Numerical Solution of Temperature and Velocity Distribution and Pressure Gradient of Oil in Heating-pipe (Rep. III)

Abstract

We have calculated numerically temperature distribution, velocity distribution and pressure gradient of castor oil which flows in a stream-line flow inner heating-pipe of a constant temperature. The method of numerical solution is same as that of the oil cooling pipe, Rep. II. The author's method for partial differential equations is to extend the idea of Simpson's integral for ordirary differential equations, and this idea is that to approximate a small part of curve by parabola. Moreover, we have calculated mean temperature tm°C of oil in cooling pipe and heating pipe, where mean temperature means that of mixed oil which issued from the pipe. And these author's resultants were compared with Nusselt's and Yamagata's result, assuming that the viscosity of oil is constant. For this comparison of these results, we have taken dimension-less groupe θm≡(ti-tm)/(ti-tw) as a mean temperature.