Heat losses from a fluid flowing in a buried pipe

Abstract

Analytical solutions are presented for heat losses from a buried pipe. Two cases are considered. The first one involves a mixed (convective) boundary condition with a uniform heat transfer coefficient at the pipe surface which would be the case for turbulent flow. A simple approximate expression, accurate within 2%, is derived for the shape factor in this case. In the second case, a laminar flow with linear temperature variation along the pipe axis is considered. The coupling of the heat transfer process inside and outside the pipe requires simultaneous solution of the energy equations for these two regions. The complicated geometry is handled in an elegant manner with the use of the bicylindrical coordinate system. The results include the temperature distributions and the shape factor in each case.