ABSTRAKT

The convective stability of a horizontal Hele-Shaw liquid layer is investigated when the time-dependent periodic temperature, T_m + T_s cos(ω*t*), is applied on the horizontal walls. Here, the stationary component of the applied temperature gradient is set to zero. The objective of the present study is to find the critical conditions under which thermal convection starts and to show that it is possible to advance or to delay the onset of convection by proper tuning of the modulation frequency. Thus, the Floquet theory and a technique of converting a boundary value problem toward an initial value problem are used to solve the linear system of equations corresponding to the onset of convection. We show that in the limit of low and high dimensionless frequency, ω < 0.5 and ω > 50, the basic state tends to a stable equilibrium configuration and for the intermediate dimensionless frequency, ω = 9.68, the system is potentially unstable. Here, only the harmonic solutions exist. The results obtained from an asymptotic study for low and high dimensionless frequencies are in good agreement with the numerical results.