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Flows in Complex Systems

Mixed Convection Flow of Micropolar Fluid in an Open Ended Arc-Shape Cavity

[+] Author and Article Information
M. Saleem, M. A. Hossain

Department of Mathematics, Comsats Institute of Information Technology, Islamabad Campus, Chak Shehzad, PakistanFormer Professor of Mathematics   Department of Mathematics, Comsats Institute of Information Technology, Islamabad Campus, Chak Shehzad, Pakistan;  University of Dhaka, Bangladesh e-mail: anwar@univdhaka.edu

Suvash C. Saha1

School of Chemistry, Physics & Mechanical Engineering, Queensland University of Technology, GPO Box 2434, George Street, Brisbane, QLD 4001, Australia e-mail: s_c_saha@yahoo.com

1

Corresponding author.

J. Fluids Eng 134(9), 091101 (Aug 21, 2012) (9 pages) doi:10.1115/1.4007268 History: Received January 26, 2012; Revised June 20, 2012; Published August 21, 2012; Online August 21, 2012

Abstract

Numerical simulations for mixed convection flow of micropolar fluid in an open ended arc-shape cavity have been carried out in this study. Computation is performed using the alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique for the solution of governing partial differential equations. The flow phenomenon is examined for a range of values of Rayleigh number 102  ≤ Ra ≤ 106 , Prandtl number 7 ≤ Pr ≤ 50, and Reynolds number 10 ≤ Re ≤ 100. The study is mainly focused on how the micropolar fluid parameters affect the fluid properties in the flow domain. It was found that despite the reduction of flow in the core region, the heat transfer rate increases, whereas the skin friction and microrotation decrease with the increase in the vortex viscosity parameter Δ.

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Figures Figure 1

The geometry of the problem Figure 2

(a) Physical domain and (b) computational domain Figure 3

Steady state pattern of streamlines at Re = 10, Pr = 7, Δ = λ = B = 0 (Newtonian fluid) for (a) Ra = 0, (b) Ra = 2 × 104 , and (c) average Nusselt number against time at Re = 10, Pr = 7, Δ = λ = B = 0 (Newtonian fluid) for different values of Rayleigh number Figure 4

Steady state pattern of streamlines at Re = Pr = 10, Ra = 5 × 104 , λ = 1.0, B = 0.1 for (a) Δ = 0 (Newtonian fluid), (b) Δ = 1, (c) Δ = 5, and (d) Δ = 10 Figure 5

Steady state pattern of isotherms at Re = Pr = 10, Ra = 5 × 104 , λ = 1.0, B = 0.1 for (a) Δ = 0 (Newtonian fluid), (b) Δ = 1, (c) Δ = 5, and (d) Δ = 10 Figure 6

Time history of the onset of steady state flow pattern of streamlines while Re = Pr = 10, Ra = 5 × 104 , λ = 1.0, B = 0.1, Δ = 1 at (a) t = 0.2, (b) t = 1.5, (c) t = 3.6, and (d) t = 5.0 Figure 7

Average Nusselt number against time while Re = Pr = 10, Ra = 5 × 104 , λ = 1.0, B = 0.1, Δ = 1 Figure 8

Steady state streamlines at Pr = 10, Ra = 105 , Δ = 2, λ = 1.0, B = 0.1 for (a) Re = 10, (b) Re = 25, (c) Re = 50, and (d) Re = 100 Figure 9

Steady state contours of microrotation at Pr = 10, Ra = 105 , Δ = 2, λ = 1.0, B = 0.1 for (a) Re = 10, (b) Re = 25, (c) Re = 50, and (d) Re = 100 Figure 10

Streamlines while Re = Pr = 25, Δ = 2, λ = 1.0, B = 0.1 for (a) Ra = 102 , (b) Ra = 104 , and (c) Ra = 106 Figure 11

Isotherms at Re = Pr = 25, Δ = 2, λ = 1.0, B = 0.1 for (a) Ra = 102 , (b) Ra = 104 , and (c) Ra = 106

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