The purpose of this study is to develop mathematical and numerical tools for modeling and simulating hot plasma in a rigid cylindrical pipe.

The equations governing this problem are the continuity, momentum, and energy equations coupled with electromagnetic equations. This system translates the magnetohydrodynamic description of plasma, and the coupling is achieved through the Lorentz force term.

The system of partial differential equations derived from this physical model is a nonlinear system of partial differential equations that will be solved numerically using the finite volume method. This is a powerful discretization method that uses a simple approximation of the unknown to transform partial differential equations into a system of algebraic equations. In this method, the calculation domain is subdivided into several non-overlapping control volumes (finite volumes), such that each volume surrounds a mesh point. The differential equation is then integrated into an elementary control volume.

The result of this integration gives an algebraic equation. This equation expresses the principle of conservation of the function over the control volume, and the solution is obtained by numerical resolution. This requires reformulating the equation using the finite volume method and implementing it in a FORTRAN program.

We carry out numerical study of natural convection of argon plasma in a rigid vertical cylindrical pipe heated from below and subjected to a uniform axial magnetic field. The objective is to analyze the effect of the magnetic field (via the Hartmann number), bottom heating, and the thermophysical properties of the plasma (via the Prandtl, Grashof, and Rayleigh numbers) on the velocity and temperature distributions. The study is based on solving the dimensionless system of MHD equations in cylindrical coordinates using the finite volume method.

hot plasma, magnetohydrodynamics (MHD), liquid metal, numerical modeling, natural convection, finite volume method