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Integral balance solution employing entire domain approximation and thepenetration dept concept to the Stokes' first problem of a viscoelasticgeneralized second grade fluid has been developed. The solution has beenperformed by a parabolic profile with an unspecified exponent allowingoptimization through minimization of the norm over the domain of thepenetration depth. The closed form solution explicitly defines twodimensionless similarity variables and, responsible for the viscous and theelastic responses of the fluid to the step jump at the boundary. The solutionwas developed with three forms of the governing equation through its twodimensional forms (the main solution and example 1) and the dimensionlessversion showing various sides of the flow field and how the dimensionlessgroups control it: mainly the effect of the Deborah number. Numericalsimulations demonstrating the effect of the various operating parameter andfluid properties on the developed flow filed have been performed.

Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid