Stationary solutions of a heated magnetic fluid model

ABSTRACT

We consider the differential system which describes the steady flow and heat transfer of an incompressible viscous magnetic fluid in the presence of a heat source and an external magnetic field. The system consists of the stationary incompressible Navier–Stokes equations, the magnetostatic equations and the stationary heat equation. We prove, for the differential system posed in a bounded domain of and equipped with boundary conditions, the existence of weak solutions by using regularization of the Kelvin body force, linearization, and the Schauder fixed point theorem.

Keywords:

• Magnetic fluid flow
• Navier–Stokes equations
• heat equation
• weak solutions

AMS Subject Classifications:

• 35Q35
• 76D05

Notes

No potential conflict of interest was reported by the authors.