Abstract :
Laminar flow forced convective heat transfer in ducts with slowly varying cross-section is analysed. The analysis is based on a simplifying assumption concerning the velocity field, called the similarity assumption. It is assumed that the axial velocity profile is locally fully developed, irrespective of the variation of the cross-sectional area with axial position. It is shown that in the axisymmetric case (circular tube with varying diameter) for boundary conditions of the first kind the diameter variation has no influence at all on the heat transferred. As in the case of a tube with constant diameter, the degree of temperature equilibration depends only on the Fourier numberFo=πaLQthat is on the ratio of length of the tube, L, to flow rate Q. In the case of a plane channel, however, variations of the channel height 2H have a pronounced influence on the transfer coefficient. It is shown that the degree of equilibration depends only on the effective Fourier numberFoeff=aBQ·∫0LdzH(z).The heat transfer is enhanced by a narrow design of the duct. These results hold for any shape of the axial velocity distribution over the duct cross-section, provided the above-mentioned similarity assumption is justified.
