Abstract: Unsteady effects of MHD free convection flow past in an infinite vertical plate with heat source in presence of radiation with reference to all critical parameters that appear in field equations are studied in this paper. The governing equations are developed by usual Boussinesq’s approximation. The problem is solved by using perturbation technique. The results are obtained for velocity, temperature, Nusselt number and skin-friction. The effects of magnetic parameter, prandtl number, Grashof number, permeability parameter, heat source/sink parameter and radiation parameter are discussed on flow characteristics and shown by means of graphs and tables.
Abstract: Natural circulation loops (NCLs) are buoyancy driven flow systems without any moving components. NCLs have vast applications in geothermal, solar and nuclear power industry where reliability and safety are of foremost concern. Due to certain favorable thermophysical properties, especially near supercritical regions, carbon dioxide can be considered as an ideal loop fluid in many applications. In the present work, a high temperature NCL that uses supercritical carbon dioxide as loop fluid is analysed. The effects of relevant design and operating variables on loop performance are studied. The system operating under steady state is modelled taking into account the axial conduction through loop fluid and loop wall, and heat transfer with surroundings. The heat source is considered to be a heater with controlled heat flux and heat sink is modelled as an end heat exchanger with water as the external cold fluid. The governing equations for mass, momentum and energy conservation are normalized and are solved numerically using finite volume method. Results are obtained for a loop pressure of 90 bar with the power input varying from 0.5 kW to 6.0 kW. The numerical results are validated against the experimental results reported in the literature in terms of the modified Grashof number (Grm) and Reynolds number (Re). Based on the results, buoyancy and friction dominated regions are identified for a given loop. Parametric analysis has been done to show the effect of loop diameter, loop height, ambient temperature and insulation. The results show that for the high temperature loop, heat loss to surroundings affects the loop performance significantly. Hence this conjugate heat transfer between the loop and surroundings has to be considered in the analysis of high temperature NCLs.
Abstract: The study of mixed convection is, usually, focused on the straight channels in which the onset of the mixed convection is well defined as function of the ratio between Grashof number and Reynolds number, Gr/Re. This is not the case for a complex channel wherein the mixed convection is not sufficiently examined in the literature. Our paper focuses on the study of the mixed convection in a complex geometry in which our main contribution reveals that the critical value of the ratio Gr/Re for the onset of the mixed convection increases highly in the type of geometry contrary to the straight channel. Furthermore, the accentuated secondary flow in this geometry prevents the thermal stratification in the flow and consequently the buoyancy driven becomes negligible. To perform these objectives, a numerical study in complex geometry for several values of the ratio Gr/Re with prescribed wall heat flux (H2), was realized by using the CFD code.
Abstract: An empirical correlation for predicting the heat transfer coefficient for a cylinder under free convection, inclined at any arbitrary angle with the horizontal has been developed in terms of Nusselt number, Prandtl number and Grashof number. Available experimental data was used to determine the parameters for the proposed correlation. The proposed correlation predicts the available data well within ±10%, for Prandtl number in the range 0.68-0.72 and Grashof number in the range 1.4×104–1.2×1010.
Abstract: An unsteady mixed free convection MHD flow of elastic-viscous incompressible fluid past an infinite vertical porous flat plate is investigated when the presence of heat Source/sink, temperature and concentration are assumed to be oscillating with time and hall effect. The governing equations are solved by complex variable technique. The expressions for the velocity field, temperature field and species concentration are demonstrated in graphs. The effects of the Prandtl number, the Grashof number, modified Grashof number, the Schimidt number, the Hall parameter, Elastic parameter & Magnetic parameter are discussed.
Abstract: In this paper, the ice melting in rectangular,
cylindrical and conical forms, which are erected vertically against air
flow, are experimentally studied in the free convection regime.The
results obtained are: Nusslet Number, heat transfer coefficient
andGrashof Number, and the variations of the said numbers in
relation to the time. The variations of ice slab area and volume are
measured, too.
Abstract: In this research, a 2-D computational analysis of
steady state free convection in a rectangular enclosure filled with an
electrically conducting fluid under Effect of Magnetic Field has been
performed. The governing equations (mass, momentum, and energy)
are formulated and solved by a finite volume method (FVM)
subjected to different boundary conditions. A parametric study has
been conducted to consider the influence of Grashof number (Gr),
Prantdl number (Pr) and the orientation of magnetic field on the flow
and heat transfer characteristics. It is observed that Nusselt number
(Nu) and heat flux will increase with increasing Grashof and Prandtl
numbers and decreasing the slope of the orientation of magnetic field.
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: We numerically study the three-dimensional
magnetohydrodynamics (MHD) stability of oscillatory natural
convection flow in a rectangular cavity, with free top surface, filled
with a liquid metal, having an aspect ratio equal to A=L/H=5, and
subjected to a transversal temperature gradient and a uniform
magnetic field oriented in x and z directions. The finite volume
method was used in order to solve the equations of continuity,
momentum, energy, and potential. The stability diagram obtained in
this study highlights the dependence of the critical value of the
Grashof number Grcrit , with the increase of the Hartmann number
Ha for two orientations of the magnetic field. This study confirms
the possibility of stabilization of a liquid metal flow in natural
convection by application of a magnetic field and shows that the
flow stability is more important when the direction of magnetic field
is longitudinal than when the direction is transversal.
Abstract: Numerical study of a plane jet occurring in a vertical
heated channel is carried out. The aim is to explore the influence of
the forced flow, issued from a flat nozzle located in the entry section
of a channel, on the up-going fluid along the channel walls. The
Reynolds number based on the nozzle width and the jet velocity
ranges between 3 103 and 2.104; whereas, the Grashof number based
on the channel length and the wall temperature difference is 2.57
1010. Computations are established for a symmetrically heated
channel and various nozzle positions. The system of governing
equations is solved with a finite volumes method. The obtained
results show that the jet-wall interactions activate the heat transfer,
the position variation modifies the heat transfer especially for low
Reynolds numbers: the heat transfer is enhanced for the adjacent
wall; however it is decreased for the opposite one. The numerical
velocity and temperature fields are post-processed to compute the
quantities of engineering interest such as the induced mass flow rate,
and the Nusselt number along the plates.
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 .