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Jordan Y. Hristov

INTEGRAL-BALANCE SOLUTION TO THE STOKES’ FIRST PROBLEM OF A VISCOELASTIC GENERALIZED SECOND GRADE FLUID

ABSTRACT
Integral balance solution employing entire domain approximation and the penetration dept concept to the Stokes’ first problem of a viscoelastic generalized second grade fluid has been developed. The solution has been performed by a parabolic profile with an unspecified exponent allowing optimization through minimization of the norm over the domain of the penetration depth. The closed form solution explicitly defines two dimensionless similarity variables and , responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. The solution was developed with three forms of the governing equation through its two dimensional forms (the main solution and example 1) and the dimensionless version showing various sides of the flow field and how the dimensionless groups control it: mainly the effect of the Deborah number. Numerical simulations demonstrating the effect of the various operating parameter and fluid properties on the developed flow filed have been performed.
KEYWORDS
Stokes' first problem, viscoelastic, generalized second grade fluid, integral-balance solution, Deborah number
PAPER SUBMITTED: 2011-04-01
PAPER REVISED: 2011-06-30
PAPER ACCEPTED: 2011-07-18
DOI REFERENCE: https://doi.org/10.2298/TSCI110401077H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE Issue 2, PAGES [395 - 410]
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Integral-balance solution to the Stokes’ first problem of a viscoelastic generalized second grade fluid

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