A Mathematical Theorem on the Onset of Stationary Convection in Couple-Stress Fluid

The thermal instability of a couple-stress fluid heated from below is investigated. Following the linearized stability theory and normal mode analysis, the paper mathematically establishes that the onset of instability at marginal state, cannot manifest itself as stationary convection, if the thermal Rayleigh number R and the couple-stress parameter F, ۳ satisfy the inequality   ۲  ۲ ۲  ۲  ۱  ۳ F  ۳ F  ۱  ۳ F  ۱    , and when the couple-stress parameter F is R  ۲ ۲ ۲۷ F  ۱  ۱  ۳ F    infinitesimally small, R    ۲۷ ۴ ۴  ۲    F  , the result which also clearly mathematically established the stabilizing ۱  ۲     character of the couple-stress.

Keywords:

Thermal convection , Couple , stress fluid , Rayleigh number