We study the instability of a Bénard layer subject to a vertical uniform magnetic field, in which the fluid obeys the Maxwell-Cattaneo (MC) heat flux-temperature relation. We extend the work of Bissell (Proc. R. Soc. A, 472: 20160649, 2016) to non-zero values of the magnetic Prandtl number p_m. With non-zero p_m, the order of the dispersion relation is increased, leading to considerably richer behaviour. An asymptotic analysis at large values of the Chandrasekhar number Q confirms that the MC effect becomes important when CQ^1/2 is O(1), where C is the Cattaneo number. In this regime, we derive a scaled system that is independent of Q. When CQ^1/2 is large, the results are consistent with those derived from the governing equations in the limit of the Prandtl number p → ∞ with p_m finite; here we identify a new mode of instability, which is due neither to inertial nor induction effects. In the large p_m regime, we show how a transition can occur between oscillatory modes of different horizontal scale. For Q >> 1 and small values of the Prandtl number p, we show that the critical Rayleigh number is non-monotonic in p, provided that C >1/6. While the analysis of this paper is performed for stress-free boundaries, it can be shown that other types of mechanical boundary conditions give the same leading order results.

MATLAB files for generating and plotting the figures. (The exception is that the data for figure 1 was produced by FORTRAN code: also included.)

Introductory comments at the head of each code.