Onset of convection in impulsively heated or cooled fluid layers

Abstract

Energy stability theory is employed to determine lower bounds on onset times and global stability bounds for initially isothermal fluid layers subjected to impulsive changes in surface temperature. Various combinations of rigid and free boundary conditions and heating or cooling are considered.

Relaxation on the energy method for the transient Rayleigh–Bénard convection

“…The last two models require the initial conditions at the heating time t = 0 and the criterion to define manifest convection. Energy method also has applied into this problem [6][7][8]. Even though energy method requires much computational load, it gives only a lower bound for the onset of the instability and * Corresponding author.…”

Theoretical analysis of Marangoni instability of an evaporating droplet by energy method

“…He also claimed that, for the cases when Ma c varied monotonically with time, the optimal stability boundary remained the same even if dk=dt > 0. Neitzel [8] reported that there existed cases where Ma c did not decrease with time monotonically (i.e. the stability curve reached a minimum first and then began to increase toward a steady-state limit) and care had to be taken for this situation.…”

“…To resolve these deficiencies, the energy method seems to be very promising. Homsy [7] employed the energy method (corrected later by Neitzel [8]) to analyze the stability of a liquid layer heated or cooled impulsively. The region of finiteamplitude convection was demarcated in a Rayleigh number-time plane.…”

“…A condition of constant heat flux from the free surface is usually used to model the evaporation. Many studies have been made to analyze the instability of a planar liquid layer suddenly cooled from above or heated from below [1,7,8,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Much less work has been done on the onset of Marangoni instability in a spherical geometry.…”

Görtler vortices in the Rayleigh layer on an impulsively started cylinder

“…12 It is one of the aims of this paper to show that these conflicting conditions can lead to results which have a rigorous mathematical justification. When quasi-steady theory is inapplicable, energy-stability theory provides an alternative approach and this technique has been employed in a range of other papers [13][14][15] concerned with both centrifugal and thermal instabilities.…”