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Research Papers: Forced Convection

# Effects of Suction and Blowing on Flow and Heat Transfer Between Two Rotating Spheres With Time-Dependent Angular Velocities

[+] Author and Article Information
Omid Mahian

Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box No. 91775-1111, Mashhad, Iran

Asgahr B. Rahimi1

Faculty of Engineering, Ferdowsi University of Mashhad, P.O. Box No. 91775-1111, Mashhad, Iranrahimiab@yahoo.com

Shahrood University of Technology, P.O. Box 316, Shahrood, Iran

1

Corresponding author.

J. Heat Transfer 133(7), 071704 (Apr 01, 2011) (13 pages) doi:10.1115/1.4003604 History: Received November 08, 2009; Revised February 06, 2011; Published April 01, 2011; Online April 01, 2011

## Abstract

The effect of suction and blowing in the study of flow and heat transfer of a viscous incompressible fluid between two vertically eccentric rotating spheres is presented when the spheres are maintained at different temperatures and rotating about a common axis while the angular velocities of the spheres 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. These presentations are for various values of the flow parameters including rotational Reynolds number Re, and the blowing/suction Reynolds number $Rew$. The effects of transpiration and eccentricity on viscous torques at the inner and outer spheres are studied, too. As the eccentricity increases and the gap between the spheres decreases the viscous torque remains nearly unchanged. Results for special case of concentric spheres are obtained by letting eccentricity tend to zero.

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## Figures

Figure 21

Flow and heat transfer for Re=1000, Pr=10, Rew=5, Ωio=2 sin(πt/2), and e=0

Figure 23

Viscous torques at the inner sphere for Re=1000, Ωio=2 sin(πt/2), and e=0.1

Figure 24

Viscous torques at the inner and outer spheres for Re=1000, Ωio=−exp(1−t), and e=0.05

Figure 1

Geometry of eccentric rotating spheres

Figure 2

Contours of ψ for Re=20, Rew=0.5, Ωoi=0, and e=0

Figure 3

Contours of ψ for Re=1000, Rew=5, Ωio=−exp(1−t), and e=0.1

Figure 4

Contours of T for Re=1000, Rew=5, Pr=1, Ωio=−exp(1−t), and e=0.1

Figure 5

Contours of ψ for Re=1000, Rew=10, Ωio=−exp(1−t), and e=0.1

Figure 6

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

Figure 14

Contours of T for Re=1000, Rew=5, Pr=10, Ωio=2 sin(πt/2), and e=0.1

Figure 15

Contours of ψ for Re=1000, Rew=10, Ωio=2 sin(πt/2), and e=0.1

Figure 16

Contours of T for Re=1000, Rew=10, Pr=10, Ωio=2 sin(πt/2), and e=0.1

Figure 17

Contours of ψ for Re=1000, Rew=−5, Ωio=2 sin(πt/2), and e=0.1

Figure 18

Contours of T for Re=1000, Rew=−5, Pr=10, Ωio=2 sin(πt/2), and e=0.1

Figure 19

Contours of ψ for Re=1000, Rew=−10, Ωio=2 sin(πt/2), and e=0.1

Figure 20

Contours of T for Re=1000, Rew=−10, Pr=10, Ωio=2 sin(πt/2), and e=0.1

Figure 22

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

Figure 26

Effect of viscous dissipation on temperature field for Re=1000, Rew=5, Pr=10, Ωio=2 sin(πt/2), e=0.1: (a) Ek=0 and (b) Ek=0.001

Figure 7

Contours of ψ for Re=1000, Rew=20, Ωio=−exp(1−t), and e=0.1

Figure 8

Contours of T for Re=1000, Rew=20, Pr=1, Ωio=−exp(1−t), and e=0.1

Figure 9

Contours of ψ for Re=1000, Rew=−5, Ωio=−exp(1−t), and e=0.1

Figure 10

Contours of T for Re=1000, Rew=−5, Pr=1, Ωio=−exp(1−t), and e=0.1

Figure 11

Contours of ψ for Re=1000, Rew=−10, Ωio=−exp(1−t), and e=0.1

Figure 12

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

Figure 13

Contours of ψ for Re=1000, Rew=5, Ωio=2 sin(πt/2), and e=0.1

Figure 25

Effect of viscous dissipation on temperature field for Re=1000, Rew=−5, Pr=1, Ωio=2 sin(πt/2), and e=0.1: (a) Ek=0 and (b) Ek=0.001

## Errata

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