Integral-Balance solution to the Stokes' first problem of a viscoelastic generalized second grade fluid
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2012-01-01
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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 L2 norm over the domain of the penetration depth. The closedform solution explicitly defines two dimensionless similarity variables ξ = y/(vt)1/2 and Do = χ2 = = (p/vtβ)1/2, 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 2-D 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.