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: 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: A numerical study has been carried out to investigate
the heat transfer by natural convection of nanofluid taking Cu as
nanoparticles and the water as based fluid in a three dimensional
annulus enclosure filled with porous media (silica sand) between two
horizontal concentric cylinders with 12 annular fins of 2.4mm
thickness attached to the inner cylinder under steady state conditions.
The governing equations which used are continuity, momentum and
energy equations under an assumptions used Darcy law and
Boussinesq-s approximation which are transformed to dimensionless
equations. The finite difference approach is used to obtain all the
computational results using the MATLAB-7. The parameters affected
on the system are modified Rayleigh number (10 ≤Ra*≤ 1000), fin
length Hf (3, 7 and 11mm), radius ratio Rr (0.293, 0.365 and 0.435)
and the volume fraction(0 ≤ ¤ò ≤ 0 .35). It was found that the
average Nusselt number depends on (Ra*, Hf, Rr and φ). The results
show that, increasing of fin length decreases the heat transfer rate and
for low values of Ra*, decreasing Rr cause to decrease Nu while for
Ra*
greater than 100, decreasing Rr cause to increase Nu and adding
Cu nanoparticles with 0.35 volume fraction cause 27.9%
enhancement in heat transfer. A correlation for Nu in terms of Ra*,
Hf and φ, has been developed for inner hot cylinder.
Abstract: We report the results of an lattice Boltzmann
simulation of magnetohydrodynamic damping of sidewall convection
in a rectangular enclosure filled with a porous medium. In particular
we investigate the suppression of convection when a steady magnetic
field is applied in the vertical direction. The left and right vertical
walls of the cavity are kept at constant but different temperatures
while both the top and bottom horizontal walls are insulated. The
effects of the controlling parameters involved in the heat transfer and
hydrodynamic characteristics are studied in detail. The heat and mass
transfer mechanisms and the flow characteristics inside the enclosure
depended strongly on the strength of the magnetic field and Darcy
number. The average Nusselt number decreases with rising values of
the Hartmann number while this increases with increasing values of
the Darcy number.
Abstract: The present paper considers the steady free
convection boundary layer flow of a viscoelastics fluid with constant
temperature in the presence of heat generation. The boundary layer
equations are an order higher than those for the Newtonian (viscous)
fluid and the adherence boundary conditions are insufficient to
determine the solution of these equations completely. The governing
boundary layer equations are first transformed into non-dimensional
form by using special dimensionless group. Computations are
performed numerically by using Keller-box method by augmenting
an extra boundary condition at infinity and the results are displayed
graphically to illustrate the influence of viscoelastic K, heat
generation γ , and Prandtl Number, Pr parameters on the velocity
and temperature profiles. The results of the surface shear stress in
terms of the local skin friction and the surface rate of heat transfer in
terms of the local Nusselt number for a selection of the heat
generation parameterγ (=0.0, 0.2, 0.5, 0.8, 1.0) are obtained and
presented in both tabular and graphical formats. Without effect of the
internal heat generation inside the fluid domain for which we take
γ = 0.0, the present numerical results show an excellent agreement
with previous publication.
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: The present paper considers the steady free convection
boundary layer flow of a viscoelastic fluid on solid sphere with
Newtonian heating. The boundary layer equations are an order higher
than those for the Newtonian (viscous) fluid and the adherence
boundary conditions are insufficient to determine the solution of
these equations completely. Thus, the augmentation an extra
boundary condition is needed to perform the numerical
computational. The governing boundary layer equations are first
transformed into non-dimensional form by using special
dimensionless group and then solved by using an implicit finite
difference scheme. The results are displayed graphically to illustrate
the influence of viscoelastic K and Prandtl Number Pr parameters on
skin friction, heat transfer, velocity profiles and temperature profiles.
Present results are compared with the published papers and are found
to concur very well.