Abstract
Abstract Delayed response (delay of the elasticity) and time needed for initial stress can lead to relaxation and retardation phenomenon; this is because of the consistent behavior of viscoelastic fluid on thermodynamic principles. In this context, the aim of this article is to investigate the unsteady, incompressible, and Oldroyd-B viscoelastic fluid under wall slip conditions to know the hidden aspects of relaxation and retardation. The motion of the liquid is assumed over a flat vertical plate which moves through an oscillating velocity. A fractional model is developed by using the modern definition of the non-singular kernel proposed by Caputo and Fabrizio. We have obtained a semi-analytical solution of the non-dimensional model by using the Laplace transformation that satisfies our imposed suitable boundary conditions. We have tackled the Laplace inverse by employing Stehfest’s and Tzou’s algorithms. The velocity is enhanced by decreasing the estimations of relaxation time λ as well as slip parameter, and the temperature is also increasing for a considerable measure of the fractional factor. The effects of different fractional and physical parameters are plotted using Mathcad software based on the relaxation and retardation phenomenon of Oldroyd-B viscoelastic fluid.
Highlights
In recent years, non-Newtonian fluids have become more important due to their applications in the industrial and engineering fields
The best subclass of rate type liquid is Maxwell liquid; in any case, this liquid demonstrates as it was depicted in terms of its relaxation time, whereas there is no evidence of its retardation time
The results of the dimensionless system are obtained through an analytical technique such as Laplace transform, its inversion, and semi-analytical solution of the shear stress, velocity, and temperature
Summary
Non-Newtonian fluids have become more important due to their applications in the industrial and engineering fields. Fetecau et al [1] demonstrated Oldroyd-B fluid flow over a plate. This idea gained attention of many researchers. Chang et al [3] investigated the Walters-B viscoelastic flow at wall suction They examined the numerical results of convective heat transport of fluid flow at the wall and gained the most important results. Azeem Khan et al [5] highlighted the Oldroyd-B nanomaterial fluid flow effects due to stretching sheets. Similar studies have been carried out in various circumstances but few researchers have developed interest in analyzing the non-Newtonian fluid’s effects on the stretching surface due to various assumptions, see latest attempts [10–15] and references therein
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