Abstract: Double-diffusive steady convection in a partially
porous cavity with partially permeable walls and under the combined
buoyancy effects of thermal and mass diffusion was analysed
numerically using finite volume method.
The top wall is well insulated and impermeable while the bottom
surface is partially well insulated and impermeable and partially
submitted to constant temperature T1 and concentration C1. Constant
equal temperature T2 and concentration C2 are imposed along the
vertical surfaces of the enclosure. Mass suction/injection and
injection/suction are respectively considered at the bottom of the
porous centred partition and at one of the vertical walls.
Heat and mass transfer characteristics as streamlines and average
Nusselt numbers and Sherwood numbers were discussed for different
values of buoyancy ratio, Rayleigh number, and injection/suction
coefficient.
It is especially noted that increasing the injection factor
disadvantages the exchanges in the case of the injection while the
transfer is augmented in case of suction. On the other hand, a critical
value of the buoyancy ratio was highlighted for which heat and mass
transfers are minimized.
Abstract: A numerical study is presented on convective heat transfer in enclosures. The results are addressed to automotive headlights containing new-age light sources like Light Emitting Diodes (LED). The heat transfer from the heat source (LED) to the enclosure walls is investigated for mixed convection as interaction of the forced convection flow from an inlet and an outlet port and the natural convection at the heat source. Unlike existing studies, inlet and outlet port are thermally coupled and do not serve to remove hot fluid. The input power of the heat source is expressed by the Rayleigh number. The internal position of the heat source, the aspect ratio of the enclosure, and the inclination angle of one wall are varied. The results are given in terms of the global Nusselt number and the enclosure Nusselt number that characterize the heat transfer from the source and from the interior fluid to the enclosure walls, respectively. It is found that the heat transfer from the source to the fluid can be maximized if the source is placed in the main stream from the inlet to the outlet port. In this case, the Reynolds number and heat source position have the major impact on the heat transfer. A disadvantageous position has been found where natural and forced convection compete each other. The overall heat transfer from the source to the wall increases with increasing Reynolds number as well as with increasing aspect ratio and decreasing inclination angle. The heat transfer from the interior fluid to the enclosure wall increases upon decreasing the aspect ratio and increasing the inclination angle. This counteracting behaviour is caused by the variation of the area of the enclosure wall. All mixed convection results are compared to the natural convection limit.
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: The mixing of pollutions and sediments in near shore regions of natural water bodies depends heavily on the characteristics such as the strength and frequency of flow instability. In the present paper, the instability of natural convection induced by absorption of solar radiation in littoral regions is considered. Spectral analysis is conducted on the quasi-steady state flow to reveal the power and frequency modes of the instability at various positions. Results indicate that the power of instability, the number of frequency modes, the prominence of higher frequency modes, and the highest frequency mode increase with the offshore distance and/or Rayleigh number. Harmonic modes are present at relatively low Rayleigh numbers. For a given offshore distance, the position with the strongest power of instability is located adjacent to the sloping bottom while the frequency modes are the same over the local depth. As the Rayleigh number increases, the unstable region extends toward the shore.
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: 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: In this work, the natural convection in a concentric
annulus between a cold outer inclined square enclosure and heated
inner circular cylinder is simulated for two-dimensional steady
state. The Boussinesq approximation was applied to model the
buoyancy-driven effect and the governing equations were solved
using the time marching approach staggered by body fitted
coordinates. The coordinate transformation from the physical
domain to the computational domain is set up by an analytical
expression. Numerical results for Rayleigh numbers 103 , 104 , 105
and 106, aspect ratios 1.5 , 3.0 and 4.5 for seven different
inclination angles for the outer square enclosure 0o , -30o
, -45o
,
-60o , -90o , -135o , -180o are presented as well. The computed flow
and temperature fields were demonstrated in the form of
streamlines, isotherms and Nusselt numbers variation. It is found
that both the aspect ratio and the Rayleigh number are critical to the
patterns of flow and thermal fields. At all Rayleigh numbers angle
of inclination has nominal effect on heat transfer.