Nonlinear stability analysis of natural convection in an inclined fluid layer

Abstract

Natural thermal convection in a viscous incompressible fluid layer bounded by two parallel planes and subjected to a temperature gradient is a model problem of hydrodynamical systems. The stability of natural convection and the heat transfer properties get affected by tilting the layer newlineat an angle to the horizontal. In this thesis, we have performed a detailed theoretical and numerical nonlinear energy stability analysis of the basic state of a heated inclined fluid layer. The numerical analysis of the Euler-Lagrange equations, resulting from the sufficient condition of stability, gives the nonlinear stability boundary in terms of the Rayleigh number which is found to depend upon the inclination of the layer with respect to the horizontal. The role of the Prandtl number is also examined. A comparison is made between the linear instability boundary and the nonlinear stability boundary. We have further investigated the stability of the transient state in an inclined fluid layer heated impulsively. The variation of the rate of heat transfer at the boundaries with time is discussed. The nonlinear energy stability of the time-dependent basic state is analysed and the global stability boundary is obtained. We have also studied the effect of uniform internal heating/cooling of the fluid layer on the stability of the inclined layer convection. We have explored the linear stability and the energy stability of an inclined fluid layer excited by time-periodic, sinusoidally varying boundary temperatures. The effect of gravity modulation on the stability is also discussed. newline newline