Laminar duct flow natural convection

J. R. Dyer, The Development of Laminar Natural Convection Flow in a Vertical Uniform Heat Flux Duct, Int. J. Heat Mass Transfer (18) 1455-1465,1975. 

Laminar Flow Normally, laminar flow occurs in closed ducts when Npe < 2100 (based on equivalent diameter = 4 x free area h-perimeter). Laminar-flow heat transfer has been subjected to extensive theoretical study. The energy equation has been solved for a variety of boundary conditions and geometrical configurations. However, true laminar-flow heat transfer very rarely occurs. Natural-convection effects are almost always present, so that the assumption that molecular conduction alone occurs is not valid. Therefore, empirically derived equations are most rehable. 

Equipment designs based on indirect conduction usually transfer the heat from the primary heat transfer fluid to the intermediate wall within some kind of internal duct or channel. Transfer coefficients for these cases depend on the nature of the flow (laminar or turbulent) and the geometry of the duct or channel (short or long). Expressions for evaluating the transfer coefficients for these cases are available in standard texts. An expression for the convective thermal resistance can be generated similar to that derived for the conductive resistance ... 

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