Summary
By means of finite Hankel transforms, the exact solutions corresponding to some unsteady flows of second grade fluids in heated cylindrical domains are obtained. For steady flows, both the velocity field and the temperature are identically to those resulting from the Navier-Stokes theory.
Similar content being viewed by others
References
Truesdell, C., Noll, W.: The nonlinear field theories of mechanics. Encyclopedia of Physics, vol. III/3. Berlin: Springer 1965.
Coleman, B. D., Noll, W.: An approximation theorem for functionals, with applications in continuum mechanics. Arch. Rat. Mech. Anal.6, 355–370 (1960).
Bandelli, R.: Unsteady unidirectional flows of second grade fluids in domains with heated boundaries. Int. J. Non-Linear Mechanics30, 263–269 (1995).
Wimmer, M.: Viscous flows and instabilities near rotating bodies. Prog. Aerospace Sci.25, 43–103 (1988).
Sneddon, I. N.: Functional analysis. Encyclopedia of Physics, vol. II. Berlin: Springer 1955.
Coleman, B. D., Markovitz, H., Noll, W.: Viscometric of non-Newtonian fluids. Berlin: Springer 1966.
Bandelli, R., Rajagopal, K. R.: Start-up flows of second grade fluids in domains with one finite dimension. Int. J. Non-Linear Mechanics30, 817–839 (1995).
Srivastava, P. N.: Non-steady helical flow of a viscoelastic fluid. Arch. Mech. Stos.18, 145–150 (1966).
Tolstov, G. P.: Serii Fourier. Bucureşti: Editura Tehnică 1955 (translation from Russian).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fetecău, C., Fetecău, C. Unsteady Couette flows of second grade fluids in heated cylindrical domains. Acta Mechanica 150, 127–134 (2001). https://doi.org/10.1007/BF01178550
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01178550