Effects of strong convection on the cooling process for a long or thin pipe

Abstract

In this Note a heat flow through a thin pipe filled with fluid is studied. The pipe is cooled by the exterior medium. Depending on the ratio between the pipe's thickness ε and the Reynolds number Re ε , we obtain three different macroscopic models via rigorous asymptotic analysis. For small Re ε the fluid in the pipe is perfectly cooled, i.e. it assumes the temperature of the surrounding medium. For large Re ε , the fluid is not cooled at all, i.e. it maintains the same temperature as it had when it entered the pipe. Between those two cases there is a critical value of Re ε when the macroscopic model is described by an ODE keeping the effects of the surrounding medium as well as the entering temperature. To cite this article: S. Marušić et al., C. R. Mecanique 336 (2008).