Similarity Analysis for a Heated Ferrofluid flow in Magnetic Field

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ABSTRACT

The aim of this paper is to introduce new results on the magneto-thermomechanical interaction between heated viscous incompressible ferrofluid and a cold wall in the presence of a spatially varying magnetic field. Similarity transformation is applied to convert the governing nonlinear boundary layer equations into coupled nonlinear ordinary differential equations. This system is numerically solved using higher derivative method. The effects of governing parameters corresponding to various physical conditions are investigated. Numerical results are represented for the distributions of velocity and temperature, for the dimensionless wall skin friction and for heat transfer coef?cients. Our results show excellent agreement with previous studies and obtained two solutions in some cases.

KEYWORDS

ferrofluid, magnetic field, boundary layer, similarity transformation (6 - 10 words)

REFERENCES

[1] M. S. Abel, N. Mahesha, Heat transfer in MHD viscoelastic fluid flow over stretching sheet with variable thermal conductivity, non-uniform heat source and radiation, Applied Mathematical Modelling 32(2008), 1965–1983.

[2] Ö. B. Adigüzel, K. A Talik, Magnetic field effects on Newtonian and non-Newtonian ferrofluid flow past a circular cylinder, Appl. Math. Modelling 42(2017), 161–174.

[3] Y. Amirat, K. Hamdache, Heat Transfer in Incompressible Magnetic Fluid, J. Math. Fluid Mech. 14 (2012), 217–247.

[4] H. I. Andersson, O. A. Valnes, Flow of a heated Ferrofluid over a stretching sheet in the presence of a magnetic dipole, Acta Mechanica 128 (1988), 39–47.

[5] H. I. Andersson, MHD flow of a viscoelastic fluid past a stretching surface, Acta Mechanica 95 (1992), 227–230.

[6] H. A. Attia, N. A. Kotb, MHD flow between two parallel plates with heat transfer, Acta Mechanica 117 (1996), 215–220.

[7] G.I. Barenblatt, Scaling, Self-similarity, and Intermediate Asymptotic, Cambridge Text in Applied Mathematics, Vol. 14, Cambridge University Press, Cambridge, 1996.

[8] M. M. Bhatti, T. Abbas, M. M. Rashidi, Numerical Study of Entropy Generation with Nonlinear Thermal Radiation on Magnetohydrodynamics non-Newtonian Nanofluid Through a Porous Shrinking Sheet, J. Magnetics 21 (2016), 468–475.

[9] G. Bognár, On similarity solutions of MHD flow over a nonlinear stretching surface in non-Newtonian power-law fluid, Electron. J. Qual. Theory Differ. Equ. 2016, 1–12.

[10] G. Bognár, Magnetohydrodynamic Flow of a Power-Law Fluid over a Stretching Sheet with a Power-Law Velocity, in: Differential and Difference Equations with Applications (Springer Proceedings in Mathematics and Statistics; 164. ICDDEA, Amadora, Portugal, 2015), Springer, Bazel, 2016, 131–139.

[11] J. Chen, D. Sonawane, K. Mitra. V. R. Subramanian, Yet another code for Boundary Value Problems- Higher Derivative Method, manuscript

[12] W. E. Milne, Numerical Solution of Differential Equations, John Wiley & Sons, 1953.

[13] J. L. Neuringer, R. E. Rosensweig, Ferrohydrodynamics, Phys. Fluids 7 (1964), 1927-1937.

[14] J. L. Neuringer, Some viscous flows of a saturated ferrofluid under the combined influence of thermal and magnetic field gradients, J. Non-linear Mech. 1 (1966), 123–127.

[15] P. G. Siddheshwar, U. S. Mahabaleshwar, Effect of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet, Int. J. Non-Linear Mech. 40 (2005), 807–820.

Cite this paper

Gabriella Bognár, Krisztián Hriczó. (2018) Similarity Analysis for a Heated Ferrofluid flow in Magnetic Field. Journal of Electromagnetics, 3, 9-13