Abstract
The interaction of a rotating flow and a stationary surface is discussed for a second-order non-Newtonian liquid. Similarity solutions of the governing partial differential equations are obtained for the case of the outer flow in solid-body rotation. The results for the Newtonian case are compared with Bödewadt's series solution of this problem. The non-Newtonian solutions indicate that for certain values of the parameters characterizing the non-linear viscous response and normal stress effects a larger secondary flow is induced in the boundary layer than in the Newtonian case.
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References
Bödewadt, U. T., Z. Angew. Math. u. Mech. 20 (1940) 241.
Kerrebrock, J. L. and R. V. Meghreblian, J. Aero. Sci. 28 (1961) 710.
Keyes, J. J., Jr. and W. K. Sartory, A study of nuclear-magnetohydrodynamic power generators, Oak Ridge National Laboratory, Oak Ridge (Tenn.) AECORNL-TM-1301, 1967.
Anderson, O. L., Theoretical solutions for the secondary flow on the end wall of a vortex tube, United Aircraft Corporation Research Laboratories, East Hartford (Conn.) R-2494-1, 1961.
King, W. S., Momentum-integral solutions for the laminar boundary layer on a finite disk in a rotating flow, Aerospace Corp., El Segundo (Cal.) ATN-63 (9227)-3, 1963.
Lewellen, W. S., Three-dimensional viscous vortices in incompressible flow, Ph.D. Dissertation, University of California, Los Angeles (Cal.), 1964.
Kidd, G. J., Jr. and G. J. Farris, J. Appl. Mech. 35 (1968) 209.
Farris, G. J., G. J. Kidd, Jr., D. W. Lick and R. E. Textor, J. Appl. Mech. 36 (1969) 687.
Chang, T. S. and C. W. Kitchens, Jr., J. Appl. Mech. 37 (1970) 557.
Nachtsheim, P. R. and P. Swigert, Satisfaction of asymptotic boundary conditions in numerical solution of systems of nonlinear equations of the boundary-layer type, NASA TN D-3004, 1965.
Coleman, B. D. and W. Noll, Arch. Ratl. Mech. Anal. 6 (1960) 335.
Rivlin, R. S. and J. L. Ericksen, J. Ratl. Mech. Anal. 4 (1955) 323.
Markovitz, H. and B. D. Coleman, Adv. Appl. Mech. 8 (1964) 69.
Maxworthy, T., J. Appl. Mech. 35 (1968) 836.
Stewartson, K., Proc. Camb. Phil. Soc. 49 (1953) 333.
Schlichting, H., Boundary Layer Theory, 4th Edition, McGraw-Hill Book Co., 1960.
Rogers, M. H. and G. N. Lance, J. Fluid Mech. 7 (1960) 617.
Kitchens, C. W., Jr., Vortex flows of second-order non-Newtonian liquids, Ph.D. Dissertation, North Carolina State University, Raleigh (N.C.), 1970.
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Also at North Carolina State University Raleigh (N.C.), U.S.A.
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Kitchens, C.W., Chang, T.S. Newtonian and non-Newtonian liquids rotating adjacent to a stationary surface. Appl. Sci. Res. 27, 283–296 (1973). https://doi.org/10.1007/BF00382492
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DOI: https://doi.org/10.1007/BF00382492