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Iterative Methods for Solving the Fractional Form of Unsteady Axisymmetric Squeezing Fluid Flow with Slip and No‐Slip Boundaries

Author

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  • A. A. Hemeda
  • E. E. Eladdad

Abstract

An unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates is proposed with slip and no‐slip boundaries. Using similarity transformation, the system of nonlinear partial differential equations of motion is reduced to a single fourth‐order nonlinear ordinary differential equation. By using the basic definitions of fractional calculus, we introduced the fractional order form of the fourth‐order nonlinear ordinary differential equation. The resulting boundary value fractional problems are solved by the new iterative and Picard methods. Convergence of the considered methods is confirmed by obtaining absolute residual errors for approximate solutions for various Reynolds number. The comparisons of the solutions for various Reynolds number and various values of the fractional order confirm that the two methods are identical and therefore are suitable for solving this kind of problems. Finally, the effects of various Reynolds number on the solution are also studied graphically.

Suggested Citation

  • A. A. Hemeda & E. E. Eladdad, 2016. "Iterative Methods for Solving the Fractional Form of Unsteady Axisymmetric Squeezing Fluid Flow with Slip and No‐Slip Boundaries," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:6021462
    DOI: 10.1155/2016/6021462
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    References listed on IDEAS

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    1. Hamid Khan & S. Islam & Javed Ali & Inayat Ali Shah, 2012. "Comparison of Different Analytic Solutions to Axisymmetric Squeezing Fluid Flow between Two Infinite Parallel Plates with Slip Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. A. A. Hemeda, 2013. "New Iterative Method: An Application for Solving Fractional Physical Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, May.
    3. A. A. Hemeda, 2013. "Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. A. A. Hemeda, 2013. "New Iterative Method: An Application for Solving Fractional Physical Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. A. A. Hemeda, 2013. "Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, December.
    6. Hamid Khan & S. Islam & Javed Ali & Inayat Ali Shah, 2012. "Comparison of Different Analytic Solutions to Axisymmetric Squeezing Fluid Flow between Two Infinite Parallel Plates with Slip Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-18, February.
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