Unsteady Mixed Convective Flow in a Porous Lid-Driven Cavity with Constant Heat Flux
In this paper, we present the numerical analysis of mixed convection in a square cavity filled with porous medium. The left wall of the enclosure is kept at a constant heat flux, and the dimensionless governing equations are solved numerically with Marker
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Abstract In this paper, we present the numerical analysis of mixed convection in a square cavity filled with porous medium. The left wall of the enclosure is kept at a constant heat flux, and the dimensionless governing equations are solved numerically with Marker and Cell (MAC) method. The numerical results are discussed graphically with the effect of Darcy number, Prandtl number, Rayleigh number, Grashof number, Reynolds number, temperature and streamlines. Nomenclature Da g k L K N Nu Gr T U U U0 V X Y
Darcy number Acceleration due to gravity, m s−2 Thermal conductivity, Wm−1 K−1 Length of the square cavity, m Permeability, m2 Total number of nodes Local Nusselt number Grashof number Temperature, K x component of velocity, m s−1 x component of dimensionless velocity x lid velocity, m s−1 y component of dimensionless velocity Dimensionless distance along x-coordinate Dimensionless distance along y-coordinate
B. Md. Hidayathulla Khan (&) R. Bhuvana Vijaya Department of Mathematics, JNTU Ananthapur, Anantapuramu 515002, India e-mail: [email protected] V. Ramachandra Prasad Department of Mathematics, Madanapalle Institute of Technology and Science, Madanapalle 517325, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2018 M.K. Singh et al. (eds.), Applications of Fluid Dynamics, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-10-5329-0_32
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V p P Pr Re Ri
B. Md. Hidayathulla Khan et al.
y component of velocity, m s−1 Pressure, Pa Dimensionless pressure Prandtl number Reynolds number Richardson number
Greek symbols a b c h t q U W
Thermal diffusivity, m2 s−1 Volume expansion coefficient, K−1 Penalty parameter Dimensionless temperature Kinematic viscosity, m2 s−1 Density, kg m−3 Basis functions Stream function
1 Introduction Mixed convection is generally the combination of free convection and forced convection. Mixed convection, in permeable medium flowing within enclosures, is found in a variety of applications in engineering and geophysical systems like lubrication technologies, cooling of electronic gadgets, drying technologies. The flow and heat transmission caused by shear and buoyancy forces in cavities have been investigated in the literature. An analysis reveals that there are two kinds of studies: the first one is horizontally sliding lid at the upper wall (Iwatsu and Hyun 1995; Mohamad and Viskanta 1991; Prasad and koseff 1996; Freitas and Street 1988; Mohamad and Viskanta 1995; Khanafer and Chamkha 1999; Sharif 2007), and the second one is horizontally sliding lid at the bottom wall (Chen et al. 1981) or oscillating lid (Iwatsu et al. 1992a, b; Nield and Bejan 2006). The bounding case Ri ! 0 and Ri ! 1 relates to the forced and natural convection flows separately. The details of Ri in convective stream with permeable medium are discussed well in the books by Pop and Ingham (2001), Bejan et al. (2004), Ingham and Pop (2005), Nield and Bejan (2006) and Vafai (2000, 2005). Al-Amiri (2000) numerically investigated the energy transfer in a lid-driven sq
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