Some exact solutions of an elastico-viscous fluid

Elastrco-vrscous fluids, m particular the model characterrzed by Walters [l] (hqmd B’), exhibit a close resemblance to real fluids hke olls and certam hrgh polymer solutrons One of the important aspects of any fluid 1s the behavror of its unsteady boundary layers A large number of papers concernmg the time-dependent flows of elastrco-viscous hqmd B' have appeared m the literature, for example, [2-71, etc The purpose of the present study 1s three-fold First, m Section 2, exact analytrc solutrons are established for the unsteady flow of an elastlco-vrscous flmd caused by perrodrc oscrllatrons of a porous plate A general perrodlc functron g(t) with perlod To 1s considered An expressron for shear stress 1s also grven The flow fields and shear stresses due to certam specral values of oscrllatrons are derived as specml cases of the perrodrc oscrllatrons Second, m Sectron 3, the wall considered 1s nonporous and the exact flow generated by general perrodrc oscrllatrons of a rrgrd plate 1s obtamed Thud, m Sectron 4, the problem of a porous drsk executmg periodic rotary oscrllatrons 1s discussed The velocrty field and the moment of the shear stresses are estabhshed In order to study the behavior of the solutron, a second-order approxrmatron of the appropriate root of the characterrstrc equation 1s found and the structure of waves 1s drscussed A comparrson of these results 1s made among the elastrco-vrscous, second grade, and Newtoman fluid cases