Article

Archive of Applied Mechanics

, Volume 67, Issue 7, pp 478-486

First online:

Unsteady compressible boundary layer flow in the stagnation region of a sphere with a magnetic field

  • H. S. TakharAffiliated withSchool of Engineering, University of Manchester, Manchester, M13 9PL, U.K.
  • , K. YanoAffiliated withDepartments of Aeronautical and Mechanical Engineering The Ohio State University, Columbus OH 43210, U.S.A.
  • , S. NakamuraAffiliated withDepartments of Aeronautical and Mechanical Engineering The Ohio State University, Columbus OH 43210, U.S.A.
  • , G. NathAffiliated withDepartment of Mathematics, Indian Institute of Science, Bangalore 560012, India.

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Summary

An analysis is performed to study the unsteady compressible laminar boundary layer flow in the forward stagnation-point region of a sphere with a magnetic field applied normal to the surface. We have considered the case where there is an initial steady state that is perturbed by the step change in the total enthalpy at the wall. The nonlinear coupled parabolic partial differential equations governing the flow and heat transfer have been solved numerically using a finite-difference scheme. The numerical results are presented, which show the temporal development of the boundary layer. The magnetic field in the presence of variable electrical conductivity causes an overshoot in the velocity profile. Also, when the total enthalpy at the wall is suddenly increased, there is a change in the direction of transfer of heat in a small interval of time.

Key words Unsteady compressible flow boundary layer stagnation point flow MHD finite difference scheme.