An Approximate Solution of Oil-Cooling Pipe

Abstract

This paper deals with a mathematical solution on the heat transfer of cooling pipe with constant temperature and laminar flow oil in it. The partial differential equation of temperature distribution and equations of velocity and of pressure gradient are derived, as the viscosity of oil varies only with temperature and the other properties of oil remain unchanged. The author attempts to solve these simultaneous equations. In the process a conception of thermal boundary layer is adopted, and a thermal equation corresponding to the Karman's momentum equation of boundary layer problems is introduced. The calculations of mean temperature θ_m are compared with the author's experimental results, although sufficient coincidence is diffcult to obtain, due to the difficulty of thermal experiments, but this theory and the experiments are found to agree with each other considerably well. Therefore, the effects of s'and K on the similarity suggested by the author were ascertained.