A general investigation has been made and analytic solutions are provided corresponding to the flows of an Oldroyd-B fluid, under the consideration of slip condition at the boundary. The fluid motion is generated by the flat plate which has a translational motion in its plane with a time-dependent velocity. The adequate integral transform approach is employed to find analytic solutions for the velocity field. Solutions for the flows corresponding to Maxwell fluid, second-grade fluid, and Newtonian fluid are also determined in both cases, namely, flows with slip on the boundary and flows with no slip on the boundary, respectively. Some of our results were compared with other results from the literature. The effects of several emerging dimensionless and pertinent parameters on the fluid velocity have been studied theoretically as well as graphically in the paper.
We investigate the unsteady flow of a viscous fluid near a vertical heated plate. The momentum and energy equations are considered as fractional differential equations with respect to the time t. Solutions of the initial-boundary values problem are determined by means of the Laplace transform technique and are represented by means of the Wright functions. The fundamental solution for the temperature field is obtained. This allows obtaining the temperature field for different conditions on the wall temperature. A numerical case is analyzed in order to obtain information regarding the influence of the fractional parameters on the temperature and velocity fields. Some physical aspects of the fluid behavior are presented by graphical illustrations.
MSC: 80A20; 76A10
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