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A NUMERICAL STUDY OF FLOW AND HEAT TRANSFER BETWEEN TWO ROTATING SPHERES WITH CONSTANT ANGULAR VELOCITIES

DOI: 10.1615/ICHMT.2008.CHT.400
17 pages

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

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

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

Abstract

Solution of steady-state motion and heat transfer of a viscous incompressible fluid contained between two concentric spheres maintained at different temperatures and rotating about a common axis with different constant angular velocities is considered. These solutions are obtained by choosing the appropriate similarity parameters. These similarity parameters change the system of partial differential governing equations into a system of ordinary differential equations along with appropriate boundary and initial conditions which can be solved numerically with a lot less complexities. Gravity has been neglected therefore forced convection is the heat transfer phenomenon. The ratio of Gr/Re2<<1, (Gr = Grashof number, Re =Reynolds number), which is the case for a big range of engine oils supports this simplification. It can be shown that the magnitude of the effect of the density variations on the rotational acceleration terms such as Coriolis and centrifugal is a function of the ratio of the gravitational acceleration to the rotational acceleration of the inner sphere. Therefore neglecting the gravitational acceleration in our study seems reasonable.
All the past solutions for the flow problem are direct numerical attempts which uses a lot of computational time. The resulting flow pattern, temperature distribution, and heat transfer characteristics are presented for the various cases. Same results as previous works are obtained for Navier-Stokes and energy equations but with less computational complexities.

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