Flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate

摘要

The velocity field and the adequate shear stress corresponding to the unsteady flow of a generalized Oldroyd-B fluid due to a constantly accelerating plate have been established using Fourier sine and Laplace transforms. In order to avoid lengthy calculations of residues and contour integrals, the discrete inverse Laplace transform method has been used. The solutions that have been obtained, presented under integral and series forms in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. The similar solutions for generalized Maxwell fluids as well as those for Oldroyd-B, Maxwell and Newtonian fluids are obtained as limiting cases of our general solutions.