Porous Channel Flows with Spontaneously Broken Symmetry

It is known that even entirely symmetric boundary value problems can admit solutions in which the inherent symmetry of the governing equations gets spontaneously broken. When this happens, two non-symmetric “twin solutions” occur so that the symmetry of the boundary value problem broken in the two individual solutions becomes restored by the twins. The present paper shows that, as a combined effect of buoyancy, viscous dissipation and pressure work, in a mixed convection flow in a vertical porous channel with isothermal walls, in addition to symmetric solutions, precisely this kind of twin solutions with broken symmetry can occur, although the walls are kept at the same temperature. The existence of another remarkable solution branch which describes symmetric adiabatic flows corresponding to nonlinear eigenvalues of the problem is also reported. The heat–work balance of all these steady-flow states is discussed in detail. The analysis is supported by an intuitive point-mechanical analogy. The equivalence of this mechanical energy analysis to the standard phase space method is also discussed shortly.