Applied Physics and Mathematics Annotation << Back ASYMPTOTIC REPRESENTATION OF THE SOLUTION OF THE PROBLEM ABOUT HEAT EXCHANGE IN A LAYER OF CURRENT LIQUID A.I. FILIPPOV, E.P. SHCHEGLOVA A mathematical model of the temperature field during the movement of the coolant in the gallery is presented, which can be used to find values averaged over the cross section of the flow and construct transverse temperature profiles. The original problem is solved on the basis of the «average exact» asymptotic method. Using the Laplace-Carson transform, analytical solutions are obtained that describe the temperature fields of the coolant. Based on numerical calculations, new possibilities for describing temperature fields under such conditions are illustrated. Keywords: temperature field, asymptotic expansions, Laplace-Carson transform, transverse temperature profile. DOI: 10.25791/pfim.05.2021.1208 Pp. 23-31.