Reduced dimension model for heat transfer of ground heat exchanger in permafrost

In this work, we present reduced dimensional model for heat transfer processes of ground heat exchanger in permafrost. A mathematical model is described by a coupled system of equations for heat transfer in the ground subdomain and in heat exchanger (pipes). Because radius of the pipes is very small compared to the size of surrounding ground, we write heat transfer problem in pipes as reduced dimensional equation, where we consider pipes as one-dimensional lines. We present a computational algorithm and numerical results for model problem.