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Research Papers: Forced Convection

# Periodic Fluid Flow and Heat Transfer in a Square Cavity Due to an Insulated or Isothermal Rotating Cylinder

[+] Author and Article Information
Y.-C. Shih

Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, 1, Sec. 3, Chung-Hsiao, E. Road, Taipei, Taiwan 106, R.O.C.f10958@ntut.edu.tw

Department of Mechanical Engineering, 270 Ross Hall, Auburn University, AL 36849-5341khodajm@auburn.edu

K.-H. Weng

Department of Energy and Refrigerating Air-Conditioning Engineering, National Taipei University of Technology, 1, Sec. 3, Chung-Hsiao, E. Road, Taipei, Taiwan 106, R.O.C.

A. Ahmed

Department of Aerospace Engineering, Auburn University, AL 36849

1

Corresponding author.

J. Heat Transfer 131(11), 111701 (Aug 19, 2009) (11 pages) doi:10.1115/1.3154620 History: Received July 30, 2008; Revised April 26, 2009; Published August 19, 2009

## Abstract

The periodic state of laminar flow and heat transfer due to an insulated or isothermal rotating cylinder object in a square cavity is investigated computationally. A finite-volume-based computational methodology utilizing primitive variables is used. Various rotating objects (circle, square, and equilateral triangle) with different sizes are placed in the middle of a square cavity. A combination of a fixed computational grid and a sliding mesh was utilized for the square and triangle shapes. For the insulated and isothermal objects, the cavity is maintained as differentially heated and isothermal enclosures, respectively. Natural convection heat transfer is neglected. For a given shape of the object and a constant angular velocity, a range of rotating Reynolds numbers are covered for a $Pr=5$ fluid. The Reynolds numbers were selected so that the flow fields are not generally affected by the Taylor instabilities $(Ta<1750)$. The periodic flow field, the interaction of the rotating objects with the recirculating vortices at the four corners, and the periodic channeling effect of the traversing vertices are clearly elucidated. The simulations of the dynamic flow fields were confirmed against experimental data obtained by particle image velocimetry. The corresponding thermal fields in relation to the evolving flow patterns and the skewness of the temperature contours in comparison to the conduction-only case were discussed. The skewness is observed to become more marked as the Reynolds number is lowered. Transient variations of the average Nusselt numbers of the respective systems show that for high Re numbers, a quasiperiodic behavior due to the onset of the Taylor instabilities is dominant, whereas for low Re numbers, periodicity of the system is clearly observed. Time-integrated average Nusselt numbers of the insulated and isothermal object systems were correlated with the rotational Reynolds number and shape of the object. For high Re numbers, the performance of the system is independent of the shape of the object. On the other hand, with lowering of the hydraulic diameter (i.e., bigger objects), the triangle and the circle exhibit the highest and lowest heat transfers, respectively. High intensity of the periodic channeling and not its frequency is identified as the cause of the observed enhancement.

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## Figures

Figure 1

Schematic diagrams of a rotating (a) insulated object within a differentially heated cavity and (b) isothermal object within a cavity with a different constant temperature

Figure 2

Comparison of the (a) steady streamlines for a rotating circle and (b) instantaneous streamlines for a rotating square with Reynolds numbers of 111 (top), 44 (middle), 6 for the circle, and 21 for square (bottom) at the end of a cycle

Figure 3

Instantaneous streamlines under periodic conditions for a rotating square with Re=31 shown at 10 deg increments during a τ/4 cycle

Figure 4

Instantaneous streamlines under periodic conditions for a rotating triangle with Re=31 shown at 10 deg increments during a τ/3 cycle

Figure 5

Instantaneous measured velocity vectors and streamlines for a rotating square with Re=31 shown at four time instants

Figure 6

Instantaneous measured velocity vectors and streamlines for a rotating triangle with Re=31 shown at six time instants

Figure 7

Temperature contours for a rotating insulated square with Reynolds numbers of 111, 44, and 21 at the end of a cycle (contour level increment of 0.05)

Figure 8

Transient variation in the instantaneous average Nusselt numbers on the left wall (left column) and right wall (right column) for the case of a rotating insulated square with Re=111 (top row) and 31 (bottom row)

Figure 9

Transient variation in the instantaneous average Nusselt numbers on the left wall (left column) and right wall (right column) for the case of a rotating insulated triangle with Re=111 (top row) and 31 (bottom row)

Figure 10

Dependence of the time-averaged Nusselt number on the left wall with the Reynolds number for various insulated objects

Figure 11

Comparison of the temperature contours for (a) steady rotating circle, (b) rotating square, and (c) rotating triangle, with Reynolds numbers of 111 (top), 44 for circle, 74 for square and triangle (middle), 6 for circle, 12 for square, and 31 for triangle (bottom) at the end of a cycle (contour level increment of 0.05)

Figure 12

Transient variation in the instantaneous average Nusselt numbers on the surface of a rotating square (left column) and cavity walls (right column) with Re=111 (top row) and 31 (bottom row)

Figure 13

Time-averaged Nusselt number versus Reynolds number on the surfaces of different isothermal rotating objects

Figure 14

Time-averaged Nusselt number versus Reynolds number on the cavity walls due to different isothermal rotating objects

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