The main problem of temperature survey

A modification of the asymptotic method [1] is used to construct the solution of the boundary-value problem of temperature survey, which enables one to derive calculation formulas for a temperature field in a well. It is demonstrated that zero approximation corresponds to the value of temperature averaged over the well cross section. Coefficients of the first and higher orders of asymptotic expansion correspond to corrections to the average value of temperature and describe the radial distributions of temperature in the well. Calculations are performed of the dependence of temperature on the radial coordinate and on the dynamics of temperature marks in the borehole, which are of fundamental importance to the methods of thermal investigations.