Abstract
Transient incompressible flows of Jeffrey fluids over a permeable, flat, and infinite plate have been investigated. The plate motion is an oscillatory translation along the x-axis. Using the Laplace transform and perturbation method, the analytical solution for the velocity field in the transform domain has been obtained. The velocity field in the real domain has been determined by using the numerical Stehfest’s algorithm for the Laplace transform inversion. To have a validation of the obtained solution, we have determined the analytical solution for the flow without transpiration. It was found that when the transpiration parameter approaches zero, the solution for the flow with transpiration tends to the solution corresponding to the case without perspiration. The influence of the system parameters on fluid motion has been investigated by numerical simulations and graphical illustrations prepared with the software package Mathcad.
Highlights
As compared with the differential equations of viscous material, the order of differential equations of non-Newtonian fluids is greater. ere are countless types of non-Newtonian fluids by means of differing properties. ese fluids have been grouped into three classifications recognized as the differential, integral, and rate type. e most widely recognized and least difficult type of non-Newtonian fluids is Jeffrey fluid
An inclusive argument of a Jeffrey fluid on steady flows using stretching sheet can be originated in [9,10,11,12,13,14]. e analytical solution over a shrinking sheet of the Jeffrey fluid for boundary layer steady flow has been underlined by Nadeem et al [15] whereas Hamad et al [16] suggested a finite difference study to analyze the thermal jump effects near a stagnation points on the shrinking sheet using variable thermal conductivity on boundary layer flow of a Jeffrey fluid
For the Jeffrey fluid, a more wide-ranging solution can be obtained when a fluid transpiration is considered on the wall. e leading equations of motion for Jeffrey fluid with wall transpiration are far complex as related with Jeffrey fluid without wall transpiration. is complexity of governing equations of Jeffrey fluid with wall transpiration creates the inconvenience to attain the exact solution, and it is challenging to handle
Summary
Is paper is extended by Hameed et al [31]; they derived exact solution for unsteady flow of a second-grade fluid above flat plates with oscillating and impulsive motions, initially at rest, and by means of wall transpiration by Laplace transform, perturbation method, and an extended variable separation technique. Using the Laplace transform and perturbation method, the analytical solution for the nondimensional velocity field in the transform domain has been obtained. E particular case of the flow without transpiration is investigated, and the analytical solution of the velocity field is determined.
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