Numerical research of double‐diffusive natural convection in elliptical cylinders: Effect of thermal Rayleigh number

Heat Transfer ◽  
2020 ◽  
Vol 49 (4) ◽  
pp. 2194-2205
Author(s):  
Djedid Taloub ◽  
Abdelkarim Bouras ◽  
Mahfoud Djezzar ◽  
Zied Driss
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Research ◽  
Elliptical Cylinders ◽  
Double Diffusive ◽  
Thermal Rayleigh Number

Towards numerical computation of double-diffusive natural convection within an eccentric horizontal cylindrical annulus

2016 ◽  
Vol 26 (5) ◽  
pp. 1346-1364 ◽  
Author(s):  
Chahinez Ghernoug ◽  
Mahfoud Djezzar ◽  
Hassane Naji ◽  
Abdelkarim Bouras
Keyword(s):  
Mass Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Content Type ◽  
Cylindrical Annulus ◽  
Buoyancy Ratio ◽  
Convective Mode ◽  
Double Diffusive

Purpose – The purpose of this paper is to numerically study the double-diffusive natural convection within an eccentric horizontal cylindrical annulus filled with a Newtonian fluid. The annulus walls are maintained at uniform temperatures and concentrations so as to induce aiding thermal and mass buoyancy forces within the fluid. For that, this simulation span a moderate range of thermal Rayleigh number (100RaT100,000), Lewis (0.1Le10), buoyancy ratio (0N5) and Prandtl number (Pr=0.71) to examine their effects on flow motion and heat and mass transfers. Design/methodology/approach – A finite volume method in conjunction with the successive under-relaxation algorithm has been developed to solve the bipolar equations. These are written in dimensionless form in terms of vorticity, stream function, temperature and concentration. Beforehand, the implemented computer code has been validated through already published findings in the literature. The isotherms, streamlines and iso-concentrations are exhibited for various values of Rayleigh and Lewis numbers, and buoyancy ratio. In addition, heat and mass transfer rates in the annulus are translated in terms of Nusslet and Sherwood numbers along the enclosure’s sides. Findings – It is observed that, for the range of parameters considered here, the results show that the average Sherwood number increases with, while the average Nusselt number slightly dips as the Lewis number increases. It is also found that, under the convective mode, the local Nusselt number (or Sherwood) increases with the buoyancy ratio. Likewise, according to Lewis number’s value, the flow pattern is either symmetric and stable or asymmetric and random. Besides that, the heat transfer is transiting from a conductive mode to a convective mode with increasing the thermal Rayleigh number, and the flow structure and the rates of heat and mass transfer are significantly influenced by this parameter. Research limitations/implications – The range of the Rayleigh number considered here covers only the laminar case, with some constant parameters, namely the Prandtl number (Pr = 0.71), and the tilt angle (α=90°). The analysis here is only valid for steady, two-dimensional, laminar and aiding flow within an eccentric horizontal cylindrical annulus. This motivates further investigations involving other relevant parameters as N (opposite flows), Ra, Pr, Le, the eccentricity, the tilt angle, etc. Practical implications – An original framework for handling the double-diffusive natural convection within annuli is available, based on the bipolar equations. In addition, the achievement of this work could help researchers design thermal systems supported by annulus passages. Applications of the results can be of value in various arrangements such as storage of liquefied gases, electronic cable cooling systems, nuclear reactors, underground disposal of nuclear wastes, manifolds of solar energy collectors, etc. Originality/value – Given the geometry concerned, the bipolar coordinates have been used to set the inner and outer walls boundary conditions properly without interpolation. In addition, since studies on double-diffusive natural convection in annuli are lacking, the obtained results may be of interest to handle other configurations (e.g., elliptical-shaped speakers) with other boundary conditions.

scholarly journals Double-diffusive instabilities at a horizontal boundary after the sudden onset of heating

2018 ◽  
Vol 859 ◽  
pp. 126-159
Author(s):  
Oliver S. Kerr
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Salinity Gradient ◽  
Constant Heat Flux ◽  
Initial Time ◽  
Sudden Increase ◽  
Constant Heat ◽  
Diffusive Convection ◽  
Double Diffusive ◽  
Thermal Rayleigh Number

When a deep body of fluid with a stable salinity gradient is heated from below at a horizontal boundary a destabilizing temperature gradient develops and can lead to instabilities. We will focus on two variants of this problem: the sudden increase in the boundary temperature at the initial time and the sudden turning on of a constant heat flux. These generate time-dependent temperature profiles. We look at the growing phase of the linear instabilities as an initial value problem where the initial time for the instabilities is a parameter to be determined. We determine numerically the optimal initial conditions and the optimal starting time for the instabilities to ensure that the maximum growth occurs at some given later time. The method that is used is an extension of the method developed by Kerr & Gumm (J. Fluid Mech., vol. 825, 2017, pp. 1002–1034) in their investigation of the stability of developing temperature boundary layers at horizontal and vertical boundaries. This requires the use of an appropriate measure of the amplitude of the disturbances which is identified. The effectiveness of this approach is verified by looking at the classic problem of double-diffusive convection in a horizontal layer, where we look at both the salt-finger regime and the diffusive regime. We show that this approach is an effective way of investigating instabilities where the background gradients time dependent. For the problem of heating a salinity gradient from below, as the heat diffuses into the fluid the effective thermal Rayleigh number based on the instantaneous diffusion length scale grows. For the case of a sudden increase in the temperature by a fixed amount the effective thermal Rayleigh number is proportional to $t^{3/2}$, and for a constant heat flux it is proportional to $t^{2}$, where $t$ is the time since the onset of heating. However, the effective salt Rayleigh number also grows as $t^{2}$. We will show that for the constant temperature case the thermal Rayleigh number initially dominates and the instabilities undergo a phase where the convection is essentially thermal, and the onset is essentially instantaneous. As the salt Rayleigh number becomes more significant the instability undergoes a transition to oscillatory double-diffusive convection. For the constant heat flux the ratio of the thermal and salt Rayleigh numbers is constant, and the instabilities are always double diffusive in their nature. These instabilities initially decay. Hence, to achieve the largest growth at some given fixed time, there is an optimal time after the onset of heating for the instabilities to be initiated. These instabilities are essentially double diffusive throughout their growth.

scholarly journals Some Aspects of the Three-Dimensional Double-Diffusive Natural Convection in a Parallelepipedic Tilted Solar Distiller

2015 ◽  
Vol 55 ◽  
pp. 47-58
Author(s):  
Fakher Oueslati ◽  
Brahim Ben Beya ◽  
Taieb Lili
Keyword(s):  
Temperature Field ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Velocity Component ◽  
Three Dimensional ◽  
Flow Situation ◽  
Flow Intensity ◽  
Volume Method ◽  
Buoyancy Ratio ◽  
Double Diffusive

Three-dimensional double-diffusive natural convection in a parallelepipedic solar distiller inclined with an angle is investigated in the current study. Computations are performed using a home code “NASIM” based on the finite volume method and a full multigrid technique. It is found that iso-surfaces relative to temperature field undergo a central stratification while the lower and upper gradients seem to be significantly strengthened by gradually increasing the Rayleigh number values. In terms of buoyancy ratio effects, projection of thermal and solutal isocontours at the mid plane (y=1) showed that the flow intensity is significantly enhanced by monotonously increasing N for aiding flow situation (N>0). In addition, and according to all Rayleigh number values, the variation of average Nusselt and Sherwood numbers seem to be minimum for N=-1 with weaker values for opposing flow situation. On another hand, isosurfaces of the transverse v-velocity component showed the importance of the 3-D effects that manifest within the solar distiller.

UNSTEADY DOUBLE-DIFFUSIVE NATURAL CONVECTION AND THERMAL RADIATION WITHIN A VERTICAL POROUS ENCLOSURE

2013 ◽  
Vol 16 (2) ◽  
pp. 167-182 ◽  
Author(s):  
Abdesslem Jbara ◽  
Hosni Souheil Harzallah ◽  
Khalifa Slimi ◽  
Abdallah Mhimid
Keyword(s):  
Natural Convection ◽  
Thermal Radiation ◽  
Double Diffusive ◽  
Porous Enclosure

Incompressible smoothed particle hydrodynamics for MHD double-diffusive natural convection of a nanofluid in a cavity containing an oscillating pipe

2019 ◽  
Vol 30 (2) ◽  
pp. 882-917 ◽  
Author(s):  
Abdelraheem M. Aly
Keyword(s):  
Natural Convection ◽  
Smoothed Particle Hydrodynamics ◽  
Cavity Wall ◽  
Lagrangian Description ◽  
Content Type ◽  
Wide Range ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Incompressible Smoothed Particle Hydrodynamics ◽  
Double Diffusive

Purpose This paper aims to adopt incompressible smoothed particle hydrodynamics (ISPH) method to simulate MHD double-diffusive natural convection in a cavity containing an oscillating pipe and filled with nanofluid. Design/methodology/approach The Lagrangian description of the governing partial differential equations are solved numerically using improved ISPH method. The inner oscillating pipe is divided into two different pipes as an open and a closed pipe. The sidewalls of the cavity are cooled with a lower concentration C_c and the horizontal walls are adiabatic. The inner pipe is heated with higher concentration C_h. The analysis has been conducted for the two different cases of inner oscillating pipes under the effects of wide range of governing parameters. Findings It is found that a suitable oscillating pipe makes a well convective transport inside a cavity. Presence of the oscillating pipe has effects on the heat and mass transfer and fluid intensity inside a cavity. Hartman parameter suppresses the velocity and weakens the maximum values of the stream function. An increase on Hartman, Lewis and solid volume fraction parameters leads to an increase on average Nusselt number on an oscillating pipe and left cavity wall. Average Sherwood number on an oscillating pipe and left cavity wall decreases as Hartman parameter increases. Originality/value The main objective of this work is to study the MHD double-diffusive natural convection of a nanofluid in a square cavity containing an oscillating pipe using improved ISPH method.

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