Combined mixed convection and radiation simulation of inclined lid driven cavity

Document Type : Research Paper

Authors

Department of Mechanical Engineering, School of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

This paper presents a numerical investigation of the laminar mixed convection flow of a radiating gas in an inclined lid-driven cavity. The fluid is treated as a gray, absorbing, emitting, and scattering medium. The governing differential equations including continuity, momentum and energy are solved numerically by the computational fluid dynamics techniques (CFD) to obtain the velocity and temperature fields. The discretized forms of these equations are obtained by the finite volume method and solved by using the SIMPLE algorithm. Since the gas is considered as a radiating medium, besides convection and conduction heat transfer, radiation also takes place in the gas flow. For computing the radiative term in the gas energy equation, the radiative transfer equation (RTE) is solved numerically by the discrete ordinate method (DOM). The streamline and isotherm plots and the distributions of convective, radiative and total Nusselt numbers along the bottom wall of the cavity are presented. In this work, an attempt is made to investigate the hydrodynamic and thermal behavior of the mixed convection flow of a radiating gas at different values of the cavity inclination angle. The numerical results reveal that the variation of inclination angle causes a sweep behavior in the flow pattern inside the cavity. Besides, it is found that the value of radiative Nusselt number along the heated wall has a decreasing trend when the medium optical thickness is increases. Comparisons between the present numerical results with those obtained by other investigators in the cases of conduction-radiation and pure convection systems show good consistencies.

Keywords


[1] Burggraf O. R., Analytical and Numerical Studies of the Structure of Steady Separated Flows, Journal of Fluid Mechcanics (1996) 24(1):113–115.
[2] Ghia U., Ghia K. N., Shin C. T., High-Re Solutions for Incompressible Flow Using the Navier–Stokes Equations and a Multigrid Method, Journal of Computational Physics (1982) 48(3): 387–411.
[3] Pilkington L. A. B., Review Lecture:The Float Glass Process, Proceedings of Royal Society of London, Series A (1969) 314 (1516): 1-25, 1969.
[4] Ideriah F. J. K., Prediction of Turbulent Cavity Flow Driven by Buoyancy and Shear, Journal of Mechanical Engineering Science (1980) 22(6): 287–295.
[5] Imberger J., Hamblin P. F., Dynamics of Lakes, Reservoirs and Cooling Ponds, Annual Review of Fluid Mechcanics (1982) 14: 153–187.
[6] Cha C. K., Jaluria Y., Recirculating Mixed Convection Flow for Energy Extraction, International Journal Heat and Mass Transfer (1984) 27(10): 1801–1810.
[7] Prasad A. K., Koseff J. R., Combined Forced and Natural Convection Heat Transfer in a Deep Lid-Driven Cavity Flow, International Journal of Heat and Fluid Flow (1996) 17: 460–467.
[8] Leong J. C., Brown N. M., Lai F. C., Mixed Convection from an Open Cavity in a Horizontal Channel, International Communications in Heat and Mass Transfer (2005) 32: 583-592.
[9] Moallemi M. K., Jang K. S., Prandtl Number Effects on Laminar Mixed Convection Heat Transfer in a Lid-Driven Cavity, International Journal of Heat Mass Transfer (1992) 35(8): 1881–1892.
[10]Oztop H. F., Salema K. A., Pop I., MHD Mixed Convection in a Lid-Driven Cavity with Corner Heater, International Journal of Heat and Mass Transfer (2011) 54: 3494-3504.
[11]Sharif M. A. R., Laminar Mixed Convection in Shallow Inclined Driven Cavities with Hot Moving Lid on Top and Cooled from Bottom, Applied Thermal Engineering (2007) 27(5): 1036-1042.
[12]Alinia M., Ganji D. D., Gorji-Bandpy M., Numerical Study of Mixed Convection in an Inclined Two Sided Lid Driven Cavity Filled with Nano Fluid Using Two-Phase Mixture Model, International Communications in Heat and Mass Transfer (2011) 38 (10): 1428-1435.
[13]Oztop H. F., Natural Convection in Partially Cooled and Inclined Porous Rectangular Enclosures, International Journal of Thermal Sciences (2007) 46:149–156.
[14] Sivasankaran S., Sivakumar V., Hussein A. K., Numerical Study on Mixed Convection in an Inclined Lid-Driven Cavity with Discrete Heating, International Communications in Heat and Mass Transfer (2013) 46:112-125.
[15]Mohammad A. A., Viskanta R., Flow Structures and Heat Transfer in a Lid-driven Cavity Filled with Liquid Gallium and Heated from below, Experimental Thermal and Fluid Science (1994) 9(3): 309–319.
[16]Abu-Nada E., Chamkha A.J., Mixed Convection Flow in a Lid-Driven Inclined Square Enclosure Filled with a Nanofluid, European Journal of Mechanics B/Fluids (2010) 29(6): 472-482.
[17]Cheng T. S., Liu W.-H., Effects of Cavity Inclination on Mixed Convection Heat Transfer in Lid-Driven Cavity Flows, Computers & Fluids (2014) 100: 108-122.
[18]Prasad Y. S., Das M. K., Hopf  Bifurcation in Mixed Convection Flow Inside a Rectangular Cavity, International Journal of Heat and Mass Transfer (2007) 50(17): 3583–3598.
[19]Sameh E. Ahmeda, Mansourb M.A., Mahdy A., MHD Mixed Convection in an Inclined Lid-Driven Cavity with Opposing Thermal Buoyancy Force: Effect of Non-uniform Heating on Both Side Walls, Nuclear Engineering and Design 265 (2013) 938– 948.
[20]Tan Z., Howell J. R., Combined Radiation and Natural Convection in a two Dimensional Participating Square Medium, International Journal of Heat and Mass Transfer (1991) 34: 785–793.
[21]Han C. Y., Baek S. W., The Effects of Radiation on Natural Convection in a Rectangular Enclosure Divided by Two Partitions, Numerical Heat Transfer, Part A (2000) 37: 249-270.
[22]Modest M. F., Radiative Heat Transfer, Academic Press, San Diego, Chapter 16 (2003).
[23]Patankar S. V., Spalding D. B., A Calculation Procedure for Heat, Mass and Momentum Transfer in Three-Dimensional Parabolic Flows. International Journal of Heat and Mass Transfer (1972) 15(10): 1787–1806.
[24]Iwatsu R., Hyun J.M., Kuwahara K., Mixed Convection in a Driven Cavity with a Stable Vertical Temperature Gradient, International Journal of Heat and Mass Transfer (1993) 36 (6): 1601–1608.
[25]Mahapatra S. K., Dandapat B. K., A. Sarkar, Analysis of Combined Conduction and Radiation Heat Transfer in Presence of Participating Medium by the Development of Hybrid Method, Journal of Quantitative Spectroscopy & Radiative Transfer (2006) 102(2): 277–292.