Transient laminar natural convection along rectangular ducts (Q5961148)

The authors derive analytical solutions for the temperature and fluid velocity in transient laminar natural convection along rectangular ducts with prescribed uniform boundary temperatures. It is proved that: the flow is necessarily thermally developed; no pressure drop occurs in the channel; the dimensionless volumetric flow rate, the mixing cup temperature and the average Nusselt number are only time-dependent. Their time response depends on the Prandtl number, while their asymptotic value is constant (for the cup temperature) or depends only on the channel aspect ratio (for the volumetric flow rate and average Nusselt number).