HEAT TRANSFER IN GRADIENT LAMINAR FLOWS

The development of new areas of research in the field of theoretical thermophysics requires reliable analytical solutions that could take into account the main aspects of physical parameters in the studied objects. One such analytical technique is symmetry groups. On the basis of symmetry groups the problem of heat transfer in gradient laminar flows is solved in the paper. For the first time, the symmetries of the energy equation for the boundary layer at an arbitrary changing velocity at marching direction are obtained. Examples of the use of group analysis methods for the study of heat transfer in the boundary layer of an incompressible fluid are demonstrated. The problems of heat transfer in the boundary layer on a heat-conducting wall with a constant temperature and on a heat-insulated wall are considered. Analytical relations for temperature and heat transfer coefficients distribution are obtained.