English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The onset of thermal convection of a Boussinesq fluid located in an unbounded layer heated from below and subject simultaneously to rotation and magnetic field, whose vectors act in different directions, is presented. To the knowledge of the authors, the convective thermal instability analysis for this complex problem has not been previously reported. In this paper, we use the Tau Chebyshev spectral method to calculate the value of the critical parameters (wave number and Rayleigh number at the onset of convection) as a function of (i) different kinds of boundaries, (ii) angle between the three vectors, and (iii) different values of the Taylor number <path id="x1D447" d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22t37 -4h417q23 0 33.5 5t25.5 21h23z" /> (rate of rotation) and magnetic parameter <path id="x1D444" d="M745 361q0 -134 -83.5 -233t-214.5 -130l16 -11q97 -67 250 -132l-8 -23q-76 3 -131 16q-81 19 -242 125l-20 13q-129 8 -209 91t-80 208q0 160 116 271t289 111q136 0 226.5 -83t90.5 -223zM645 356q0 127 -57.5 201.5t-169.5 74.5q-126 0 -210.5 -104.5t-84.5 -248.5q0 -97 46 -166.5t129 -87.5l84 15l29 -19q104 21 169 121.5t65 213.5z" /> (strength of the magnetic force). For the classical problems previously reported in the literature, we compare our calculations with Chandrasekhar’s variational method results and show that the present method is applicable.

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