( plateau mode) or zones of steep gradients ( peak mode) accurately. The convection of ions due to EOF reduces the resolution of the ITP transition zones and produces a dispersion in analyte zones. The role of the electrokinetic parameters which induces dispersion is analyzed. A one-dimensional model for the area-averaged concentrations based on the Taylor-Aristype effective diffusivity is found to be in good agreement with the computed solutions.
Abstract: The major part of light weight timber constructions
consists of insulation. Mineral wool is the most commonly used
insulation due to its cost efficiency and easy handling. The fiber
orientation and porosity of this insulation material enables flowthrough.
The air flow resistance is low. If leakage occurs in the
insulated bay section, the convective flow may cause energy losses
and infiltration of the exterior wall with moisture and particles. In
particular the infiltrated moisture may lead to thermal bridges and
growth of health endangering mould and mildew. In order to prevent
this problem, different numerical calculation models have been
developed. All models developed so far have a potential for
completion. The implementation of the flow-through properties of
mineral wool insulation may help to improve the existing models.
Assuming that the real pressure difference between interior and
exterior surface is larger than the prescribed pressure difference in the
standard test procedure for mineral wool ISO 9053 / EN 29053,
measurements were performed using the measurement setup for
research on convective moisture transfer “MSRCMT".
These measurements show, that structural inhomogeneities of
mineral wool effect the permeability only at higher pressure
differences, as applied in MSRCMT. Additional microscopic
investigations show, that the location of a leak within the
construction has a crucial influence on the air flow-through and the
infiltration rate. The results clearly indicate that the empirical values
for the acoustic resistance of mineral wool should not be used for the
calculation of convective transfer mechanisms.
Abstract: In this paper, Lattice Boltzmann Method (LBM) is used to study laminar flow with mixed convection heat transfer inside a two-dimensional inclined lid-driven rectangular cavity with aspect ratio AR = 3. Bottom wall of the cavity is maintained at lower temperature than the top lid, and its vertical walls are assumed insulated. Top lid motion results in fluid motion inside the cavity. Inclination of the cavity causes horizontal and vertical components of velocity to be affected by buoyancy force. To include this effect, calculation procedure of macroscopic properties by LBM is changed and collision term of Boltzmann equation is modified. A computer program is developed to simulate this problem using BGK model of lattice Boltzmann method. The effects of the variations of Richardson number and inclination angle on the thermal and flow behavior of the fluid inside the cavity are investigated. The results are presented as velocity and temperature profiles, stream function contours and isotherms. It is concluded that LBM has good potential to simulate mixed convection heat transfer problems.
Abstract: In this work the numerical simulation of transient heat
transfer in a cylindrical probe is done. An experiment was conducted
introducing a steel cylinder in a heating chamber and registering its
surface temperature along the time during one hour. In parallel, a
mathematical model was solved for one dimension transient heat
transfer in cylindrical coordinates, considering the boundary
conditions of the test. The model was solved using finite difference
method, because the thermal conductivity in the cylindrical steel bar
and the convection heat transfer coefficient used in the model are
considered temperature dependant functions, and both conditions
prevent the use of the analytical solution. The comparison between
theoretical and experimental results showed the average deviation is
below 2%. It was concluded that numerical methods are useful in
order to solve engineering complex problems. For constant k and h,
the experimental methodology used here can be used as a tool for
teaching heat transfer in mechanical engineering, using mathematical
simplified models with analytical solutions.
Abstract: In this experiment, we investigated the performance of
two types of heat sink, swaged- and extruded-type, used in the inverter
of industrial electricity generator. The swaged-type heat sink has 62
fins, and the extruded-type has 38 fins having the same dimension as
that of the swaged-type. But the extruded-type heat sink maintains the
same heat transfer area by the laterally waved surface which has 1 mm
in radius. As a result, the swaged- and extruded-type heat sinks
released 71% and 64% of the heat incoming to the heat sink,
respectively. The other incoming heat were naturally convected and
radiated to the ambient. In spite of 40% decrease in number of fins, the
heat release performance of the extruded-type heat sink was lowered
only 7% than that of the swaged-type. We believe that, this shows the
increment of effective heat transfer area by the laterally waved surface
of fins and the better heat transfer property of the extruded-type heat
sink.
Abstract: In this research, the laminar heat transfer of natural convection on vertical surfaces has been investigated. Most of the studies on natural convection have been considered constantly whereas velocity and temperature domain, do not change with time, transient one are used a lot. Governing equations are solved using a finite volume approach. The convective terms are discretized using the power-law scheme, whereas for diffusive terms the central difference is employed. Coupling between the velocity and pressure is made with SIMPLE algorithm. The resultant system of discretized linear algebraic equations is solved with an alternating direction implicit scheme. Then a configuration of rectangular fins is put in different ways on the surface and heat transfer of natural convection on these surfaces without sliding is studied and finally optimization is done.
Abstract: The temperature distribution and the heat transfer
rates through a multi-layer door of a furnace were investigated. The
inside of the door was in contact with hot air and the other side of the
door was in contact with room air. Radiation heat transfer from the
walls of the furnace to the door and the door to the surrounding area
was included in the problem. This work is a two dimensional steady
state problem. The Churchill and Chu correlation was used to find
local convection heat transfer coefficients at the surfaces of the
furnace door. The thermophysical properties of air were the functions
of the temperatures. Polynomial curve fitting for the fluid properties
were carried out. Finite difference method was used to discretize for
conduction heat transfer within the furnace door. The Gauss-Seidel
Iteration was employed to compute the temperature distribution in
the door.
The temperature distribution in the horizontal mid plane of the
furnace door in a two dimensional problem agrees with the one
dimensional problem. The local convection heat transfer coefficients
at the inside and outside surfaces of the furnace door are exhibited.
Abstract: The effect of streamwise conduction on the thermal
characteristics of forced convection for nanofluidic flow in
rectangular microchannel heat sinks under isothermal wall has been
investigated. By applying the fin approach, models with and without
streamwise conduction term in the energy equation were developed
for hydrodynamically and thermally fully-developed flow. These two
models were solved to obtain closed form analytical solutions for the
nanofluid and solid wall temperature distributions and the analysis
emphasized details of the variations induced by the streamwise
conduction on the nanofluid heat transport characteristics. The effects
of the Peclet number, nanoparticle volume fraction, thermal
conductivity ratio on the thermal characteristics of forced convection
in microchannel heat sinks are analyzed. Due to the anomalous
increase in the effective thermal conductivity of nanofluid compared
to its base fluid, the effect of streamwise conduction is expected to be
more significant. This study reveals the significance of the effect of
streamwise conduction under certain conditions of which the
streamwise conduction should not be neglected in the forced
convective heat transfer analysis of microchannel heat sinks.
Abstract: We deal with the numerical solution of time-dependent convection-diffusion-reaction equations. We combine the local projection stabilization method for the space discretization with two different time discretization schemes: the continuous Galerkin-Petrov (cGP) method and the discontinuous Galerkin (dG) method of polynomial of degree k. We establish the optimal error estimates and present numerical results which shows that the cGP(k) and dG(k)- methods are accurate of order k +1, respectively, in the whole time interval. Moreover, the cGP(k)-method is superconvergent of order 2k and dG(k)-method is of order 2k +1 at the discrete time points. Furthermore, the dependence of the results on the choice of the stabilization parameter are discussed and compared.
Abstract: The flow and heat transfer characteristics for natural
convection along an inclined plate in a saturated porous medium with
an applied magnetic field have been studied. The fluid viscosity has
been assumed to be an inverse function of temperature. Assuming
temperature vary as a power function of distance. The transformed
ordinary differential equations have solved by numerical integration
using Runge-Kutta method. The velocity and temperature profile
components on the plate are computed and discussed in detail for
various values of the variable viscosity parameter, inclination angle,
magnetic field parameter, and real constant (λ). The results have also
been interpreted with the aid of tables and graphs. The numerical
values of Nusselt number have been calculated for the mentioned
parameters.
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.