Unsteady Mixed Convection in a Cubic Lid-Driven Cavity Partially Heated from the Bottom
Journal of Advanced Research in Fluid Mechanics and Thermal Sciences
Volume 57, No. 2, May 2019, Pages 275-287
Eutamene Salim1, Boudebous Saadoun2, Berrahil Farid3, Kholai Omar4, Dahdi Bachir1, Filali Abdelkader5,*
1 Département de Génie Mécanique, Université Mentouri Constantine, Route de Ain El Bey, 25000, Constantine, Algérie
2 Département Génie Mécanique, Université Oum El Bouaghi, Algérie
3 Département des Sciences et Techniques, Faculté des Sciences et de la Technologie, Centre Universitaire Abdelhafid Boussouf – Mila, Algérie
4 Département de Génie des Transport, Université Mentouri Constantine, Route de Ain El Bey, 25000, Constantine, Algérie
5 Département Génie Mécanique, Ecole National Polytechnique de Constantine ENPC, Constantine, Algérie
*Corresponding author: firstname.lastname@example.org
Eutamene, Salim, et al. "Unsteady Mixed Convection in a Cubic Lid-Driven Cavity Partially Heated from the Bottom." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 57.2 (2019): 275-287.
Eutamene, S., Boudebous, S., Berrahil, F., Kholai, O., Dahdi, B., & Filali, A.(2019). Unsteady Mixed Convection in a Cubic Lid-Driven Cavity Partially Heated from the Bottom. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 57(2), 275-287.
Eutamene Salim, Boudebous Saadoun, Berrahil Farid, Kholai Omar, Dahdi Bachir, and Filali Abdelkader."Unsteady Mixed Convection in a Cubic Lid-Driven Cavity Partially Heated from the Bottom." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences. 57, no. 2 (2019): 275-287.
Eutamene, S., Boudebous, S., Berrahil, F., Kholai, O., Dahdi, B., Filali, A., 2019. Unsteady Mixed Convection in a Cubic Lid-Driven Cavity Partially Heated from the Bottom. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 57(2), pp. 275-287.
Eutamene S, Boudebous S, Berrahil F, Kholai O, Dahdi B, Filali, A. Unsteady Mixed Convection in a Cubic Lid-Driven Cavity Partially Heated from the Bottom. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences. 2019;57(2): 275-287.
Mixed Convection; Cubic Lid-Driven Cavity; Finite Volume method; Richardson number
A numerical study of transient laminar mixed convection heat transfer characteristics confined within a square (2D) and cubic shape (3D) lid-driven cavity has been carried out. Lateral walls are maintained at a constant cold temperature and move upwards with a constant velocity. A heat source is located at the center of the bottom wall of the cavity and maintained at a constant high temperature. All the remaining parts of the cavity are considered adiabatic. The general conservation equations are discretized according to the Finite Volume method based on the SIMPLER algorithm. Richardson number (Ri) is varied from 0.1 to 10 and the competition between the natural and forced convection forces can lead the flow to adopt, under certain conditions, intricate behaviours such as loss of symmetry, bifurcations and so on. Obtained results showed that the critical Ri numbers that characterize the transition from the forced convection (two symmetric vortices) to the mixed convection (two asymmetric vortices) happens at Ri = 2.51 and Ri = 4.7 for the 3D and 2d cases, respectively. Then, the second transition from mixed convection to natural convection (four symmetrical vortices) happens at Ri = 6.29 and Ri = 7 for the 3D and 2d cases, respectively. Results indicated also that the heat transfer process was strongly affected by the dominant heat convection regime in which the rate of heat transfer increased in the case of asymmetric branch which is characterized by a dominance of natural convection mode.
 Bénard, Henri. "Les tourbillons cellulaires dans une nappe liquide." Rev. Gen. Sci. Pures Appl. 11 (1900): 1261-1271.
 Bénard, Henri. "Les tourbillons cellulaires dans une nappe liquide transportant de la chaleur par convection en régime permanent." Ann. Chim. Phys. 23, (1901): 62-144.
 Rayleigh, Lord. "LIX. On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side." The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 32, no. 192 (1916): 529-546.
 Gelfgat, A. Yu, P. Z. Bar-Yoseph, and A. L. Yarin. "Stability of multiple steady states of convection in laterally heated cavities." Journal of Fluid Mechanics 388 (1999): 315-334.
 Erenburg, V., A. Yu Gelfgat, E. Kit, P. Z. Bar-Yoseph, and A. Solan. "Multiple states, stability and bifurcations of natural convection in a rectangular cavity with partially heated vertical walls." Journal of Fluid Mechanics 492 (2003): 63-89.
 Lappa, Marcello. "On the existence and multiplicity of one-dimensional solid particle attractors in time-dependent Rayleigh-Bénard convection." Chaos: An Interdisciplinary Journal of Nonlinear Science 23, no. 1 (2013): 013105.
 Lappa, Marcello. "A mathematical and numerical framework for the simulation of oscillatory buoyancy and Marangoni convection in rectangular cavities with variable cross section." In Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics, pp. 419-458. Springer, Cham, 2019.
 Gelfgat, A. (2019) Computational Modeling of Bifurcations and Instabilities in Fluid Dynamics, Computational Methods in Applied Sciences. 1st edition.Cham, Switzerland
 Esfe, Mohammad Hemmat, Seyed Sadegh Mirtalebi Esforjani, Mohammad Akbari, and Arash Karimipour. "Mixed-convection flow in a lid-driven square cavity filled with a nanofluid with variable properties: effect of the nanoparticle diameter and of the position of a hot obstacle." Heat Transfer Research 45, no. 6 (2014).
 Sivasankaran, S., Ananthan, S. S., Bhuvaneswari, M., and Abdulhakeem, A. K. "Double-diffusive mixed convection in a lid-driven cavity with nonuniformheating onsidewalls." S?dhan? 42, no. 11 (2017): 1929–1941.
 Kareem, Ali Khaleel, H. A. Mohammed, Ahmed Kadhim Hussein, and Shian Gao. "Numerical investigation of mixed convection heat transfer of nanofluids in a lid-driven trapezoidal cavity." International Communications in Heat and Mass Transfer 77 (2016): 195-205.
 El moustaine, B., Cheddadi, A., "Flows Generated by Critical Opposing Thermosolutal Convection in Fluid Annular Cavities." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 50, no.1 (2018): 81-88.
 Yang, K.T. "Transitions and Bifurcations in Laminar Buoyant Flows in Confined Enclosures. " Journal of Heat Transfer, Transactions of the ASME 110, (1988): 1191-1204.
 Bodenschatz, Eberhard, Werner Pesch, and Guenter Ahlers. "Recent developments in Rayleigh-Bénard convection." Annual review of fluid mechanics 32, no. 1 (2000): 709-778.
 Lappa, Marcello. Thermal convection: patterns, evolution and stability. John Wiley & Sons, 2009.
 Baïri, Abderrahmane, Esther Zarco-Pernia, and J-M. García De María. "A review on natural convection in enclosures for engineering applications. The particular case of the parallelogrammic diode cavity." Applied Thermal Engineering 63, no. 1 (2014): 304-322.
 Hussein, Ahmed Kadhim, Mohamed M. AWAD, Lioua Kolsi, Farshid Fathinia, and I. Adegun. "A comprehensive review of transient natural convection flow in enclosures." J. Basic Appl. Sci. Res 4, no. 11 (2014): 17-27.
 Öztop, Hakan F., Patrice Estellé, Wei-Mon Yan, Khaled Al-Salem, Jamel Orfi, and Omid Mahian. "A brief review of natural convection in enclosures under localized heating with and without nanofluids." International Communications in Heat and Mass Transfer 60 (2015): 37-44.
 Akhil Soman, P. Anu Nair, Remil Babu, P. K. Sambath Kiran, V. S. Sumesh. "Study on Natural Convection Heat TransferIn an Enclosure–Areview." IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) 13, no. 4 (2016): 26-30.
 Arun, S., Satheesh, A. Mohan, C.G. Padmanathan, P. Santhoshkumar. D. "A review on natural convection heat transfer problems by Lattice Boltzmann Method." Journal of Chemical and Pharmaceutical Sciences (JCPS) 10, no. 1 (2017): 635-645.
 Mohamad, A. A., and R. Viskanta. "Flow structures and heat transfer in a lid-driven cavity filled with liquid gallium and heated from below." Experimental Thermal and Fluid Science 9, no. 3 (1994): 309-319.
 Prasad, Ajay K., and Jeffrey R. Koseff. "Combined forced and natural convection heat transfer in a deep lid-driven cavity flow." International Journal of Heat and Fluid Flow 17, no. 5 (1996): 460-467.
 Teamah, M. A., MM Abo Elazm, and Ahmed Zaki. "Numerical study of mixed convection heat transfer and fluid flow in cubical liddriven cavity." Eur. J. Sci. Res 72, no. 3 (2012): 460-473.
 Elazm, MM Abo, A. I. Shahata, A. F. Elsafty, and M. A. Teamah. "Numerical Investigation of a Three-Dimensional Laminar Mixed Convection Flows in Lid-Driven Cavity for Very Small Richardson Numbers." In ASME 2015 Power Conference collocated with the ASME 2015 9th International Conference on Energy Sustainability, the ASME 2015 13th International Conference on Fuel Cell Science, Engineering and Technology, and the ASME 2015 Nuclear Forum, pp. V001T12A007-V001T12A007. American Society of Mechanical Engineers, 2015.
 Benmansour, Nabil, Nabil Bencheikh, Brahim Ben Beya, and Lili Tong. "Etude numérique de la convection mixte dans une cavité cubique entraînée chauffé par le bas." In 22e Congrès Français de Mécanique. 2015.
 Sidik, Nor Azwadi Che. "Prediction of natural convection in a square cavity with partially heated from below and symmetrical cooling from sides by the finite difference Lattice Boltzmann Method." European Journal of Scientific Research 35, no. 3 (2009): 347-354.
 Benderradji, R., Gouidmi, H., Taloub, D. and Beghidja, A., "Numerical study three-dimensional of mixed convection in a cavity: Influence of Reynolds and Grashof numbers. " Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 51, no.1 (2018): 42-52.
 Mohamad, A. A., and R. Viskanta. "Flow and heat transfer in a lid-driven cavity filled with a stably stratified fluid." Applied mathematical modelling 19, no. 8 (1995): 465-472.
 Iwatsu, Reima, and Jae Min Hyun. "Three-dimensional driven-cavity flows with a vertical temperature gradient." International Journal of Heat and Mass Transfer 38, no. 18 (1995): 3319-3328.
 Ouertatani, Nasreddine, Nader Ben Cheikh, Brahim Ben Beya, Taieb Lili, and Antonio Campo. "Mixed convection in a double lid-driven cubic cavity." International Journal of Thermal Sciences 48, no. 7 (2009): 1265-1272.
 Benkacem, N., Ben Cheikh, N. and Ben Beya, B. "Three-dimensional Analysis of Mixed Convection in a Differentially Heated Lid-driven Cubic Enclosure." J. Appl. Mech. Eng. 4 (2015): 159.
 Rani, H.P., Narayana V. and Rameshwar, Y. "Analysis of vortical structures in a differentially heated lid driven cubical cavity." Int. J. Heat and Technology 36, no. 2 (2018): 548-556.
 Nor Azwadi, C. S., and T. Tanahashi. "Three-dimensional thermal lattice Boltzmann simulation of natural convection in a cubic cavity." International Journal of Modern Physics B 21, no. 01 (2007): 87-96.
 Guo, Guanghong, and Muhammad AR Sharif. "Mixed convection in rectangular cavities at various aspect ratios with moving isothermal sidewalls and constant flux heat source on the bottom wall." International journal of thermal sciences 43, no. 5 (2004): 465-475.
 Yang, Orhan Aydin, Wen-Jei. "Mixed convection in cavities with a locally heated lower wall and moving sidewalls." Numerical Heat Transfer: Part A: Applications 37, no. 7 (2000): 695-710.
 Khaleel Kareem, A. and Gao, S. "CFD Investigation of Turbulent Mixed Convection Heat Transfer in a Closed Lid-Driven Cavity." International Journal of Civil, Environmental, Structural, Construction and Architectural Engineering 9, no. 12 (2015): 1546-1551.
 Khaleel Kareem, A., Gao Shian and Ahmed Qasim Ahmed. "Unsteady simulations of mixed convection heat transfer in a 3D closed lid-driven cavity." International Journal of Heat and Mass Transfer 100, (2016): 121-130.
 Kareem, Ali Khaleel, and Shian Gao. "Computational study of unsteady mixed convection heat transfer of nanofluids in a 3D closed lid-driven cavity." International Communications in Heat and Mass Transfer 82 (2017): 125-138.
 Patankar, Suhas (1980). Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York.
 Hernandez, R. H. "Natural convection in thermal plumes emerging from a single heat source." International Journal of Thermal Sciences 98 (2015): 81-89.