scholarly journals Natural convection in a triangular cavity filled with a nanofluid-saturated porous medium using three heat equation model

2016 ◽  
Vol 94 (6) ◽  
pp. 604-615 ◽  
Author(s):  
Mahmoud Sabour ◽  
Mohammad Ghalambaz
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Nusselt Number ◽  
Natural Convection ◽  
Base Fluid ◽  
Concentration Distribution ◽  
Average Nusselt Number ◽  
Equation Model ◽  
Buoyancy Forces ◽  
Buoyancy Ratio

The present study aims to examine the local thermal non-equilibrium natural convection heat and mass transfer of nanofluids in a triangular enclosure filled with a porous medium. The effect of the presence of nanoparticles and the thermal interaction between phases on the flow, temperature distribution of phases, the concentration distribution of nanoparticles as well as the Nusselt number of phases is theoretically studied. The interaction between the phases of nanoparticles and the base is taken into account by using a three thermal energy equation model while the concentration distribution of nanoparticles is modeled by Buongiorno’s model. A hot flush element is mounted at the vertical wall of the triangle enclosure to provide a constant temperature of Th while the inclined wall is at a constant temperature of Tc. A three heat equation model by considering the local thermal non-equilibrium model of nanoparticles, the porous medium, and the base fluid is developed and utilized for natural convection of nanofluids in an enclosure. The drift-flux of nanoparticles due to the nano-scale effects of thermophoresis and Brownian motion effects is addressed. The governing equations are represented in a non-dimensional form and solved by employing the finite element method. The results indicate that the increase of Rayleigh number shows a significant increase in the average Nusselt number for the base fluid phase, a less significant increase in the average Nusselt number for the solid matrix phase, and almost an insignificant effect in the average Nusselt number of the nanoparticle phase. Increasing the buoyancy ratio parameter (the ratio of mass transfer buoyancy forces to the thermal buoyancy forces) tends to reduce and increase the average Nusselt number in fluid and porous phases, respectively. An optimum value of buoyancy ratio parameter for the average Nusselt number of the nanoparticle phase is observed.

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.

Study on Natural Convection in Horizontal Parallel Plate Channels Heated on Upper Wall and Partially Filled With Metal Foam

2020 ◽  
Author(s):  
Bernardo Buonomo ◽  
Vincenzo Fardella ◽  
Oronzio Manca ◽  
Sergio Nardini ◽  
Salvatore Pragliola
Keyword(s):  
Porous Medium ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Metal Foam ◽  
Open Cavity ◽  
Temperature Fields ◽  
Local Thermal Equilibrium ◽  
Uniform Heat Flux

Abstract In this work, a numerical investigation on two-dimensional steady state natural convection in a horizontal channel partially filled with a porous medium and heated at uniform heat flux from above is carried out. The lower plate is adiabatic. The porous medium is modeled using the Brinkman–Forchheimer-extended Darcy model and the local thermal equilibrium (LTE) hypothesis is assumed. The structure of the porous medium is homogenous and isotropic, the thermophysical properties of the air and the porous medium are temperature independent and the fluid flow is laminar and incompressible. The aluminum foam has 10, 20 and 40 pore per inches (PPI) and its porosity ranges from 0.90 and 0.95. Rayleigh number values are examined, from 6.0 × 104 and 1.2 × 107. Results are presented in terms of velocity and temperature fields, temperature and velocity profiles at different significant sections are shown, to obtain a description of the natural convection inside the open-ended cavity. Finally, Average Nusselt number values are evaluated. The horizontal open cavity partially filled with metal foam presents improved heat transfer behavior for higher Rayleigh numbers. The enhancement depends on the porosity and pore density. The average Nusselt number for the partially filled open cavity is the double of the configuration without the foam, clear configuration, for the highest considered Rayleigh number.

Natural Convection Heat and Mass Transfer in the Vertical Cylindrical Porous Channel Under the Effects of Time-Periodic Boundary Condition

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Hayder I. Mohammed ◽  
Donald Giddings
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Boundary Condition ◽  
Porous Medium ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Heat And Mass Transfer ◽  
Vertical Wall

Abstract Heat and mass transfer are investigated numerically with steady-state laminar natural convection through a vertical cylindrical enclosure filled with a liquid-saturated porous medium. The vertical wall is under a constant magnetic field and various durations of periodic heating boundary condition; the top and bottom surfaces are kept at a constant cold temperature. Continuity, momentum, and energy equations are transformed to dimensionless equations. The finite difference approach with the line successive over-relaxation (LSOR) method is used to obtain the computational results. This study covers the heat transfer, the temperature distribution, and the velocity field in the domain under the variation of different parameters. The code used is validated by modifying it to analyze the Nusselt number in the existing experimental literature of Izadpanah et al. (1998, “Experimental and Theoretical Studies of Convective Heat Transfer in a Cylindrical Porous Medium,” Int. J. Heat Fluid Flow, 19(6), pp. 629–635). This work shows that Nusselt number decreases (with varying gradient) as the aspect ratio increases, and that it increases as the Rayleigh number increases. The centerline temperature has a proportional relationship with the heating amplitude and the heating period (as the system receives more heat) and is inversely proportional with Rayleigh number. Increasing the Rayleigh number causes increased convective velocity, which affects the position of the hot region, and causes a decrease in the temperature field. Increasing the aspect ratio results in a warm stream at the center of the cylinder, and when the time period of the heating increases, the circulation becomes faster and the intensity of the temperature contour layers decreases. In this work, a correlation for Nu as a function of the mentioned parameters is developed.

scholarly journals Numerical Study of Thermophoresis on Mass Transfer from Natural Convection Flow over a Vertical Porous Medium with Variable Wall Heat Fluxes

2021 ◽  
Vol 11 (21) ◽  
pp. 10418
Author(s):  
Jian-Sheng Huang
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Numerical Solutions ◽  
Gas Diffusion ◽  
Heat Fluxes ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Variable Wall ◽  
Buoyancy Ratio

This study investigates heat and mass transfer under natural convection flow along a vertical permeable surface with variable wall heat fluxes through a porous medium. The non-Darcian model is employed for the medium. The effects of suction/blowing, inertia, buoyancy ratio, exponent of heat flux, position parameter, Schmidt number, and thermophoresis are considered. The governing equations of continuity, momentum, energy, and concentration are solved by adopting similarity transformation and Runge–Kutta integration with a shooting technique. Results of interest, such as velocity, temperature, and concentration profiles related to local Nusselt and Sherwood numbers, are obtained for the selected buoyancy ratio at different magnitudes of the thermophoretic effect. The numerical solutions help us to realize the gas diffusion phenomena and control the transport technology.

scholarly journals Natural convection in a differentially heated enclosure with triangular roof

1970 ◽  
Vol 39 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Sumon Saha ◽  
Noman Hasan ◽  
Chowdhury Md Feroz
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Element Analysis ◽  
Left Wall ◽  
Square Enclosure

A numerical study has been carried out for laminar natural convection heat transfer within a two-dimensional modified square enclosure having a triangular roof. The vertical sidewalls are differentially heated considering a constant flux heat source strip is flush mounted with the left wall. The opposite wall is considered isothermal having a temperature of the surrounding fluid. The rest of the walls are adiabatic. Air is considered as the fluid inside the enclosure. The solution has been carried out on the basis of finite element analysis by a non-linear parametric solver to examine the heat transfer and fluid flow characteristics. Different heights of the triangular roof have been considered for the present analysis. Fluid flow fields and isotherm patterns and the average Nusselt number are presented for the Rayleigh numbers ranging from 103 to 106 in order to show the effects of these governing parameters. The average Nusselt number computed for the case of isoflux heating is also compared with the case of isothermal heating as available in the literature. The outcome of the present investigation shows that the convective phenomenon is greatly influenced by the inclined roof height. Keywords: Natural convection, triangular roof, Rayleigh number, isoflux heating. Doi:10.3329/jme.v39i1.1826 Journal of Mechanical Engineering, vol. ME39, No. 1, June 2008 1-7

scholarly journals Modeling of natural convection of a concentrated solar power receiver absorber tube in interaction with neighbouring absorbers

2021 ◽  
pp. 53-61
Author(s):  
Olanrewaju Miracle Oyewola ◽  
Niyi Ezekiel Olukayode ◽  
Olusegun Olufemi Ajide
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Solar Power ◽  
Renewable Energy Sources ◽  
Navier Stokes ◽  
Element Formulation ◽  
Concentrated Solar Power ◽  
Set Up ◽  
Energy Equations

Concentrated Solar Power (CSP) technology stands out among other renewable energy sources not only because of its ability to address current energy security and environmental challenges but because its energy can be stored for future use. To ensure optimum performance in this system, the heat losses need to be evaluated for better design. This work studies the natural convection in the receiver absorber tube of a CSP plant taking into consideration the influence of neighboring absorbers. A 2-Dimensional model was adopted in this study. Initially, a single absorber tube was considered, it was subjected to heat flux at the top wall, the bottom wall was insulated and a temperature differential was set up at the lateral walls. The dimensionless forms of Navier-Stokes and energy equations were solved using the finite element formulation of COMSOL Multiphysics software. The result obtained for a single absorber tube showed good agreement with existing research works. This validated model was then extended to multiple absorber tubes (two to six absorber tubes). On the basis of the study, there is an observed increase in the intensity and dominance of convective heat transfer with an increase in the number of absorber tubes. This is occasioned by an increase in the average surface temperature as well as average Nusselt number. For the Rayleigh number of 104, 105 and 106, the average Nusselt number increases with the number of absorber tubes by 13.87 %, 6.26 %, and 1.55 %, respectively. This increment suggests effect of thermal interactions among the neighboring absorber tubes

Natural convection in differentially heated enclosures subjected to variable temperature boundaries

2019 ◽  
Vol 29 (11) ◽  
pp. 4130-4141 ◽  
Author(s):  
Abdulmajeed Mohamad ◽  
Mikhail A. Sheremet ◽  
Jan Taler ◽  
Paweł Ocłoń
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Uniform Heating ◽  
Content Type ◽  
Left Hand ◽  
Heating And Cooling ◽  
Right Hand ◽  
The Right

Purpose Natural convection in differentially heated enclosures has been extensively investigated due to its importance in many industrial applications and has been used as a benchmark solution for testing numerical schemes. However, most of the published works considered uniform heating and cooling of the vertical boundaries. This paper aims to examine non-uniform heating and cooling of the mentioned boundaries. The mentioned case is very common in many electronic cooling devices, thermal storage systems, energy managements in buildings, material processing, etc. Design/methodology/approach Four cases are considered, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature is kept at a constant, cold temperature. In the second case, the left-hand wall’s temperature linearly increases along the wall, while the right-hand wall’s temperature is kept a constant, cold temperature. The third case, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature linearly increases along the wall. In the fourth case, the left-hand and the right-hand walls’ temperatures decrease along the wall, symmetry condition. Hence, four scenarios of natural convection in enclosures were covered. Findings It has been found that the average Nusselt number of the mentioned cases is less than the average Nusselt number of the uniformly heated and cooled enclosure, which reflects the physics of the problem. The work quantifies the deficiency in the rate of the heat transfer. Interestingly one of the mentioned cases showed two counter-rotating horizontal circulations. Such a flow structure can be considered for passively, highly controlled mechanism for species mixing processes application. Originality/value Previous works assumed that the vertical boundary is subjected to a constant temperature or to a sinusoidal varying temperature. The subject of the work is to examine the effect of non-uniformly heating and/or cooling vertical boundaries on the rate of heat transfer and flow structure for natural convection in a square enclosure. The temperature either linearly increases or decreases along the vertical coordinate at the boundary. Four scenarios are explored.

Sign in / Sign up

Export Citation Format

Share Document