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

The problem of heat transfer from a constant-wall-temperature pipe buried i n a semi-infinite solid medium with a plane surface exposed to a fluid flow is solved semi-analytically. Using a conformal mapping, the original semii nfinite physical domain is transformed into a finite rectangular domain. A singular Fredholm integral equation of the second kind is derived and solve d numerically to find the temperature distribution for the solid. The total heat flux Q from the exposed surface is expressed by modifying the convent ional expression Q=kS Delta T to Q=eta kS Delta T, where S is the conductio n shape factor, k is the thermal conductivity of the solid, and Delta T rep resents the temperature difference between the pipe wall and the surroundin g fluid. The panel efficiency eta and maximum surface temperature are prese nted in terms of the Plot number and a geometric parameter, LID. (C) 1999 E lsevier Science Ltd. All rights reserved.