Dual mixed convection flows in a vertical channel

Abstract

The classical problem of the fully developed mixed convection flow with frictional heat generation in a vertical channel bounded by isothermal plane walls having the same temperature is revisited in this paper. The existence of dual solutions of the local balance equations is pointed out. They are either columnar upflows or cellular down–up–down flows. Below a maximum value Ξ max of the governing parameter Ξ = Ge Pr Re (the product of the Gebhart, Prandtl and Reynolds numbers), for any given Ξ a pair of different solutions occurs. The value Ξ max corresponds to a maximum value of the Reynolds number above which no laminar solution can be found. At this maximum value, the two solution branches bifurcate from each other. In the neighborhood of the bifurcation point Ξ max even small perturbations can cause transitions from one flow regime to the other. In the paper, the mechanical and thermal characteristics of the dual flow regimes are discussed in detail both analytically and numerically.