Semi-analytical solution for heat transfer from a buried pipe with convection on the exposed surface

Abstract

The problem of heat transfer from a constant-wall-temperature pipe buried in a semi-infinite solid medium with a plane surface exposed to a fluid flow is solved semi-analytically. Using a conformal mapping, the original semi-infinite physical domain is transformed into a finite rectangular domain. A singular Fredholm integral equation of the second kind is derived and solved numerically to find the temperature distribution for the solid. The total heat flux Q from the exposed surface is expressed by modifying the conventional expression Q=kSΔ T to Q=ηkSΔ T, where S is the conduction shape factor, k is the thermal conductivity of the solid, and Δ T represents the temperature difference between the pipe wall and the surrounding fluid. The panel efficiency η and maximum surface temperature are presented in terms of the Biot number and a geometric parameter, L/ D.