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

Table 10

Thermal instability analysis in the presence of a rotation and a magnetic field when both bounding surfaces are free: gravity vector 𝐠 parallel to both rotation vector 𝛀 and magnetic field vector 𝐇. Critical Rayleigh numbers and wave numbers at marginal stability for the onset of stationary convection. Taylor number 𝑇₁ = 𝑇/𝜋⁴=10⁵ for various values of the dimensionless magnetic parameter 𝑄₁ = 𝑄/𝜋². 𝑅 and 𝑎 are the Rayleigh number and the wave number, respectively, obtained by the Tau Chebyshev method. 𝑅_Ch and 𝑎_Ch are the Rayleigh number and the wave number, respectively, obtained by Chandrasekhar [1]. The superscripts 1 and 2 mean the two minima of the Rayleigh number.

𝑄1	𝑎^1	𝑅^1	𝑎^1Ch	𝑅^1Ch	𝑎^2	𝑅^2	𝑎^2Ch	𝑅^2Ch
10	18.87	4.066𝐸5	18.9	4.067𝐸5	—	—	—	—
50	18.58	4.028𝐸5	18.6	4.028𝐸5	3.49	7.261𝐸5	3.48	7.261𝐸5
100	18.2	3.976𝐸5	18.2	3.977𝐸5	3.365	3.932𝐸5	3.37	3.933𝐸5
1000	—	—	—	—	5.675	1.828𝐸5	5.67	1.829𝐸5
10000	—	—	—	—	12.29	1.081𝐸6	12.3	1.082𝐸6
100000	—	—	—	—	18.9	1.015𝐸7	18.9	1.015𝐸7