Coefficient-by-coefficient averaging in a problem of laminar gas flow in a well

This paper describes the problem of determining the temperature of laminar gas flow, in which the equation of convective heat transfer contains two variable coefficients, is reduced to nonclassical problems for zero and first asymptotic expansion coefficient with respect to a formal parameter. The Laplace–Carson transform are used to obtain analytical expressions for the temperature field of ascending laminar gas flow in a well with account for the relationships of density and velocity with spatial coordinates in zero and first asymptotic approximations. Expressions for the temperature asymptotically averaged along the cross section of the well and temperature distributions over the cross-sectional radius are obtained.