The first problem of Stokes for an Oldroyd-B fluid

Exact solutions for the flow of an Oldroyd-B fluid due to an infinite flat plate

“…Such, for V = 0 one obtains the flow produced by a constantly accelerating plate while for A = 0 we recover the solutions that have been recently obtained for the flow due to the impulsive motion of the plate (Vieru et al, personal communication). In both cases the solutions obtained by means of the Laplace transforms are in accordance with those that have been recently determined using Fourier sine transforms [10,14]. Furthermore, these solutions reduce, as limiting cases, to the classical solutions for a Newtonian fluid.…”

“…By letting now A = 0 into Equations (23), (27), (28) and (29) we recover the solutions for the first problem of Stokes. These solutions, as it was proved by graphical illustrations, are identical to those obtained in [10] using the Fourier sine transform. In the special case when V = 0, the resulting solutions correspond to the motion of an Oldroyd-B fluid due to a constantly accelerating plate.…”

“…Later, Rajagopal and Bhatnagar [7] established two simple but elegant solutions for the flow of an Oldroyd-B fluid around an oscillating rod. Many other exact solutions corresponding to different motions of Oldroyd-B fluids have been also presented as Fourier or FourierBessel series or under integral forms [8][9][10][11][12][13][14]. Recently, the exact solutions for the first problem of Stokes [10] have been extended to porous media by Tan and Masuoka [15].…”

Stokes first problem for an unsteady MHD fourth-grade fluid in a non-porous half space with Hall currents

“…Erdogan [10] analyzed the unsteady unidirectional flows generated by impulsive motion of a boundary or sudden application of a pressure gradient. Fetecau and Fetecau [11] solved Stokes' first problem for ordinary Oldroyd-B fluid by sine transform. Stokes' first problem for Oldroyd-B and second grade fluid in a porous half space is studied by Tan and Masuoka [12][13].…”

Numerical results for the conservation of energy of Maxwell media for the Rayleigh–Stokes problem

“…This solution, obtained by means of the Fourier sine transform, satisfy both the governing equation and all imposed initial and boundary conditions. Its extension to rate type fluids has been realized in [11] and [12]. The velocity field and the adequate shear stress obtained in [11] have been recently used by Zierep and Fetecau [13] to develop a complete energetic study for the Rayleigh-Stokes problem of a Maxwell fluid.…”