A compressible Walters' (Model B') elastico-viscous dusty fluid layer heated from below in the presence of a vertical magnetic field to include the effect of Hall currents is considered. For the case of stationary convection, Walters' (Model B') elastico-viscous fluid behaves like an ordinary Newtonian fluid. The Hall currents and dust particles are found to have a destabilizing effect on the thermal convection, whereas compressibility and the magnetic field are found to have a stabilizing effect on the thermal convection. The viscoelasticity and magnetic field (and hence the Hall currents) introduce oscillatory modes in the system, which were non-existent in their absence. Graphs are also plotted for the critical Rayleigh number and various parameters by giving some numerical values to the parameters
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