An Observation on the use of Dimensional Analysis and Similarity Relations in Non-Uniform Heat Transfer

Abstract

The theoretical study of heat transfer in ducts and passages which are not circular is difficult. In addition to geometrical and hydrodynamic problems, thermal aspects such as non-uniformity of heat transfer at the section boundary, increase the number of variables to be taken into account. The popular and perhaps simplest technique for the prediction of heat transfer in forced turbulent convection in non-circular ducts, is to use the more easily determined equation for an equivalent circular section. The form of the equation, which is used to correlate experimental data for the simpler case of heat transfer in the circular section, may be derived from considerations of similarity or alternatively by dimensional analysis. (Reference may be made to the classical work of W. Nusselt at the early part of the present century for the derivation of such an equation.) The equivalent circular pipe is equivalent in two respects. It is a pipe which has the same pressure drop and same heat transfer as the non-circular duct under consideration for the same conditions. The diameter of the equivalent pipe which replaces the non-circular section will be discussed later.