Abstract
An Oberbeck-Bussinesq type model for convection in isothermically incompressible liquid crystals (nematics and cholesterics) is proposed. For its derivation, the nonequilibrium thermodynamics and asymptotic methods are employed. The model is based on the Leslie-Ericksen-Parodi (LEP) continuum theory [1–4] taken with some minor modifications. The problem of the thermal gravity convection in a plane horizontal layer with ‘free undeformable’ boundary and under the action of external magnetic or electric field is considered. Solution of this problem is obtained and presented in an explicit analytical form. Existence of the explicit analytical solution is very useful, since it allows us to investigate the influence of various parameters (Leslie coefficients, Frank moduli, anisotropic thermo-diffusivity, etc.) at the onset of convection.
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