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Research Papers: Forced Convection

# A Numerical Study of Flow and Heat Transfer Between Two Rotating Spheres With Time-Dependent Angular Velocities

[+] Author and Article Information

Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad 91775, Iran

Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad 91775, Iranrahimiab@yahoo.com

1

Corresponding author.

J. Heat Transfer 130(7), 071703 (May 19, 2008) (9 pages) doi:10.1115/1.2907434 History: Received February 27, 2007; Revised September 15, 2007; Published May 19, 2008

## Abstract

The transient motion and the heat transfer of a viscous incompressible fluid contained between two vertically eccentric spheres maintained at different temperatures and rotating about a common axis with different angular velocities are numerically considered when the angular velocities are arbitrary functions of time. The resulting flow pattern, temperature distribution, and heat transfer characteristics are presented for the various cases including exponential and sinusoidal angular velocities. Long delays in heat transfer of large portions of the fluid in the annulus are observed because of the angular velocities of the corresponding spheres. As the eccentricity increases and the gap between the spheres decreases, the Coriolis forces and convection heat transfer effect in the narrower portion increase. Special results for concentric spheres are obtained by letting eccentricity tends to zero.

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## Figures

Figure 1

Geometry of eccentric rotating spheres

Figure 2

Contours of ψ for Re=1000, Ωio=−exp(1−t), e=0.1

Figure 3

Contours of ω for Re=1000, Ωio=−exp(1−t), e=0.1

Figure 4

Contours of T for Re=1000, Pr=10, Ek=0, Ωio=−exp(1−t), e=0.1

Figure 5

Contours of (T−Tc) for Re=1000, Pr=10, Ek=0, Ωio=−exp(1−t), e=0.1

Figure 6

Contours of T for Re=1000, Pr=1, Ek=0, Ωio=−exp(1−t), e=0.1

Figure 7

Contours of (T−Tc) for Re=1000, Pr=1, Ek=0, Ωio=−exp(1−t), e=0.1

Figure 8

Contours of T for Re=1000, Pr=1, Ek=0.001, Ωio=−exp(1−t), e=0.1

Figure 9

Contours of (T−Tc) for Re=1000, Pr=1, Ek=0.001, Ωio=−exp(1−t), e=0.1

Figure 10

Contours of ψ for Re=1000, Pr=10, Ek=0, Ωio=2sin(πt∕2), e=0.1

Figure 11

Contours of ω for Re=1000, Pr=10, Ek=0, Ωio=2sin(πt∕2), e=0.1

Figure 12

Contours of T for Re=1000, Pr=10, Ek=0, Ωio=2sin(πt∕2), e=0.1

Figure 13

Contours of (T−Tc) for Re=1000, Pr=10, Ek=0, Ωio=2sin(πt∕2), e=0.1

Figure 14

Flow and heat transfer for Re=1000, Pr=10, Ek=0, Ωio=−exp(1−t)

Figure 15

Contours of ψ for Re=1000 and Ωio=−exp(1−t) for e=0

Figure 16

Contours of ω for Re=1000 and Ωio=−exp(1−t) for e=0

Figure 17

Contours of T for Re=1000, Pr=10, Ek=0, and Ωio=−exp(1−t) for e=0

Figure 18

Wall heat flux for Re=1000, Pr=10, Ek=0, Ωio=−exp(1−t), e=0.1

Figure 19

Wall heat flux for Re=1000, Pr=10, Ek=0, Ωio=2sin(πt∕2), e=0.1

Figure 20

Total heat transfer for Re=1000, Ek=0, selected values of Prandtl numbers, e=0.1 and (a) Ωio=−exp(1−t), (b) Ωio=2sin(πt∕2)

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