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Convection by a horizontal thermal gradient

This paper considers a paradigm large-Prandtl-number, large-Rayleigh-number forced convection problem suggested by the batch melting process in the glass industry. Although the fluid is heated from above, non-uniform heating in the horizontal direction induces thermal boundary layers in which colder liquid is driven over hotter liquid. This leads to an interesting selection problem in the boundary layer analysis, whose resolution is suggested by a combination of analytical and numerical evidence.