EFFECT OF SECONDARY FLOW ON TEMPERATURE FIELD AND PRIMARY FLOW IN A HEATED HORIZONTAL TUBE

Density variations in a fluid flowing in a heated horizontal tube can cause a secondary flow as well as variations in the axial pressure gradient over the tube cross section. The effect of the secondary flow on the temperature field and the primary flow at the outlet of a long electrically heated tube haying thick walls of high conductivity is analyzed for the case of large Grashof-Prandtl number for which a thin temperature boundary layer exists near the wall A model for the flow field is developed which is consistent with the experimental observation that over most of the tube the isotherms are horizontal By dimensional reasoning it is found that the secondary flow controls the rate of heat transfer. For P = 1 the primary flow also shows a boundary layer behavior while for P → ∞ the primary flow is independent of the secondary flow. For constant viscosity and infinite Prandtl number, the Nusselt number is directly proportional to the fourth root of the product of the Grashof and the Prandtl number. N = C1 (GP) 1 4 By integral methods it is estimated that C1 = 0·471. Good agreement is obtained between calculations based on the proposed model and experiment. © 1969.