Thermal instability of compressible electrically conducting couple-stress fluid in the presence of a uniform magnetic field

The problem of thermal instability of compressible, electrically conducting couple-stress fluid in the presence of a uniform magnetic field is considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For stationary convection, the compressibility, couple-stress and magnetic field postpone the onset of convection. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. The principle of exchange of stabilities is found to be satisfied. The magnetic field introduces oscillatory modes in the system that were non-existent in its absence. The case of overstability is also studied wherein a sufficient condition for the non-existence of overstability is obtained.