Centrifugal Convection due to Mass Transfer Near a Rotating Disk at High Schmidt Number

[+] Author and Article Information
M. Toren, M. Ungarish, G. Pinchuk, A. Solan

Technion—Israel Institute of Technology, Haifa 32000, Israel

J. Appl. Mech 58(2), 566-571 (Jun 01, 1991) (6 pages) doi:10.1115/1.2897222 History: Received February 20, 1989; Revised December 20, 1989; Online March 31, 2008


The centrifugally-driven flow due to a density gradient between the surface of an infinite disk and the ambient fluid in a rotating system with mass transfer is studied for the case of high Schmidt number. Under certain assumptions the velocity and density fields exhibit a similarity like the classical von Karman disk flow, and the governing equations reduce to a nonlinear system of ordinary differential equations. These equations are solved by boundary layer technique or numerically, for high Schmidt number σ = v/D and finite or small density difference ερ = (ρd - ρ∞ )/ρ∞ . In the latter case it is shown that the major scaling parameter is the product σερ . For σρ ≫ 1 the flow field consists of a constant density (ρ∞ ), linear Ekman layer driven by a buoyancy sublayer of relative thickness (σερ )-1/4 in which ρ varies from ρd to ρ∞ . The representative Rossby number of the buoyancy driven flow is (σερ )-1/2 . The general case ερ = O(1), σ ≫ 1 shows similar trends, i.e., a σ-1/4 sublayer. The case of simultaneous driving by density difference and angular velocity difference εv = (Ωd - Ω∞ )/Ω∞ is also discussed.

Copyright © 1991 by The American Society of Mechanical Engineers
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