Volume 4, Issue 3, September 2018, Page: 67-72
Double Lid Driven Cavity with Different Moving Wall Directions for Low Reynolds Number Flow
Kajal Chandra Saha, Department of Applied Mathematics, University of Dhaka, Dhaka, Bangladesh
Goutam Saha, Department of Mathematics, University of Dhaka, Dhaka, Bangladesh
Doli Rani Pal, Department of Mathematics, University of Dhaka, Dhaka, Bangladesh
Received: Aug. 14, 2018;       Accepted: Aug. 30, 2018;       Published: Oct. 15, 2018
DOI: 10.11648/j.ijamtp.20180403.11      View  313      Downloads  17
In this paper, a numerical examination used to analyze the flow and heat transfer characteristics inside a double lid-driven cavity underneath buoyancy consequences of thermal diffusion. The lid is due to the movement of the isothermal vertical sidewalls of different constant temperatures, while other walls are kept adiabatic. Also, the upright walls are moving at a constant rate and four different moving wall directions are considered along these walls. Further, the governing equations of the flow and thermal fields are transformed into dimensionless equations and then solved numerically using finite difference method. A contrast of the current learn is additionally carried out with the formerly published works and observed excellent agreement. Moreover, the results from numerical simulations have been presented in the form of velocities and isothermal profiles, shown graphically and discussed for different Reynolds number. Result unveils that, the influence of the development of the velocity profiles in the chamber decreases with the augmentation of Re. Besides, the intensification of Reynolds number ends in forming diminution of thermal boundary layers near the heated wall. In addition, the maximum Average Nusselt number can be obtained when the left lid poignant towards positive direction and the right lid poignant to the same direction.
Heat Transfer, Reynolds Number, Nusselt Number, Richardson Number, Prandtl Number
To cite this article
Kajal Chandra Saha, Goutam Saha, Doli Rani Pal, Double Lid Driven Cavity with Different Moving Wall Directions for Low Reynolds Number Flow, International Journal of Applied Mathematics and Theoretical Physics. Vol. 4, No. 3, 2018, pp. 67-72. doi: 10.11648/j.ijamtp.20180403.11
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Choi, S. U. S. (1995). Enhancing thermal conductivity of fluids with nanoparticles.ASME Fluids Eng. Div., 231, 99–105.
Ghia, U., Ghia, K. N., & Shin, C. T. (1982). High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method. J. Comput. Physics, 48, 387- 411.
Moallemi, M. K., & Jang, K. S. (1992). Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity. Int. J. Heat Mass Transfer, 35(8), 1881- 1892.
Hakan, F., & Oztop, I. D. (2004). Mixed convection in two-sided lid driven differentially heated square cavity. Int. J. Heat Mass Transfer, 47, 1761-1769.
Chamkha, A. J. (2002). Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal heat generation or absorption. Numerical Heat Transfer, Part A, 41, 529-546.
Hussain, S. (2017). Effects of inclination angle on mixed convective nanofluid flow in a double lid-driven cavity with discrete heat sources. Int. J. Heat Mass Transfer, 106, 847- 860.
Sivasankaran, V. S. (2013). Numerical study on mixed convection in an inclined lid-driven cavity with discrete heating. Int. Comm. Heat Mass Transfer, 46, 112- 125.
Sharif, M. A. R. (2007). Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom, Appl. Therm. Eng, 27, 1036-1042.
Cheng, T. S. (2011). Characteristics of mixed convection heat transfer in a lid-driven square cavity with various Richardson and Prandtl numbers. Int. J. Thermal Sciences, 50, 197- 205.
Sousa, S. K. (2014). A detailed study of lid-driven cavity flow at moderate Reynolds numbers using Incompressible SPH. Int. J. Num. Methods Fluids, 76, 653- 668.
Omari, R. (2016). Numerical Investigation of a Mixed Convection Flow in a Lid-Driven Cavity. American J. Computational Mathematics, 6, 251- 258.
Adair, M. J. (2015). Developing an Understanding of the Steps Involved in Solving Navier-Stokes Equations. The Mathematica Journal, 17, 1-19.
Benjamin, A. S., & Denny, V. E. (1979). On the convergence of numerical solutions for 2-D flows in a cavity at large Re, J. Comput. Phys., 33, 340–358.
Ghia, U., Ghia, K. N., & Shin, C. T. (1982). High-Re solutions for incompressible flow using the Navier–Stokes equations and a multigrid method. J. Comput. Phys., 48, 387–411.
Cao, Z., & Esmail, M. N. (1995). Numerical study on hydrodynamics of short-dwell paper coaters, AIChE J., 41, 1833–1842.
Triantafillopoulos, N. G., & Aidun, C. K. (1990). Relationship between flow instability in short-dwell ponds and cross directional coat weight non-uniformities, TAPPI J., 73, 127–136.
Gaskell, P. H., Summers, J. L., Thompson, H. M., & Savage, M. D. (1996). Creeping flow analyses of free surface cavity flows, Theoret. Comput. Fluid Dynam., 8, 415–433.
Hellebrand, H. Tape Casting, in: R. J. Brook (Ed.), Processing of Ceramics, Part1, VCH Verlagsgesellschaft mbH, 17A, Weinheim, 1996, 190–265.
Leong, C. W., & Ottino, J. M. (1989). Experiments on mixing due to chaotic advection in a cavity. J. Fluid Mech., 209, 463–499.
Alleborn, N., Raszillier, H., &Durst, F. (1999). Lid-driven cavity with heat and mass transport. Int. J. Heat Mass Trans., 42, 833–853.
Pal, D. R., Saha, G., & Saha, K. C. (2018). A case study of double lid driven cavity for low Reynolds number flow. Dhaka University J. Science, 66(2), 95-101.
Kuhlmann, H. C., Wanschura, M., & Rath, H. J. (1997). Flow in two-sided lid-driven cavities: non-uniqueness, instabilities, and cellular structures. J. Fluid Mech., 336, 267–299.
Abu-Nada, E., & Chamkha, A. J. (2010). Mixed convection flow in a lid-driven inclined square enclosure filled with a nanofluid. European Journal of Mechanics B Fluids, 29, 472- 482.
Waheed, M. A. (2009). Mixed convective heat transfer in rectangular enclosures driven by a continuously moving horizontal plate. Int. J. Heat Mass Transfer, 52, 5055-5063.
Malik, S., & Nayak, A. K. (2016). A comparative study of mixed convection and its effect on partially active thermal zones in a two sided lid-driven cavity filled with nanofluid. Engineering Science and Technology, an International Journal, 19, 1283–1298.
Browse journals by subject