Analysis of the temperature field of cylindrical flow based on an on-the-average exact solution

The temperature field in a well is constructed on the basis of an on-the-average exact solution, which allows investigation of problems of subterranean thermodynamics and heat and mass transfer. The problem is represented in the form of a sequence of problems of a mixed type, whose solutions give corresponding asymptotic-expansion coefficients and the form of the remainder term and the functions taking into account the presence of the boundary layer, for which analytical solutions are also found. It is shown that the proposed modified asymptotic method provides vanishing of the solution of the averaged problem for the remainder term.