Effects of Important Parameters on the Transition from Forced to Mixed Convection Flow in a Square Cavity

Abstract:

Combined free and forced convection in a square cavity filled with a viscous fluid characterized by a small Prandtl number is studied numerically. The left wall is moving with a constant velocity v and is maintained at a local cold temperature Tc, while the right wall is fixed and maintained at a local hot temperature Th (Tc <Th). The top and bottom walls of the cavity is assumed to be adiabatic. The governing Navier-Stokes, and energy equations along with appropriate boundary conditions are solved using the finite-volume method. The flow and temperature fields are presented by stream function and isotherms, respectively. The effects of important parameters such as Reynolds number, Prandtl number, and Grashof number on the transition from forced convection to mixed convection are investigated. Results indicate that increasing Reynolds number results to fluid acceleration and, thus, to flow transition. Results also show that Grashof and Prandtl's numbers influenced the conditions for the transition to the mixed convection regime.

• Periodical: Defect and Diffusion Forum (Volume 406)
• Pages: 36-52
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.406.36
• Online since: January 2021
• Authors: Sofiane Boulkroune*, Omar Kholai, Brahim Mahfoud
• Keywords: Forced Convection, Mixed Convection, Parameters, Square Cavity, Transition

References

[1] J. Chamkha, S.H. Hussain and Q.R. Abd-Amer, Mixed Convection Heat Transfer of Air Inside a Square Vented Cavity with a Heated Horizontal Square Cylinder, Numer. Heat Transfer A 59, 58–79 (2011).

DOI: 10.1080/10407782.2011.541216

[2] P. Talukdar, Mixed Convection and Non-Gray Radiation in a Horizontal Rectangular Duct, Numer. Heat Transfer A 59, 185–208 (2011).

DOI: 10.1080/10407782.2011.540966

[3] D. Ramakrishna, T. Basak, S. Roy and I. Pop, A complete heat line analysis on mixed convection within a square cavity: Effects of thermal boundary conditions via thermal aspect ratio, Int. J. of Thermal Science 57, 98-111 (2012).

DOI: 10.1016/j.ijthermalsci.2012.01.010

[4] A.K. Hussein, and S.Hussain , Natural convection in a modified square enclosure with an inclined triangular top wall subjected to uniform heat flux in its left vertical wavy side wall , Third Asian Symposium on Computational Heat Transfer and Fluid Flow , 22-26 September, 2011, Kyoto, Japan , pp : 1-10.

DOI: 10.1615/heattransres.2011002615

[5] S.Hussain, and A.K. Hussein, Numerical investigation of natural convection phenomena in a uniformly heated circular cylinder immersed in square enclosure filled with air at different vertical locations, International Communications in Heat and Mass Transfer 37, 1115–1126 (2010).

DOI: 10.1016/j.icheatmasstransfer.2010.05.016

[6] A.K. Hussein, Computational analysis of natural convection in a parallelogrammic cavity with a hot concentric circular cylinder moving at different vertical locations, International Communications in Heat and Mass Transfer 46, 126-133 (2013).

DOI: 10.1016/j.icheatmasstransfer.2013.05.008

[7] S.Hussain, A.K. Hussein, and M.Mahdi, Natural convection in a square inclined enclosure with vee-corrugated sidewalls subjected to constant flux heating from below, Nonlinear Analysis: Modelling and Control16, 152-169 (2011).

DOI: 10.15388/na.16.2.14102

[8] K.Ghachem, L.Kolsi, C.Mâatki, A.K. Hussein, and M.Borjini, Numerical simulation of three-dimensional double diffusive free convection flow and irreversibility studies in a solar distiller , International Communications in Heat and Mass Transfer39, 869-876 (2012).

DOI: 10.1016/j.icheatmasstransfer.2012.04.010

[9] C.Mâatki, K.Ghachem, L.Kolsi, A.K. Hussein, M.Borjini, and H.Ben Aissia , Inclination effects of magnetic field direction in 3D double-diffusive natural convection, Applied Mathematics and Computation 273,178-189(2016).

DOI: 10.1016/j.amc.2015.09.043

[10] A.K. Hussein, Finite volume simulation of natural convection in a trapezoidal cavity filled with various fluids and heated from the top wall , Universal Journal of Fluid Mechanics, 1, 24-36 (2013).

[11] S.Ahmed A.K. Hussein, H.Mohammed, I.Adegun,X.Zhang,L.Kolsi,A.Hasanpour, and S.Sivasankaran, Viscous dissipation and radiation effects on MHD natural convection in a square enclosure filled with a porous medium , Nuclear Engineering and Design266, 34-42 (2014).

DOI: 10.1016/j.nucengdes.2013.10.016

[12] W. Jaeger, F.Trimborn, M. Niemann, V. Saini, W.Hering, R. Stieglitz,B Pritz, J. Fröhlich and M. Gabi, Transition between free, mixed and forced convection, IOP Conf. Series: Materials Science and Engineering 228, 012011,.

DOI: 10.1088/1757-899x/228/1/012011

[13] A. Belaid,O. Kholai, S. Boulkron, T. Arrif, A. Gama et H. Merarda, Etude numérique de la convection mixte transitoire conjuguée dans un tube vertical, ElWahat pour les Recherches et les Etudes10, 27-36(2017).

DOI: 10.54246/1548-010-001-010

[14] S.Kachi, F. Bensouici, N.Ferroudj and S.Boudebous. Effect of richardsonnumber on unsteady mixed convection in a square cavity partially heated from below, Tech Science Press FDMP15, 89-105 (2019).

DOI: 10.32604/fdmp.2019.00263

[15] T.S. Cheng and W.H. Liu, Effects of cavity inclination on mixed convection heat transfer in lid-driven cavity flows, Computers and Fluids 100, 108–122(2014).

DOI: 10.1016/j.compfluid.2014.05.004

[16] M. Roy, S. Roy, T. Basak, Role of various moving walls on energy transfer rates via heat flowvisualization during mixed convection in square cavities, Energy, 1-22 (2014), http://dx.doi.org/10.1016/j.energy.2014.11.059.

DOI: 10.1016/j.energy.2014.11.059

[17] M.K. Moallemi, and K.S. Jang, Prandtl number effects on laminar mixed convection heat transfer in a lid-riven cavity, Int. J. Heat Mass Transfer 35, 1881–1892 (1992).

DOI: 10.1016/0017-9310(92)90191-t

[18] R. Iwatsu, J.M. Hyun and K. Kuwahara, Mixed convection in a driven cavity with a stable vertical temperature gradient, Intl. J. Heat Mass Transfer 36, 1601-1608 (1993).

DOI: 10.1016/s0017-9310(05)80069-9

[19] R. Iwatsu and J.M. Hyun, Three-dimensional driven cavity flows with a vertical temperature gradient, Int. J. Heat Mass Transfer 38, 3319-3328 (1995).

DOI: 10.1016/0017-9310(95)00080-s

[20] B. Gebhart, Y. Jaluria, R.L. Mahajan and B. Sammakia, Buoyancy induced flows and transport, Hemisphere New York, 699-723 (1988).

[21] M. Hasnaoui, E. Bilgen and P. Vasseur, Natural convection above an array of open cavities heated from below, AIAA J. Thermophys. Heat Transfer 6, 255-264 (1990).

DOI: 10.1080/10407789008944803

[22] O. Ayden and W.J. Yang, Mixed convection in cavities with a locally heated lower wall and moving sidewalls, Numerical Heat Transfer A 37, 695-710 (2004).

DOI: 10.1080/104077800274037

[23] H.F. Oztop and I. Dagtekin, Mixed convection in two sided lid driven differentially heated square cavity, Int. J. Heat. Mass Transfer 47, 1761-1769 (2004).

DOI: 10.1016/j.ijheatmasstransfer.2003.10.016

[24] T. Basak, S. Roy, P.K. Sharma and I. Pop, Analysis of mixed convection flows within a square cavity with uniform and non-uniform heating of bottom wall, Int. J. of Thermal Science 48, 891-912 (2009).

DOI: 10.1016/j.ijthermalsci.2008.08.003

[25] T. Basak, S. Roy, P.K. Sharma and I. Pop, Analysis of mixed convection flows within a square cavity with linearly heated side walls, Int. J. Heat. Mass Transfer 52, 2224-2242 (2009).

DOI: 10.1016/j.ijheatmasstransfer.2008.10.033

[26] D. Angirasa, Mixed Convection in a Vented Enclosure with an Isothermal Vertical Surface, Fluid Dynamics Research 26, 219-233 (2000).

DOI: 10.1016/s0169-5983(99)00024-6

[27] A. Raji and M. Hasnaoui, Correlations on Mixed Convection in Ventilated Cavities, Rev. Gen. Therm. 37, 874-884 (1998).

[28] A. Raji and M. Hasnaoui, Mixed Convection Heat Transfer in a Rectangular Cavity Ventilated and Heated from the Side, Numerical Heat Transfer A 33, 533-548 (1998).

DOI: 10.1080/10407789808913953

[29] A. Raji and M. Hasnaoui, Mixed Convection Heat Transfer in Ventilated Cavities with Opposing and Assisting Flows, Engineering Computations 17, 556-572 (2000).

DOI: 10.1108/02644400010339770

[30] H.F. Oztop, C. Sun and B. Yu, Conjugate-mixed convection heat transfer in a lid-driven enclosure with thick bottom wall, Int. Comm. of Heat and Mass Transfer 35, 779-785 (2008).

DOI: 10.1016/j.icheatmasstransfer.2008.02.003

[31] A. Al-Amiri, K. Khanafer, J. Bull and I. Pop, Effect of sinusoidal wavy bottom surface on mixed convection heat transfer in a lid-driven cavity, Int. J. Heat. Mass Transfer 50, 1771-1780 (2007).

DOI: 10.1016/j.ijheatmasstransfer.2006.10.008

[32] O. Aydın, Aiding and opposing mechanisms of mixed convection in a shear-and buoyancy-driven cavity, Int. Comm. Heat Mass Transfer 26, 1019–1028(1999).

DOI: 10.1016/s0735-1933(99)00091-3

[33] A. Bejan, Convective Heat Transfer, Wiley, New York, (1984).

[34] A.A. Mohamad and R. Viskanta, Effects of the upper lid shear on the stability of flow in a cavity heated from below, Int. J. Heat Mass Transfer 32, 2155-2166 (1989).

DOI: 10.1016/0017-9310(89)90122-1

[35] V.S. Arpaci, P.S. Larsen, Convection Heat Transfer, Prentice-Hall, (1984).

[36] A.A. Mohamad, R. Viskanta, Transient low Prandtl number fluid convection in a lid-driven cavity, Numer. Heat Transfer A 19, 187-205 (1991).

DOI: 10.1080/10407789108944845

[37] T.S. Cheng, Characteristics of mixed convection heat transfer in a lid-driven square cavity with various Richardson and Prandtl numbers, Int. J. Thermal Sci. 50, 197-205 (2011).

DOI: 10.1016/j.ijthermalsci.2010.09.012

[38] S. Saha, G. Saha , M. Ali and Q. Islam, Combined free and forced convection inside a two-dimensional multiple ventilated rectangular enclosure. ARPN J. Eng. Appl. Sci. 1, 23-35 (2006).

[39] R.SureshBabu, B. Rushi Kumar and P.A. Dinesh, Soret and Dufour Effects on MHD Mixed Convection Flow over a Vertical Plate with Variable Fluid Properties. Defect and Diffusion Forum ISSN: 1662-9507, Vol. 389, pp.1-17.

DOI: 10.4028/www.scientific.net/ddf.389.1

[40] X.Zhang, and A.K. Hussein, Asymptotic solution of natural convection in a uniformly Joule-heating shallow cavity , Journal of Physics : Conference Series 574 (012156),1-4 (2015).

DOI: 10.1088/1742-6596/574/1/012156

[41] S.V. Patankar, Numerical heat transfer and fluid flow, Hemisphere, Washington DC, (1980).