The paper is devoted to the theoretical investigation of the possible existence of
stationary mixing layers and of their structure in nearly perfectly conducting, nearly
inviscid fluids with a longitudinal magnetic field. A system of two equations is used,
which generalizes the well-known Blasius equation (for flow around a semi-infinite
plate) to the case under consideration. The system depends on the magnetic Prandtl
number, Pm=ν/νm, where ν and νm are the usual and the magnetic viscosities,
respectively.For the existence of stationary flows the ratio between the flow velocity vx and
the Alfvén velocity cA=Hx/(4πρ)1/2 (ρ being the fluid density) plays a critical role.
Super-Alfvén (vx>cA) flows are possible at any value of Pm and for any values of vx
and Hx on the layer boundaries. Sub-Alfvén (vx<cA) stationary flows are impossible
at any value of Pm and for any values of the differences in vx and Hx across the
layer, except for two cases: Pm=0 and Pm=1. When Pm=0, i.e. when the fluid is
strictly inviscid, ν=0, flow is possible in both the super- and sub-Alfvén regimes;
however, the magnetic field must be uniform, Hx=const, Hy=0 in this case. For
Pm=1 both flow regimes are also possible; however, the sub-Alfvén flow is possible
only for a definite relationship between the magnetic field and velocity differences:
ΔHx=−δvx (in corresponding units). For the case where the relative differences in
vx and Hx across the layer are small, Δvx[Lt ]vx, ΔHx[Lt ]Hx, solutions are obtained in
explicit form for arbitrary Pm (here vx and Hx are averaged over the layer). For the
specific case Pm=1, exact analytical solutions of basic system are found and studied
in detail.
Heat Transfer Effects on Free Convection of Viscous Dissipative Fluid Flow Over an Inclined Plate with Thermal Radiation in the Presence of Induced Magnetic Field
