Analytic expressions for the moving infinite line source model

Groundwater flow can have a significant impact on the thermal response of ground heat exchangers. The moving infinite line source model is thus widely used in practice as it considers both conductive and advective transfert processes. Solution this involves relatively heavy numerical quadrature. Contrarily to model, there currently no known first-order approximation that could be useful for many practical applications. In paper, analytical expressions Hantush well function generalized incomplete gamma are first revisited. A clear link between these functions then established. Then, two new exact integral-free proposed, along with approximations. proposed take form convergent power series involving recursive evaluations. It shown relative errors less than 1% obtained only few summands. convergence properties series, their accuracy validity domain approximations also presented discussed.