Chebyshev Spectral Collocation Method Approximation to Thermally Coupled MHD Equations

Authors : Önder TÜRK

Pages : 355-366

View : 17 | Download : 11

Publication Date : 2018-10-05

Article Type : Research Paper

Abstract :In this study, a Chebyshev spectral collocation method insert ignore into journalissuearticles values(CSCM); approximation is proposed for solving the full magnetohydrodynamics insert ignore into journalissuearticles values(MHD); equations coupled with energy equation. The MHD flow is two-dimensional, unsteady, laminar and incompressible, and the heat transfer is considered using the Boussinesq approximation for thermal coupling. The flow takes place in a square cavity which is subjected to a vertically applied external magnetic field, and the presence of the induced magnetic field is also taken into account due to the electrical conductivity of the fluid. The governing equations given in terms of stream function, vorticity, temperature, magnetic stream function, and current density, are solved iteratively using CSCM for the spatial discretisation, and an unconditionally stable backward difference scheme for the time integration. The induced magnetic field is obtained by means of its relation to the magnetic stream function. The behaviours of the flow and the heat transfer are investigated for varying values of Reynolds insert ignore into journalissuearticles values($Re$);, magnetic Reynolds insert ignore into journalissuearticles values($Rem$);, Rayleigh insert ignore into journalissuearticles values($Ra$); and Hartmann insert ignore into journalissuearticles values($Ha$); numbers.
Keywords : MHD, CSCM, Heat transfer