Recirculating Combined Convection in Laminar Pipe Flow

Investigations are conducted into situations where flow recirculation occurs in laminar combined convection flows in vertical circular tubes. Particular attention is given to flows in which finite sections of the tube wall are maintained at constant temperatures, which may be either hotter or colder than the temperature of the fluid at the entrance of the tube. A numerical study is carried out in which the governing elliptic partial differential equations are expressed in finite difference form and solved using a relaxation technique. The values of the governing parameters, namely the Reynolds, Prandtl, and Grashof numbers, and the thermal and viscous boundary conditions are chosen to correspond as closely as possible to an experimental investigation that involves water being forced along a perspex vertical circular tube, which is heated and/or cooled over finite sections. It is found that the numerical model is able to predict quite accurately the location, shape, and size of the recirculation regions observed in the experiments.