The similarity solution for the unsteady laminar incompressible boundary layer flow
of a viscous electrically conducting fluid in stagnation point region of an impulsively
rotating and translating sphere with a magnetic field and a buoyancy force gives a system
of non-linear partial differential equations. These non-linear differential equations are
analytically solved by applying a newly developed method, namely the homotopy analysis
method (HAM). The analytic solutions of the system of non-linear differential equations are
constructed in the series form. The convergence of the obtained series solutions is carefully
analyzed. Graphical results are presented to investigate the influence of the magnetic
parameter, buoyancy parameter and rotation parameter on the surface shear stresses and
surface heat transfer. It is noted that the behavior of the HAM solution for the surface shear
stresses and surface heat transfer is in good agreement with the numerical solution given
in reference [H. S. Takhar, A. J. Chamkha, G. Nath, 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 Mass Transfer 37 (2001) 397].
کلید واژگان :
Impulsive motion Magnetic parameter Buoyancy parameter Rotation parameter Stagnation-point Series solution Convergence Homotopy analysis method
