Abstract
We propose two friendly analytical techniques called Adomian decomposition and Picard methods to analyze an unsteady axisymmetric flow of nonconducting, Newtonian fluid. This fluid is assumed to be squeezed between two circular plates passing through porous medium channel with slip and no-slip boundary conditions. A single fractional order nonlinear ordinary differential equation is obtained by means of similarity transformation with the help of the fractional calculus definitions. The resulting fractional boundary value problems are solved by the proposed methods. Convergence of the two methods’ solutions is confirmed by obtaining various approximate solutions and various absolute residuals for different values of the fractional order. Comparison of the results of the two methods for different values of the fractional order confirms that the proposed methods are in a well agreement and therefore they can be used in a simple manner for solving this kind of problems. Finally, graphical study for the longitudinal and normal velocity profiles is obtained for various values of some dimensionless parameters and fractional orders.
Highlights
The importance of the fluid flow through a porous medium goes back a long time in various applications in life such as agriculture, industry, and oil and gas production, where the focus was on estimating and optimizing production
The homotopy perturbation method (HPM) has been developed by Qayyum et al [15], to model and analyze the unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates passing through a porous medium channel with slip boundary condition
Our objective of this article is to prepare and utilize the proposed methods to obtain an analytical solution to the fractional form of an unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates passing through porous medium with slip and no-slip boundary conditions
Summary
The importance of the fluid flow through a porous medium goes back a long time in various applications in life such as agriculture, industry, and oil and gas production, where the focus was on estimating and optimizing production. The homotopy perturbation method (HPM) has been developed by Qayyum et al [15], to model and analyze the unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates passing through a porous medium channel with slip boundary condition. The new iterative and Picard methods had been used by Hemeda and Eladdad in [16] for solving the fractional form of unsteady axisymmetric flow of a nonconducting, Newtonian fluid squeezed between two circular plates with slip and no-slip boundaries. Our objective of this article is to prepare and utilize the proposed methods to obtain an analytical solution to the fractional form of an unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates passing through porous medium with slip and no-slip boundary conditions. The effects of various fractional order, constant containing permeability, Reynolds number, and slip parameter on the solution are studied tabularly and graphically
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