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A study on magneto hydrodynamics Jeffery-Hamel flow with heat transfer problem in Eyring-Powell fluid using differential transform method

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we study and analyse the variations of velocity profiles for different values of the Reynolds number, Eckert number, Prandtl number and Hartmann number in the Magneto Hydrodynamics Jeffery-Hamel flow with heat transfer in Eyring-Powell fluid in both divergent and convergent channels. The Differential Transform Method (DTM) is used to obtain an analytical solution of the Jeffery Hamel flow problem and to determine the velocity profiles of the fluid flow. Finally, the efficiency of DTM has been shown, and the results have been validated by comparing the obtained results with the numerical results (fourth order RK method) in both convergent and divergent channels.
Rocznik
Strony
57--68
Opis fizyczny
Bibliogr. 21 poz., rys., tab.
Twórcy
  • Department of Mathematics, S.V National Institute of Technology, Surat, Gujarat, India
autor
  • Department of Mathematics, S.V National Institute of Technology, Surat, Gujarat, India
Bibliografia
  • [1] Jeffery, G.B. (1915). The two-dimensional steady motion of a viscous fluid. Philosophical Magazine Series, 6, 29, 455-465.
  • [2] Hamel, G. (1917). Spiralformige bewegungen zaher flussigkeiten. Jahresbericht der Deutschen Mathematiker-Vereinigung, 25, 34-60.
  • [3] Akulenko, L.D., Georgevskii, D.V., & Kumakshev, S.A. (2004). Solutions of the Jeffery-Hamel problem regularly extendable in the Reynolds number. Fluid Dynamics, 39, 1, 12-28.
  • [4] Makinde, O.D., & Mhone P.Y. (2006). Hermite-Padé approximation approach to MHD Jeffery-Hamel flows. Appl. Math. Comput., 181, 966-972.
  • [5] Esmaili, Q., Ramiar, A., Alizadeh, E., & Ganji, D.D. (2008). An approximation of the analytical solution of the Jeffery-Hamel flow by decomposition method. Phys. Lett., 372, 3434-3439.
  • [6] Rivkind, L., & Solonnikov, V.A. (2000). Jefery Hamel asymptotics for steady state Navier Stokes flow in domains with sector-like outlets to infinity. J. Math. Fluid Mech, 324-352.
  • [7] Egashira, R., Fujikawa, T., Yaguchi, H., & Fujikawa, S. (2018). Microscopic and low Reynolds number flows between two intersecting permeable walls. Fluid Dynamics Research, 50(3), 035502.
  • [8] Rana, P., Shukla, N., Gupta, Y., & Pop, I. (2019). Analytical prediction of multiple solutions for MHD Jeffery-Hamel flow and heat transfer utilizing KKL nano-fluid model. Physics Letters A, 383(2-3), 176-185.
  • [9] Muhammad, U., Muhammad, H, Khan, U, Syed, T, Muhammad, A., & Wei W. (2017). Differential transform method for unsteady nano-fluid flow and heat transfer. Alexandria Engineering Journal (in press).
  • [10] Zhou, J.K, & Pukhov. (1986). Differential Transformation and Application for Electrical Circuits. Wuhan, China: Huazhong University Press.
  • [11] Hossein, J., Maryam, A., & Hale T.(2010). Two dimensional differential transform method for solving non-linear partial differential equations. International Journal of Research and Reviews in Applied Sciences, 2, 1, 47-52.
  • [12] Patil, N., & Khambayat, A. (2014). Differential transform method for system of linear differential equations. Research Journal of Mathematical and Statistical Sciences, 2(3), 4-6.
  • [13] Chen, C.K., & Ho, S.H. (1999). Solving partial differential equations by two dimensional differential transform method. Applied Mathematics and Computation, 106, 171-179.
  • [14] Ayaz, F. (2004). Solutions of the systems of differential equations by differential transform method. Appl. Math. Comput., 147, 547-567.
  • [15] Nazari, D., & Shahmorad, S. (2010). Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions. J. Comput. Appl. Math., 234, 883-891.
  • [16] Farshid, M., & Mohammad, K.Y. (2016). A novel computing three dimensional differential transform method for solving fuzzy partial differential equations. Ain Shams Engineering, 7, 695-708.
  • [17] Farshid, M. (2011). Differential transform method for solving linear and nonlinear systems of ordinary differential equations. Applied Mathematical Sciences, 5(70), 3465-3472.
  • [18] Patel, H.S., & Meher, R. (2016). Analytical investigation of Jeffery-Hemal flow by modified adomian decomposition method, Ain Shams Engineering Journal.
  • [19] Patel, N.D., & Meher, R. (2016). Differential transformation method for solving Kolmogrove-Petrovskii-Piskunov equation and porous medium equation. Mathematical Sciences, IMRF Journals, 5, 1, 47-51.
  • [20] Patel, N.D., Meher R. (2017). Differential transform method for solving for fingero-imbibition phenomena arising in double phase flow through homogeneous porous media. Mathematical Sciences, IMRF Journals, 6, 1, 1-5.
  • [21] Rana, P., Shukla, N., Gupta, Y., & Pop, I. (2019). Homotopy analysis method for predicting multiple solutions in the channel flow with stability analysis. Communications in Nonlinear Science and Numerical Simulation, 66, 183-193.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bd531354-6668-4e21-b591-b583c988d806
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