© 1959 by Oxford University Press
LAMINAR CONVECTION IN UNIFORMLY HEATED HORIZONTAL PIPES AT LOW RAYLEIGH NUMBERS
( (Department of Mathematics, Manchester University) )
The well-known solution for laminar forced convection in a uniformly heated pipe neglects the effect of buoyancy forces caused by temperature variations in the fluid. This effect depends on the orientation, but in a horizontal pipe it produces a circulation of the fluid in a direction normal to the pipe axis, with a consequent modification of the main flow. The present treatment includes these buoyancy effects, but is restricted to small rates of heating (which correspond with small temperature gradients along the pipe wall) so that the motion due to buoyancy can be regarded as a secondary flow. In this way solutions for the velocity and temperature fields far from the pipe entrance have been obtained as power series, which are shown to depend on the dimensionless parameter AB, where A is a Rayleigh number based on temperature gradient along the pipe wall and B is a Reynolds number based on pressure gradient along the pipe axis. The Nusselt number and the resistance coefficient have been calculated up to the terms in (AB)2, and the forced convection solution is shown to be in error by about 10 per cent for AB = 3,000.