Mathematical model of heat transfer through a conductive pipe

The standard engineer’s model for heat transfer between the fluid flowing through the pipe and the exterior medium neglects the effects of the pipe’s wall. The goal of this paper is to prove that they are not always negligible. Comparing the ratio between diffusivities of the fluid and the wall with the wall’s thickness, using rigorous asymptotic analysis, we find five different models for effective description of the heat exchange process.