Title:

Heat transfer in a pipe with an abrupt change of section : the effect of an abrupt change of section on the coefficient of heat transfer between a pipe and water flowing through it

When a fluid is heated while flowing through a pipe the phenomenon of heat transfer between the pipe and the fluid may be broadly classified into two types. If the pipe is straight, of uniform diameter and of sufficient length, a fully developed condition will be reached such that the nature and degree of turbulence will no longer vary. Such turbulence is called "normal turbulence". Under this condition, heat transfer coefficients do not vary with distance along the pipe. If, on the other hand, the fluid has just passed an abrupt change of section in the pipe, "excess turbulence" will exist with a resulting increase in heat transfer coefficient. The author has carried out a series of experiments, from which a measurement has been obtained of the variation of local heat transfer coefficient due to both all abrupt enlargement, and an abrupt contraction, in a pipe. The experimental pipe, which was of brass, consisted of 9 feet of 1 inch diameter pipe coupled to 18 feet of 2 inch diameter pipe, the coupling being in the form of an abrupt change of section. Water flowed through the pipe which was heated by the passage of a high, lowvoltage current through it. The same experimental pipe was used for both abrupt enlargement and abrupt contraction experiments, the direction of water flow relative to the pipe being adjusted accordingly. Local heat transfer coefficients were measured at positions sufficient to give a complete picture of their distribution along the pipe. Tests were carried out for Reynolds Numbers ranging from 4,000 to 100,000 in the 1 inch diameter pipe. Three values of heat input were used at each Reynolds Number. For the normal turbulent flow sections of the pipe, neglecting the effect of heat input, the experimental results were well expressed by the equation Nu = 0.023 Re0.8PR0.4 This equation is in good agreement with the most recent data on heat transfer in normal turbulent flow in pipes. The effect of heat input on the heat transfer coefficient for normal turbulent flow was taken into account by introducing an extra term into the above equation. Thus Nu = 0.023 Re0.8PR0.4 (mua)0.07/(muw) where mua is the viscosity of water at its bulk temperature and muw the viscosity of water at the pipe wall temperature. This effect had not previously been noticed for fluids with viscosities less than twice that of water. The effect of the abrupt change of section on the heat transfer coefficient was expressed in two ways. Firstly, Nusselt equations were derived from which the local heat transfer coefficient could be calculated at any position in the excess turbulent flow sections of the pipe. Secondly, the total effect of the change of section was estimated in terms of an equivalent number of extra ''normal" diameters of pipe length.
