Another approach to the extended Stokes problems for the Oldroyd-B fluid (Q1954361)

Summary: The extended Stokes problems, which study the flow suddenly driven by relatively moving half-planes, are reexamined for the Oldroyd-B fluid. This topic has been studied by the author [Math. Probl. Eng. 2011, Article ID 709836, 16 p. (2011; Zbl 1264.76034)] by applying the series expansion to calculate the inverse Laplace transform. The derived solution was correct but tough to perform the calculation due to the series expansion of infinite terms. Herein another approach, the contour integration, is applied to calculate the inversion. Moreover, the Heaviside unit step function is included into the boundary condition to ensure the consistence between boundary and initial conditions. Mathematical methods used herein can be applied to other fluids for the extended Stokes' problems.