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Existence and uniqueness for magnetohydrodynamic flows in pipes with viscosity dependent on the temperature. (English) Zbl 1162.76058

Summary: We study the steady motion of a viscous fluid in pipes of arbitrary cross-sections under a transverse magnetic field, assuming that the viscosity and electric and thermal conductivities are given functions of the temperature. Theorems on existence and uniqueness for the nonlinear elliptic system governing the problem are presented.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
35Q60 PDEs in connection with optics and electromagnetic theory
80A20 Heat and mass transfer, heat flow (MSC2010)
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