A Linear Stability Analysis of Thermal Convection in a Fluid Layer with Simultaneous Rotation and Magnetic Field Acting in Different Directions

Table 3

Critical Rayleigh numbers and wave numbers at marginal stability for the onset of stationary convection when both bounding surfaces are free. Gravity vector 𝐠 parallel to the rotation vector 𝛀. 𝑇 is the Taylor number. 𝑅 is the Rayleigh number obtained by the Tau Chebyshev method. 𝑅_Ch is the Rayleigh number obtained by Chandrasekhar [1].

𝑇	𝑎	𝑅	𝑅Ch	𝑇	𝑎	𝑅	𝑅Ch
10^2	2.594	8.262𝐸2	8.263𝐸2	10^6	12.86	9.222𝐸4	9.222𝐸4
10^3	3.710	1.676𝐸3	1.676𝐸3	10^8	28.02	1.897𝐸6	1.897𝐸6
10^4	5.698	5.377𝐸3	5.377𝐸3	10^11	88.87	1.875𝐸8	1.876𝐸8
10^5	8.626	2.130𝐸4	2.131𝐸4	10^13	191.51	4.037𝐸9	4.037𝐸9