Effect of Hartmann Number on Free Convective Flow in a Square Cavity with Different Positions of Heated Square Block

Authors: Abdul Halim Bhuiyan, M. A. Alim, Md. Nasir Uddin

Abstract:

This paper is concerned with the effect of Hartmann number on the free convective flow in a square cavity with different positions of heated square block. The two-dimensional Physical and mathematical model have been developed, and mathematical model includes the system of governing mass, momentum and energy equations are solved by the finite element method. The calculations have been computed for Prandtl number Pr = 0.71, the Rayleigh number Ra = 1000 and the different values of Hartmann number. The results are illustrated with the streamlines, isotherms, velocity and temperature fields as well as local Nusselt number.

Keywords: Finite element method, free convection, Hartmann number, square cavity.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1091320

References:

[1] K. Kahveci, S. Oztuna, "MHD Natural Convection Flow and Heat Transfer in a Laterally Heated Partitioned Enclosure”, European Journal of Mechanics, vol. 28, pp. 744, 2009.
[2] M. A. Taghikhani, H. R. Chavoshi, "Two Dimensional MHD Free Convection with Internal Heating in a Square Cavity”, Thermal Energy and Power Engineering, vol. 2, pp. 22-28, 2013.
[3] S. Parvin, R. Nasrin, "Analysis of the Flow and Heat Transfer Characteristics for MHD Free Convection in an Enclosure with a Heated Obstacle”, Nonılinear Analysis: Modeling and Control, vol. 16, No. 1, pp. 89–99, 2011.
[4] M. M. Ganzarolli, L. F. Milanez, "Natural Convection in Rectangular Enclosure Heated from Below and Symmetrically Cooled from the Sides”, Int. J. Heat Mass Transf., vol. 38, pp. 1063-1073, 1995.
[5] M. Sathiyamoorty, Tanmay Basak and S. Roy, "Steady Natural Convection Flow in a Square Cavity with Linearly Heated Side Walls”, International Journal of Heat and Mass Transfer, vol. 50, p.766, 2007.
[6] H. Saeid Nawaf, "Natural Convection in a Square Porous Cavity with an Oscillating Wall Temperature”, The Arabian Journal for Science and Engineering, vol. 61, no. 1B, April 2006.
[7] F. Oztop Hakan, Khaled Al- Salem, and Loan Pop, "MHD Mixed Convection in a Lid-Driven Cavity with Corner Heater”, International Journal of Heat and mass Transfer, vol. 54, pp. 3494-3504, 2011
[8] F. Oztop Hakan, Abu-Nada Eiyad, Varol Yasin, and Chamkha Ali, "Natural Convection in Wavy Enclosures with Volumetric Heat Sources”, International Journal of Thermal Sciences, vol. 50, pp. 502-514, 2011
[9] Y. Bakhshan, H. Ashoori, "Analysis of a Fluid Behavior in a Rectangular Enclosure under the Effect of Magnetic Field”, World Academy of Science, Engineering and Technology, vol. 61, pp.637-641, 2012.
[10] C. Taylor, P. Hood, "A Numerical Solution of the Navier-Stokes Equations Using Finite Element Technique”, Computer and Fluids, vol. 1, no. 1, pp. 73-89, 1973.
[11] P. Dechaumphai, "Finite Element Method in Engineering”, Second edition, Chulalongkorn University Press, Bangkok, 1999.
[12] B. Santosh, G. Archana, Aswatha, and K. N. Seetharamu, "Natural Convection in a Square Cavity Localized Heating from Below”, The 37th National & 4th International Conference on Fluid Mechanics and Fluid Power December16-18, IIT Madras, Chennai, India, 2010.