Linear and non-linear magneto-convection in couple stress fluid with non-classical heat conduction law

A theoretical examination of the thermal convection for a couple stress fluid which is electrically conductive and possessing significant thermal relaxation time with an externally applied magnetic field is carried out. Fourier's law fails when fluids are subjected to rapid heating or when it is confined and in the case of nano-devices. A frame invariant constitutive equation for heat flux is considered. The linear analysis is carried out implementing a normal mode solution and the non-linear stability of the system is analyzed using a double Fourier series. The analysis of the transfer of heat is determined in terms of the Nusselt number. (paper)