Effects of Viscous Dissipation on the Thermal Instability of Plane Couette Flow Heated from Below

밑으로부터 가열되는 평면 Couette 유동에서 점성소산이 열적 불안정성에 미치는 영향

An analysis has been given for the effect of viscous dissipation on the thermal instability of plane Couette flow between two parallel plates maintained at different constant temperatures. Under the assumption that the principle of the exchange of stabilities holds, stationary disturbance quantities in the form of longitudinal vortices are considered. The magnitudes of disturbance quantities are then represented as fast convergent power series so that the eigenvalue problem for determining the onset conditions of the thermal instability may be reduced to a simplified problem of finding the roots of a $4{\times}4$ determinant. It is shown that as the magnitude of the visucous dissipation increases the flow becomes more susceptible to instabilities, which is in very good agreement with previous results obtained in some related researches.