Summary
Magnetohydrodynamic natural convection boundary layer flow on a sphere with uniform heat flux in presence of heat generation has been investigated in this paper. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is then solved numerically by two distinct efficient methods, namely (i) implicit finite difference method together with the Keller box scheme and (ii) perturbation or series solution technique. The results of the surface shear stress in terms of local skin friction and the rate of heat transfer in terms of local Nusselt number, velocity distribution as well as temperature distribution are shown graphically for a selection of parameter sets consisting of the heat generation parameter and the magnetic parameter.
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References
K. Vajravelu A. Hadjinicolaou (1997) ArticleTitleConvective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream Int. J. Engng. Sci. 35 1237–1244 Occurrence Handle0907.76084 Occurrence Handle10.1016/S0020-7225(97)00031-1
M. K. Chowdhury M. N. Islam (2000) ArticleTitleMHD free convection flow of visco-elastic fluid past an infinite porous plate Heat Mass Transf. 36 439–447 Occurrence Handle10.1007/s002310000103
A. Raptis N. Kafousian (1982) ArticleTitleMagnetohydrodynamic free convection flow and mass transfer through a porous medium bounded by an infinite vertical porous plate with constant heat flux Can. J. Phys. 60 1725–1729
M. A. Hossain M. Ahmed (1990) ArticleTitleMHD forced and free convection boundary layer flow near the leading edge Int. J. Heat Mass Transf. 33 IssueID3 571–575 Occurrence Handle10.1016/0017-9310(90)90190-6
M. A. Hossain K. C. A. Alam D. A. S. Rees (1997) ArticleTitleMHD forced and free convection boundary layer flow along a vertical porous plate Appl. Mech. Engng. 2 33–51 Occurrence Handle0896.76086
T. Chiang A. Ossin C. L. Tien (1964) ArticleTitleLaminar free convection from a sphere ASME J. Heat Transf. 86 537–542
M. J. Huang C. K. Chen (1987) ArticleTitleLaminar free convection from a sphere with blowing and suction ASME J. Heat Transf. 109 529–532 Occurrence Handle10.1115/1.3248117
I. Pop T. Grosan N. Amin R. Nazar (2002) ArticleTitleFree convection boundary layer on an isothermal sphere in a micropolar fluid Int. Comm. Heat Mass Transf. 29 377–386 Occurrence Handle10.1016/S0735-1933(02)00327-5
T. S. Chen A Mocoglu (1977) ArticleTitleAnalysis of mixed forced and free convection about a sphere Int. J. Heat Mass Transf. 20 867–875 Occurrence Handle0379.76077 Occurrence Handle10.1016/0017-9310(77)90116-8
M. M. Molla M. A. Hossain R. S. R. Gorla (2004) ArticleTitleConjugate effect heat and mass transfer in natural convection flow from an isothermal sphere with chemical reaction Int. J. Fluid Mech. Res. 31 319–331 Occurrence Handle10.1615/InterJFluidMechRes.v31.i4.20
Molla, M. M., Hossain, M. A., Paul, M. C.: Radiation effect on natural convection flow from an isothermal sphere. Int. J. Fluid Mech. Res. (in press).
K. Vajravelu A. Hadjinicolaou (1993) ArticleTitleHeat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation Int. Comm. Heat Mass Transf. 20 417–430 Occurrence Handle10.1016/0735-1933(93)90026-R
A. J. Chamkha I. Camille (2000) ArticleTitleEffects of heat generation/absorption and the thermophoresis on hydromagnetic flow with heat and mass transfer over a flat plate Int. J. Numer. Methods Heat Fluid Flow 10 432–448 Occurrence Handle0948.76636 Occurrence Handle10.1108/09615530010327404
M. M. Molla M. A. Hossain L. S Yao (2004) ArticleTitleNatural convection flow along a vertical wavy surface with heat generation/absorption Int. J. Thermal Sci. 43 157–163 Occurrence Handle10.1016/j.ijthermalsci.2003.04.001
T. Cebeci P Bradshaw (1984) Physical and computational aspects of convective heat transfer Springer New York Occurrence Handle0545.76090
H. B. Keller (1978) ArticleTitleNumerical methods in boundary layer theory Ann. Rev. Fluid Mech. 10 417–433 Occurrence Handle0403.76042 Occurrence Handle10.1146/annurev.fl.10.010178.002221
J. C. Butcher (1974) ArticleTitleImplicit Runge-Kutta process Math Comp. 18 50–55 Occurrence Handle159424 Occurrence Handle10.2307/2003405
Nachtsheim, P. R., Swigert, P.: Satisfaction of asymptotic boundary conditions in numerical solutions systems of non-linear equations of boundary layer type. NASA TN-D3004 (1965).
I. Pop D. B. Ingham (2001) Convective heat transfers mathematical and computational modelling of viscous fluids and porous media Pergamon Amsterdam
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Molla, M.M., Hossain, M.A. & Taher, M.A. Magnetohydrodynamic natural convection flow on a sphere with uniform heat flux in presence of heat generation. Acta Mechanica 186, 75–86 (2006). https://doi.org/10.1007/s00707-006-0373-0
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DOI: https://doi.org/10.1007/s00707-006-0373-0