두개의 수직 다공성 벽면을 가진 좁은 간격에서의 유체의 열적 불안정성

Thermal Instability of Fluid in a Slot between Two Vertical Permeable Walls

An analytical study on the thermal instability of fluid in a vertical solt between two permeable walls has been carried out using fast converging power series solution method. For given values of prandtl number Pr and permeability paramter ${\sigma}$, the critical Grashof number $Gr_c$ and the critical wave number ac are found as eigenvalues of the problem formulated by the stability equations and the appropriate boundary conditions which are derived on the basis of linear stability theory. In the case of ${\sigma}\;>\;10^4$, the results approach those of solid boundary case, but in the case of ${\sigma}\;<\;10^3$, the decrease of $Gr_c$ and $a_c$become more prominent. In other words, the permeable walls cause the flow to be more unstable than the solid walls. This is considered to be due to the slip of the fluid on the wail, which decrease the friction force.