Abstract: The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.
Abstract: Laminar natural-convective heat transfer from a
horizontal cylinder is studied by solving the Navier-Stokes and
energy equations using higher order compact scheme in cylindrical
polar coordinates. Results are obtained for Rayleigh numbers of 1,
10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt
number and mean Nusselt number are calculated and compared with
available experimental and theoretical results. Streamlines, vorticity -
lines and isotherms are plotted.
Abstract: The aim of this paper is to investigate twodimensional unsteady flow of a viscous incompressible fluid about stagnation point on permeable stretching sheet in presence of time dependent free stream velocity. Fluid is considered in the influence of transverse magnetic field in the presence of radiation effect. Rosseland approximation is use to model the radiative heat transfer. Using time-dependent 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 by using Runge-Kutta Fehlberg method with the help of Newton-Raphson shooting technique. In the present work the effect of unsteadiness parameter, magnetic field parameter, radiation parameter, stretching parameter and the Prandtl number on flow and heat transfer characteristics have been discussed. Skin-friction coefficient and Nusselt number at the sheet are computed and discussed. The results reported in the paper are in good agreement with published work in literature by other researchers.
Abstract: Natural convection heat transfer from a heated
horizontal semi-circular cylinder (flat surface upward) has been
investigated for the following ranges of conditions; Grashof number,
and Prandtl number. The governing partial differential equations
(continuity, Navier-Stokes and energy equations) have been solved
numerically using a finite volume formulation. In addition, the role of
the type of the thermal boundary condition imposed at cylinder
surface, namely, constant wall temperature (CWT) and constant heat
flux (CHF) are explored. Natural convection heat transfer from a
heated horizontal semi-circular cylinder (flat surface upward) has
been investigated for the following ranges of conditions; Grashof
number, and Prandtl number, . The governing partial differential
equations (continuity, Navier-Stokes and energy equations) have
been solved numerically using a finite volume formulation. In
addition, the role of the type of the thermal boundary condition
imposed at cylinder surface, namely, constant wall temperature
(CWT) and constant heat flux (CHF) are explored. The resulting flow
and temperature fields are visualized in terms of the streamline and
isotherm patterns in the proximity of the cylinder. The flow remains
attached to the cylinder surface over the range of conditions spanned
here except that for and ; at these conditions, a separated flow
region is observed when the condition of the constant wall
temperature is prescribed on the surface of the cylinder. The heat
transfer characteristics are analyzed in terms of the local and average
Nusselt numbers. The maximum value of the local Nusselt number
always occurs at the corner points whereas it is found to be minimum
at the rear stagnation point on the flat surface. Overall, the average
Nusselt number increases with Grashof number and/ or Prandtl
number in accordance with the scaling considerations. The numerical
results are used to develop simple correlations as functions of
Grashof and Prandtl number thereby enabling the interpolation of the
present numerical results for the intermediate values of the Prandtl or
Grashof numbers for both thermal boundary conditions.
Abstract: In this manuscript, the LBM is applied for simulating of Mixed Convection in a Lid-Driven cavity with an open side. The cavity horizontal walls are insulated while the west Lid-driven wall is maintained at a uniform temperature higher than the ambient. Prandtl number (Pr) is fixed to 0.71 (air) while Reynolds number (Re) , Richardson number (Ri) and aspect ratio (A) of the cavity are changed in the range of 50-150 , of 0.1-10 and of 1-4 , respectively. The numerical code is validated for the standard square cavity, and then the results of an open ended cavity are presented. Result shows by increasing of aspect ratio, the average Nusselt number (Nu) on lid- driven wall decreases and with same Reynolds number (Re) by increasing of aspect ratio (A), Richardson number plays more important role in heat transfer rate.
Abstract: In this study, an analysis has been performed for
free convection with radiation effect over a thermal forming
nonlinearly stretching sheet. Parameters n, k0, Pr, G represent
the dominance of the nonlinearly effect, radiation effect, heat
transfer and free convection effects which have been presented
in governing equations, respectively. The similarity
transformation and the finite-difference methods have been
used to analyze the present problem. From the results, we find
that the effects of parameters n, k0, Pr, Ec and G to the
nonlinearly stretching sheet. The increase of Prandtl number Pr,
free convection parameter G or radiation parameter k0 resulting
in the increase of heat transfer effects, but increase of the
viscous dissipation number Ec will decrease of heat transfer
effect.
Abstract: The effect of variable chemical reaction on heat and mass transfer characteristics over unsteady stretching surface embedded in a porus medium is studied. The governing time dependent boundary layer equations are transformed into ordinary differential equations containing chemical reaction parameter, unsteadiness parameter, Prandtl number and Schmidt number. These equations have been transformed into a system of first order differential equations. MATHEMATICA has been used to solve this system after obtaining the missed initial conditions. The velocity gradient, temperature, and concentration profiles are computed and discussed in details for various values of the different parameters.
Abstract: This paper presents and discusses the numerical simulations of transient laminar natural convection cooling of high Prandtl number fluids in cubical cavities, in which the six walls of the cavity are subjected to a step change in temperature. The effect of the fluid Prandtl number on the heat transfer coefficient is studied for three different fluids (Golden Syrup, Glycerin and Glycerin-water solution 50%). The simulations are performed at two different Rayleigh numbers (5·106 and 5·107) and six different Prandtl numbers (3 · 105 ≥Pr≥ 50). Heat conduction through the cavity glass walls is also considered. The propsed correlations of the averaged heat transfer coefficient (N u) showed that it is dependant on the initial Ra and almost independent on P r. The instantaneous flow patterns, temperature contours and time evolution of volume averaged temperature and heat transfer coefficient are presented and analyzed.
Abstract: In the present analysis an unsteady laminar
forced convection water boundary layer flow is considered.
The fluid properties such as viscosity and Prandtl number are
taken as variables such that those are inversely proportional to
temperature. By using quasi-linearization technique the nonlinear
coupled partial differential equations are linearized and
the numerical solutions are obtained by using implicit finite
difference scheme with the appropriate selection of step sizes.
Non-similar solutions have been obtained from the starting
point of the stream-wise coordinate to the point where skin
friction value vanishes. The effect non-uniform mass transfer
along the surface of the cylinder through slot is studied on the
skin friction and heat transfer coefficients.
Abstract: This paper presents a linear stability analysis of
natural convection in a horizontal layer of a viscoelastic
nanofluid. The Oldroyd B model was utilized to describe the
rheological behavior of a viscoelastic nanofluid. The model
used for the nanofluid incorporated the effects of Brownian
motion and thermophoresis. The onset criterion for stationary
and oscillatory convection was derived analytically. The effects
of the Deborah number, retardation parameters, concentration
Rayleigh number, Prandtl number, and Lewis number on the
stability of the system were investigated. Results indicated that
there was competition among the processes of thermophoresis,
Brownian diffusion, and viscoelasticity which caused
oscillatory rather than stationary convection to occur.
Oscillatory instability is possible with both bottom- and
top-heavy nanoparticle distributions. Regimes of stationary and
oscillatory convection for various parameters were derived and
are discussed in detail.
Abstract: This paper is a numerical investigation of a laminar
isothermal plane two dimensional wall jet. Special attention has been
paid to the effect of the inlet conditions at the nozzle exit on the
hydrodynamic and thermal characteristics of the flow. The
behaviour of various fluids evolving in both forced and mixed
convection regimes near a vertical plate plane is carried out. The
system of governing equations is solved with an implicit finite
difference scheme. For numerical stability we use a staggered non
uniform grid. The obtained results show that the effect of the Prandtl
number is significant in the plume region in which the jet flow is
governed by buoyant forces. Further for ascending X values, the
buoyancy forces become dominating, and a certain agreement
between the temperature profiles are observed, which shows that the
velocity profile has no longer influence on the wall temperature
evolution in this region. Fluids with low Prandtl number warm up
more importantly, because for such fluids the effect of heat diffusion
is higher.
Abstract: The present study investigates numerically the
phenomenon of vortex-shedding and its suppression in twodimensional
mixed convective flow past a square cylinder under the
joint influence of buoyancy and free-stream orientation with respect
to gravity. The numerical experiments have been conducted at a
fixed Reynolds number (Re) of 100 and Prandtl number (Pr) of 0.71,
while Richardson number (Ri) is varied from 0 to 1.6 and freestream
orientation, α, is kept in the range 0o≤ α ≤ 90o, with 0o
corresponding to an upward flow and 90o representing a cross-flow
scenario, respectively. The continuity, momentum and energy
equations, subject to Boussinesq approximation, are discretized using
a finite difference method and are solved by a semi-explicit pressure
correction scheme. The critical Richardson number, leading to the
suppression of the vortex-shedding (Ric), is estimated by using
Stuart-Landau theory at various free-stream orientations and the
neutral curve is obtained in the Ri-α plane. The neutral curve
exhibits an interesting non-monotonic behavior with Ric first
increasing with increasing values of α upto 45o and then decreasing
till 70o. Beyond 70o, the neutral curve again exhibits a sharp
increasing asymptotic trend with Ric approaching very large values
as α approaches 90o. The suppression of vortex shedding is not
observed at α = 90o (cross-flow). In the unsteady flow regime, the
Strouhal number (St) increases with the increase in Richardson
number.
Abstract: In the present study, the lattice Boltzmann Method (LBM) is applied for simulating of Natural Convection in an inclined open ended cavity. The cavity horizontal walls are insulated while the west wall is maintained at a uniform temperature higher than the ambient. Prandtl number is fixed to 0.71 (air) while Rayligh numbers, aspect ratio of the cavity are changed in the range of 103 to 104 and of 1-4, respectively. The numerical code is validated for the previously results for open ended cavities, and then the results of an inclined open ended cavity for various angles of rotating open ended cavity are presented. Result shows by increasing of aspect ratio, the average Nusselt number on hot wall decreases for all rotation angles. When gravity acceleration direction is opposite of standard gravity direction the convection heat transfer has a manner same as conduction.
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: Double-diffusive natural convection in an open top
square cavity and heated from the side is studied numerically.
Constant temperatures and concentration are imposed along the right
and left walls while the heat balance at the surface is assumed to obey
Newton-s law of cooling. The finite difference method is used to
solve the dimensionless governing equations. The numerical results
are reported for the effect of Marangoni number, Biot number and
Prandtl number on the contours of streamlines, temperature and
concentration. The predicted results for the average Nusselt number
and Sherwood number are presented for various parametric
conditions. The parameters involved are as follows; the thermal
Marangoni number, 0 ≤ MaT ≤1000 , the solutal Marangoni number,
0 1000 c ≤ Ma ≤ , the Biot number, 0 ≤ Bi ≤ 6 , Grashof number,
5 Gr = 10 and aspect ratio 1. The study focused on both flows; thermal
dominated, N = 0.8 , and compositional dominated, N = 1.3 .
Abstract: Proper orthogonal decomposition (POD) is used to reconstruct spatio-temporal data of a fully developed turbulent channel flow with density variation at Reynolds number of 150, based on the friction velocity and the channel half-width, and Prandtl number of 0.71. To apply POD to the fully developed turbulent channel flow with density variation, the flow field (velocities, density, and temperature) is scaled by the corresponding root mean square values (rms) so that the flow field becomes dimensionless. A five-vector POD problem is solved numerically. The reconstructed second-order moments of velocity, temperature, and density from POD eigenfunctions compare favorably to the original Direct Numerical Simulation (DNS) data.
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: A steady two-dimensional magnetohydrodynamics
flow and heat transfer over a stretching vertical sheet influenced by
radiation and porosity is studied. The governing boundary layer
equations of partial differential equations are reduced to a system of
ordinary differential equations using similarity transformation. The
system is solved numerically by using a finite difference scheme
known as the Keller-box method for some values of parameters,
namely the radiation parameter N, magnetic parameter M, buoyancy
parameter l , Prandtl number Pr and permeability parameter K. The
effects of the parameters on the heat transfer characteristics are
analyzed and discussed. It is found that both the skin friction
coefficient and the local Nusselt number decrease as the magnetic
parameter M and permeability parameter K increase. Heat transfer
rate at the surface decreases as the radiation parameter increases.
Abstract: In this work, we experimentally study heat transfer
from exhaust particulate air of detergent spray drying tower to water
by using coiled tube heat exchanger. Water flows in the coiled
tubes, where air loaded with detergent particles of 43 micrometers
in diameter flows within the shell. Four coiled tubes with different
coil pitches are used in a counter-current flow configuration. We
investigate heat transfer coefficients of inside and outside the heat
transfer surfaces through 400 experiments. The correlations between
Nusselt number and Reynolds number, Prandtl number, mass flow
rate of particulates to mass flow rate of air ratio and coiled tube
pitch parameter are proposed. The correlations procured can be used
to predicted heat transfer between tube and shell of the heat
exchanger.
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.