http://orcid.org/0000-0003-4272-8342
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ABSTRACT
This paper deals with natural convection flows evolving inside an ended and differentially heated cavity, which is filled either with an air or an air–CO2 mixture. The investigation was conducted through the laminar regime to analyze buoyancy ratio changes' effect on heat and mass transfers both in aiding and opposing flows. The thermal Rayleigh number was varied from 103 to 107. Streamlines, isotherms, iso-concentrations, and local and average Nusselt and Sherwood numbers are provided to demonstrate the convective flow induced. The governing equations are solved by finite volume method using SIMPLEC algorithm to handle the pressure–velocity coupling. The buoyancy ratio effect on dynamic, thermal, and mass fields is noteworthy, exhibiting both the competition between thermosolutal forces and fields' stratification. From the results, it turned out that, in general, when the buoyancy ratio is: (1) positive, thermosolutal buoyancy forces are cooperative, (2) nil, solutal buoyancy forces are weak and the flow is merely thermoconvective, (3) negative and greater than −1, buoyancy effects are competing and thermal convection dominates, (4) −1, buoyancy effects are canceled and heat and mass transfers are driven only by diffusion, and (5) less than −1, buoyancy forces compete with a dominant solutal convection.
Acknowledgments
We are grateful to anonymous referees for their insightful review and rewarding comments that helped in improving the original manuscript.
Nomenclature
| A | = | Aspect ratio, A = L/H |
| C | = | Specie concentration (kg m−3 or ppm) |
| Ch | = | High concentration (kg m−3 or ppm) |
| Cl | = | Low concentration (kg m−3 or ppm) |
| Cp | = | Specific heat (J kg−1 K−1) |
| C0 | = | Reference concentration, C0 = (Ch + Cl)/2, (kg m−3 or ppm) |
| = | Dimensionless concentration, | |
| D | = | Diffusion coefficient (m2 s−1) |
| = | Vertical and unit vector (m) | |
| g | = | Gravitational acceleration (m s−2) |
| H | = | Cavity's height (m) |
| k | = | Turbulent kinetic energy (m2 s−2) |
| L | = | Cavity's width (m) |
| Le | = | Lewis number, Le = α0/D |
| N | = | Buoyancy ratio, N = βCΔC/(βTΔT) |
| Nu | = | Nusselt number |
| P | = | Dimensionless pressure |
| p | = | Fluid pressure (Pa) |
| Pr | = | Prandtl number, Pr = ν0/α0 |
| Q | = | Heat, (W) |
| RaT | = | Thermal Rayleigh number, RaT = gβTΔTH3/ν0α0 |
| Sh | = | Sherwood number |
| T | = | Fluid temperature (K) |
| Tc | = | Cold temperature (K) |
| Th | = | Hot temperature (K) |
| T0 | = | Reference temperature, T0 = (Th+Tc)/2, (K) |
| u, w | = | Horizontal and vertical velocities (m s−1) |
| U, W | = | Dimensionless velocity components, (U, W) = (u, w)/V0 |
| V0 | = | Characteristic velocity (m s−1) |
| = | Dimensionless velocity vector | |
| x, z | = | Horizontal and vertical coordinates (m) |
| X, Z | = | Dimensionless coordinates, (X,Z) = (x,z)/H |
Greek symbols
| α | = | Thermal diffusivity (m2 s−1) |
| βC | = | Solutal expansion coefficient (m3 kg−1 ) |
| βT | = | Thermal expansion coefficient (K−1) |
| ΔC | = | Characteristic concentration difference, ΔC = (Ch−Cl), (kg m−3 or ppm) |
| ΔT | = | Characteristic temperature difference, ΔT = (Th−Tc), (K) |
| ϵ | = | Turbulence dissipation rate (m2 s−3) |
| λ | = | Thermal conductivity (W m−1 K−1) |
| µ | = | Dynamic viscosity (kg m−1 s−1) |
| ν | = | Kinematic viscosity (m2 s−1) |
| ρ | = | Density (kg m−3) |
| θ | = | Dimensionless temperature, θ = (T−T0)/ΔT |
Subscripts
| C | = | Concentration (constant) |
| c | = | Cold |
| h | = | High or hot |
| in | = | Inlet |
| l | = | Low |
| L | = | Local |
| m | = | Mean |
| max | = | Maximum |
| min | = | Minimum |
| out | = | Outlet |
| p | = | Pressure (constant) |
| T | = | Thermal |
| 0 | = | Reference |
Funding
We would like to thank “Hautes Etudes d'Ingénieur (HEI), France” and “Hauts de France” region for their financial support.
Additional information
Notes on contributors
Lounes Koufi
Lounes Koufi is an Assistant Professor at “Haute Étude d'Ingénieur (HEI)”, Catholic University of Lille, France. In 2012, he received his M.S. degree in Mechanical Sciences and Engineering from École Centrale de Lille, France. In 2015, he completed his Ph.D. thesis in Civil Engineering of Artois University, France. His research works deal with numerical modeling in heat and mass transfers, energy efficiency, and buildings' indoor air quality.
Yassine Cherif
Yassine Cherif is an Associate Professor at Artois University, France. His teachings are mainly held in the Department of Civil Engineering, Faculty of Applied Sciences/Artois University, France. He conducts his research in the Civil Engineering and Geo-Environment laboratory, which deals with the numerical simulation of thermal transfer and air quality in buildings.
Zohir Younsi
Zohir Younsi is an Associate Professor in Building Physics at “Hautes Etudes d'Ingénieur (HEI)”, Catholic University of Lille, France. His research interests include the following fields: building thermal physics, energy efficiency in buildings, solar energy and indoor environmental quality. His main research activity focuses on computational fluid dynamics, dynamic thermal simulations, ventilation, and an indoor air quality.
Hassane Naji
Hassane Naji is a full Professor of Mechanical Engineering at Artois University (France), and the Head of the International Master's Degree of Urban and Habitat Engineering at Artois and Lille Universities, France. He holds a Ph.D. degree in Physical Sciences from the Lille University (France) and an M.Sc. in Thermal-Fluid Sciences from the National Polytechnic Institute of Lorraine (INPL), Nancy, France. His research and teaching focus on thermal-fluid sciences and engineering, advanced heat transfers, and numerical methods for multi-scale simulations (mesoscopic and macroscopic approaches). He is the author and co-author of more than 200 referred papers and conference papers, and has received diverse awards for his research. In addition, he is a referee for many international peer-reviewed scientific journals.