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Numerical investigation of the MHD suction–injection model of viscous fluid using a kernel-based method

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Abstract

In this paper, a numerical investigation MHD squeezing flow between two parallel plates is presented. A method of stable approximation based on Gaussian Hilbert–Schmidt SVD (HS-SVD) is used. In the HS-SVD approach, by eliminating a significant portion of the ill-conditioning, an alternate basis for data-dependent subspace of “native” Hilbert space is obtained. The well-conditioning linear system is one of the critical advantages of using the alternate basis obtained from HS-SVD. There are three parameters A, S, and M, in the dimensionless equations and the effect of parameters on the flow field is investigated. The results show that by increasing Hartmann number (M) the axial velocity of the fluid flow decreases without a significant effect on the vertical velocity.

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References

  1. Sulochana, C., Sandeep, N., Sugunamma, V., Rushi Kumar, B.: Aligned magnetic field and cross-diffusion effects of a nanofluid over an exponentially stretching surface in porous medium. Appl. Nanosci. 6, 737–746 (2016)

    Article  Google Scholar 

  2. Ismail, H.N.A., Abourabia, A.M., Hammad, D.A., Ahmed, N.A., Desouky, A.A.E.: On the MHD flow and heat transfer of a micropolar fluid in a rectangular duct under the effects of the induced magnetic field and slip boundary conditions. SN Appl. Sci. 2, 25 (2020)

    Article  Google Scholar 

  3. Dimitrienko, Y.I., Li, S.: Numerical simulation of MHD natural convection heat transfer in a square cavity filled with Carreau fluids under magnetic fields in different directions. Comput. Appl. Math. 39, 252 (2020)

    Article  MathSciNet  Google Scholar 

  4. Xiao, X., Yang, S., Kim, C.N.: Effect of the magnetic field direction on the mass-imbalance of MHD flows in a multi-channel conduit with spatially non-uniform electric conductivity. J. Mech. Sci. Technol. 34, 3635–3646 (2020)

    Article  Google Scholar 

  5. Turkyilmazoglu, M.: Effects of uniform radial electric field on the MHD heat and fluid flow due to a rotating disk. Int. J. Eng. Sci. 51, 233–240 (2012)

    Article  MathSciNet  Google Scholar 

  6. Turkyilmazoglu, M.: Latitudinally deforming rotating sphere. Appl. Math. Model. 71, 1–11 (2019)

    Article  MathSciNet  Google Scholar 

  7. Turkyilmazoglu, M.: Magnetic field and slip effects on the flow and heat transfer of stagnation point Jeffrey fluid over deformable surfaces. Zeitschrift Für Naturforschung A 71(6), 549–556 (2016)

    Article  MathSciNet  Google Scholar 

  8. Turkyilmazoglu, M.: MHD natural convection in saturated porous media with heat generation/absorption and thermal radiation: closed-form solutions. Arch. Mech. 71(1), 49–64 (2019)

    MathSciNet  MATH  Google Scholar 

  9. Li, Z., Shafee, A., Ramzan, M., Rokni, H.B., Al-Mdallal, Q.M.: Simulation of natural convection of \(Fe_{3}O_{4}\)-water ferrofluid in a circular porous cavity in the presence of a magnetic field. Eur. Phys. J. Plus 134, 77 (2019)

    Article  Google Scholar 

  10. Mercer, J.: Functions of positive and negative type and their connection with the theory of integral equations. Philos. Trans. Roy. Soc. A 209, 415–446 (1909)

    MATH  Google Scholar 

  11. Aronszajn, N.: Theory of Reproducing Kernels. Harvard University, Cambridge (1951)

    MATH  Google Scholar 

  12. Driscoll, T.A., Fornberg, B.: Interpolation in the limit of increasingly flat radial basis functions. Comput. Math. Appl. 43(3–5), 413–422 (2002)

    Article  MathSciNet  Google Scholar 

  13. Larsson, E., Fornberg, B.: Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions. Comput. Math. Appl. 49(1), 103–130 (2005)

    Article  MathSciNet  Google Scholar 

  14. Schaback, R.: Multivariate interpolation by polynomials and radial basis functions. Constr. Approx. 21, 293–317 (2005)

    Article  MathSciNet  Google Scholar 

  15. Schaback, R.: Limit problems for interpolation by analytic radial basis functions. J. Comput. Appl. Math. 212, 127–149 (2008)

    Article  MathSciNet  Google Scholar 

  16. Lee, Y.J., Micchelli, C.A.: On collocation matrices for interpolation and approximation. J. Approx. Theory 174, 148–181 (2013)

    Article  MathSciNet  Google Scholar 

  17. Song, G., Riddle, J., Fasshauer, G.E., Hickernell, F.J.: Multivariate interpolation with increasingly flat radial basis functions of finite smoothness. Adv. Comput. Math. 36(3), 485–501 (2012)

    Article  MathSciNet  Google Scholar 

  18. Fasshauer, G.E.: Meshfree Approximation Methods with Matlab. Interdisciplinary Mathematical Sciences. World Scientific Publishing Co., Berlin (2007)

    MATH  Google Scholar 

  19. Fasshauer, G.E., McCourt, M.: Kernel-Based Approximation Methods with Matlab. Interdisciplinary Mathematical Sciences. World Scientific Publishing Co., Berlin (2016)

    MATH  Google Scholar 

  20. Fornberg, B., Wright, G.: Stable computation of multiquadric interpolants for all values of the shape parameter. Comput. Math. Appl. 48(5–6), 853–867 (2004)

    Article  MathSciNet  Google Scholar 

  21. Fornberg, B., Piret, C.: A stable algorithm for flat radial basis functions on a sphere. SIAM J. Sci. Comput. 30(1), 60–80 (2008)

    Article  MathSciNet  Google Scholar 

  22. Pazouki, M., Schaback, R.: Bases for kernel-based spaces. J. Comput. Appl. Math. 236(4), 575–588 (2011)

    Article  MathSciNet  Google Scholar 

  23. De Marchi, S., Santin, G.: A new stable basis for radial basis function interpolation. J. Comput. Appl. Math. 253, 1–13 (2013)

    Article  MathSciNet  Google Scholar 

  24. Fornberg, B., Larsson, E., Flyer, N.: Stable computations with Gaussian radial basis functions. SIAM J. Sci. Comput. 33(2), 869–892 (2011)

    Article  MathSciNet  Google Scholar 

  25. Fornberg, B., Lehto, E., Powell, C.: Stable calculation of Gaussian-based RBF-FD stencils. Comput. Math. Appl. 65(4), 627–637 (2013)

    Article  MathSciNet  Google Scholar 

  26. Larsson, E., Lehto, E., Heryudono, A., Fornberg, B.: Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions. SIAM J. Sci. Comput. 35(4), A2096–A2119 (2013)

    Article  MathSciNet  Google Scholar 

  27. Cavoretto, R., Fasshauer, G.E., McCourt, M.J.: An introduction to the Hilbert–Schmidt SVD using iterated Brownian bridge kernels. Numer. Algorithms 68, 393–422 (2015)

    Article  MathSciNet  Google Scholar 

  28. Foroutan, M., Ebadian, A., Asadi, R.: Reproducing kernel method in Hilbert spaces for solving the linear and nonlinear four-point boundary value problems. Int. J. Comput. Math. 95(10), 2128–2142 (2018)

    Article  MathSciNet  Google Scholar 

  29. Jiwari, R.: A Haar wavelet quasilinearization approach for numerical simulation of Burgers’ equation. Comput. Phys. Commun. 183(24), 13–23 (2012)

    MathSciNet  MATH  Google Scholar 

  30. Kaur, H., Mittal, R.C., Mishra, V.: Haar wavelet approximate solutions for the generalized Lane–Emden equations arising in astrophysics. Comput. Phys. Commun. 184(21), 69–77 (2013)

    MathSciNet  MATH  Google Scholar 

  31. Khan, S.I.U., Ahmad, N., Khan, U., Jan, S.U., Mohyud-Din, S.T.: Heat transfer analysis for squeezing flow between parallel disks. J. Egypt. Math. Soc. 23(2), 445–450 (2015)

    Article  MathSciNet  Google Scholar 

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Correspondence to Yasir Khan.

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Fardi, M., Pishkar, I., Alidousti, J. et al. Numerical investigation of the MHD suction–injection model of viscous fluid using a kernel-based method. Arch Appl Mech 91, 4205–4221 (2021). https://doi.org/10.1007/s00419-021-02003-2

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  • DOI: https://doi.org/10.1007/s00419-021-02003-2

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