Abstract
Analytical solutions to the Navier–Stokes equations for non-Newtonian fluids are rare and tend to be mathematically complicated. We analytically solve Stokes’ second problem — the flow due to an infinite plate oscillating in-plane — for a viscoelastic fluid described by the Oldroyd-B constitutive relation, using mathematical techniques familiar to third- or fourth-year undergraduate students in physics, engineering, or mathematics. The solution is compared to the well-known solution of Stokes’ second problem for a Newtonian fluid to illustrate the effects of fluid elasticity on the flow, and we provide a straightforward interpretation of these effects in terms of the quality factor of the oscillations. This calculation provides a mathematically accessible introduction to non-Newtonian fluid flow that illustrates important physical effects while limiting the mathematical complications.
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