THERMAL SCIENCE

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Mohammad Mehdi Rashidi

,

Navid Freidooni Mehr

SERIES SOLUTIONS FOR THE FLOW IN THE VICINITY OF THE EQUATOR OF AN MHD BOUNDARY-LAYER OVER A POROUS ROTATING SPHERE WITH HEAT TRANSFER

ABSTRACT
In this paper, an analytical method (DTM-Padé) is employed to solve the flow and heat transfer near the equator of an MHD boundary-layer over a porous rotating sphere. This method is used to give solutions of nonlinear ordinary differential equations with boundary conditions at infinity. The velocity components in all directions (meridional, rotational and radial) and temperature fields are derived. The obtained results are verified with the results of numerical solution. A very good agreement can be observed between them. The effect of involved parameters such as magnetic strength parameter, rotation number, suction/blowing parameter and Prandtl number on the all-different types of velocity components, temperature field and surface shear stresses in meridional and rotational directions, infinite radial velocity and rate of heat transfer is checked and discussed.
KEYWORDS
MHD flow, rotating sphere, heat transfer, DTM-Padé, boundary-layer, shear stresses
PAPER SUBMITTED: 2012-03-01
PAPER REVISED: 2012-08-27
PAPER ACCEPTED: 2012-08-27
DOI REFERENCE: https://doi.org/10.2298/TSCI120301155R
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2014, VOLUME 18, ISSUE Supplement 2, PAGES [S527 - S537]
REFERENCES
  1. Singh, S.N., Laminar Boundary Layer on a Rotating Sphere, Physics of Fluids, 13 (1970), 10, pp. 2452-2454
  2. Ranger, K.B., M.H.D. Rotation of a Conducting Sphere in the Presence of a Uniform Magnetic Field, SIAM Journal on Applied Mathematics, 19 (1970), 2, pp. 351-355
  3. Ingham, D., Non-unique solutions of the boundary layer equations for the flow near the equator of a rotating sphere in a rotating fluid, Acta mechanica, 42 (1982), 1, pp. 111-122
  4. Takhar, H., Chamkha, A., Nath, G., Unsteady laminar MHD flow and heat transfer in the stagnation region of an impulsively spinning and translating sphere in the presence of buoyancy forces, Heat and Mass Transfer, 37 (2001), 4, pp. 397-402
  5. Chamkha, A.J., Takhar, H.S., Nath, G., Unsteady MHD rotating flow over a rotating sphere near the equator, Acta mechanica, 164 (2003), 1-2, pp. 31-46
  6. Kumari, M., Nath, G., Transient MHD rotating flow over a rotating sphere in the vicinity of the equator, International Journal of Engineering Science, 42 (2004), 17-18, pp. 1817-1829
  7. Dinarvand, S., Doosthoseini, A., Doosthoseini, E., Rashidi, M.M., Series solutions for unsteady laminar MHD flow near forward stagnation point of an impulsively rotating and translating sphere in presence of buoyancy forces, Nonlinear Analysis: Real World Applications, 11 (2010), 2, pp. 1159-1169
  8. Bég, O.A., Takhar, H.S., Nath, G., Chamkha, A.J., Mathematical modelling of hydromagnetic convection from a rotating sphere with impulsive motion and buoyancy effects, Nonlinear Analysis: Modelling and Control, 11 (2006), 3, pp. 227-245
  9. Sweet, E., Vajravelu, K., Van Gorder, R., Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator, Central European Journal of Physics, 9 (2011), 1, pp. 167-175
  10. Dorch, S., Magnetohydrodynamics, Scholarpedia, 2 (2007), 4, pp. 2295-2297
  11. Davidson, P.A., An introduction to magnetohydrodynamics, Cambridge University Press, 2001
  12. Torabi, M., Yaghoobi, H., Saedodin, S., Assessment of homotopy perturbation method in nonlinear convective-radiative non-fourier conduction heat transfer equation with variable coefficient, Thermal Science, 15 (2011), 2, pp. 263 - 274
  13. Domairry, D., Ziabkhsh, Z., Domiri, H., Determination of temperature distribution for annular fins with temperature dependent thermal conductivity by HPM, Thermal Science, 15 (2011), 5, pp. 111-115
  14. Liao, S.J., Beyond perturbation: introduction to the homotopy analysis method, Chapman & Hall/CRC, 2004
  15. Fatma, A., Applications of differential transform method to differential-algebraic equations, Applied Mathematics and Computation, 152 (2004), 3, pp. 649-657
  16. Fatma, A., Solutions of the system of differential equations by differential transform method, Applied Mathematics and Computation, 147 (2004), 2, pp. 547-567
  17. Rashidi, M.M., Erfani, E., A new analytical study of MHD stagnation-point flow in porous media with heat transfer, Computers and Fluids, 40 (2011), 1, pp. 172-178
  18. Arikoglu, A., Ozkol, I., Solution of differential-difference equations by using differential transform method, Applied Mathematics and Computation, 181 (2006), 1, pp. 153-162
  19. Arikoglu, A., Ozkol, I., Solution of boundary value problems for integro-differential equations by using differential transform method, Applied Mathematics and Computation, 168 (2005), 2, pp. 1145-1158
  20. Rashidi, M.M., The modified differential transform method for solving MHD boundary-layer equations, Computer Physics Communications, 180 (2009), 11, pp. 2210-2217
  21. Rashidi, M.M., Mohimanian Pour, S.A., A novel analytical solution of heat transfer of a micropolar fluid through a porous medium with radiation by DTM-Padé, Heat Transfer—Asian Research, 39 (2010), 8, pp. 575-589
  22. Rashidi, M.M., Keimanesh, M., Using Differential Transform Method and Pade Approximant for Solving MHD Flow in a Laminar Liquid Film from a Horizontal Stretching Surface, Mathematical Problems in Engineering, 2010 (2010), pp. 1-14
  23. Turkyilmazoglu, M., Numerical and analytical solutions for the flow and heat transfer near the equator of an MHD boundary layer over a porous rotating sphere, International Journal of Thermal Sciences, 50 (2011), 5, pp. 831-842
  24. Kármán, T.V., Über laminare und turbulente Reibung, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1 (1921), 4, pp. 233-252
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Series solutions for the flow in the vicinity of the equator of an MHD boundary-layer over a porous rotating sphere with heat transfer

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