On the first problem of Stokes for Burgers’ fluids. II: The cases γ = λ2/4 and γ > λ2/4

摘要

The velocity fields and the associated tangential stresses corresponding to the flow of a Burgers’ fluid over a suddenly moved flat plate are established when the relaxation times satisfy the conditions γ = λ2/4 and γ > λ2/4. Using the Laplace transform, the solutions are presented in forms of simple or multiple integrals in term of Bessel functions J0( · ), J1( · ), I0 ( · ) and I1( · ). The simplest solutions are obtained when γ=λr2 and λ = 2λr. The corresponding diagrams for velocity and shear stress are compared with those for a Newtonian fluid.