RT Journal Article
ID 208167523f1ab575
A1 Souhar, K.
A1 Aniss, S.
A1 Ouazzani, M. T.
T1 EFFECT OF TEMPERATURE MODULATION ON THE ONSET OF CONVECTION IN A HELE-SHAW CELL
JF Journal of Porous Media
JO JPM
YR 2011
FD 2011-06-23
VO 14
IS 6
SP 533
OP 539
K1 Hele-shaw cell
K1 convection
K1 temperature modulation
AB 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.
PB Begell House
LK http://dl.begellhouse.com/journals/49dcde6d4c0809db,77fb6f130f547d4a,208167523f1ab575.html