Completely passive natural convection

Natural convection is a basic process which is important in a wide variety of practical applications [1,2]. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. The effects of added viscous dissipation heat have been considered [3–8]. The fluid motions in all previous works are driven by either an applied pressure gradient or by applied heating of the walls. We consider a long duct, with no pressure gradient, and with the temperature of the walls the same as the ambient reference temperature. In such a completely passive environment there is no energy input, no temperature difference, and no motion. But is there a possibility of nontrivial fluid motion? The purpose of the present Note is to investigate whether a completely passive vertical duct (no applied pressure gradient or applied boundary heat) can support sustained fluid motion. The idea is simple. Fluid motion causes dissipative heat, heat causes buoyancy, and buoyancy causes fluid motion.