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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (6): 687-702.doi: https://doi.org/10.1007/s10483-013-1700-7

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Conduction-radiation effect on natural convection flow in fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls

M. A. HOSSAIN1, M. SALEEM1, S. C. SAHA2, A. NAKAYAMA3   

  1. 1. Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000, Pakistan;
    2. School of Chemistry, Physics & Mechanical Engineering, Queensland University of Technology, Brisbane 4000, Australia;
    3. Department of Mechanical Engineering, Shizuoka University, Hamamatsu 422-8529, Japan
  • 出版日期:2013-06-03 发布日期:2013-06-03
  • 通讯作者: M. A. HOSSAIN E-mail:anwar@univdhaka.edu

Conduction-radiation effect on natural convection flow in fluid-saturated non-Darcy porous medium enclosed by non-isothermal walls

M. A. HOSSAIN1, M. SALEEM1, S. C. SAHA2, A. NAKAYAMA3   

  1. 1. Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000, Pakistan;
    2. School of Chemistry, Physics & Mechanical Engineering, Queensland University of Technology, Brisbane 4000, Australia;
    3. Department of Mechanical Engineering, Shizuoka University, Hamamatsu 422-8529, Japan
  • Online:2013-06-03 Published:2013-06-03
  • Contact: M. A. HOSSAIN E-mail:anwar@univdhaka.edu

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被引次数

5

摘要： The combined effect of conduction-convection-radiation on natural convection flow of an optically thick Newtonian fluid with gray radiant properties, confined in a porous media square cavity with Darcy-Brinkman-Forchheimer drag is studied numerically. For a gray fluid, Rosseland diffusion approximation is considered. It is assumed that (i) the temperature of the left vertical wall varies linearly with height, (ii) the right vertical
and top walls are at a lower temperature, and (iii) the bottom wall is uniformly-heated. The governing equations are solved using the alternate direct implicit method together with the successive over relaxation technique. The investigation of the effect of governing parameters, namely, the Forschheimer resistance (Γ), the temperature difference (Δ), and the Plank number (Rd), on the flow pattern and heat transfer characteristics is carried out. It can be seen that the reduction of flow and heat transfer occur as the Forschheimer resistance is increased. On the other hand, both the flow strength and heat transfer increase as the temperature ratio Δ is increased.

关键词: enclosure, porous medium, conduction-convection-radiation, Darcy-Brinkman-Forchheimer drag

Abstract: The combined effect of conduction-convection-radiation on natural convection flow of an optically thick Newtonian fluid with gray radiant properties, confined in a porous media square cavity with Darcy-Brinkman-Forchheimer drag is studied numerically. For a gray fluid, Rosseland diffusion approximation is considered. It is assumed that (i) the temperature of the left vertical wall varies linearly with height, (ii) the right vertical
and top walls are at a lower temperature, and (iii) the bottom wall is uniformly-heated. The governing equations are solved using the alternate direct implicit method together with the successive over relaxation technique. The investigation of the effect of governing parameters, namely, the Forschheimer resistance (Γ), the temperature difference (Δ), and the Plank number (Rd), on the flow pattern and heat transfer characteristics is carried out. It can be seen that the reduction of flow and heat transfer occur as the Forschheimer resistance is increased. On the other hand, both the flow strength and heat transfer increase as the temperature ratio Δ is increased.

Key words: nonlinear dynamical system, dissipative system, projection operator, long-term behaviour, porous medium, conduction-convection-radiation, enclosure, Darcy-Brinkman-Forchheimer drag

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