Heat exchange during a slow flow of a liquid between coaxial conical surfaces

The problem of convective heat transfer during a slow liquid flow in conical annular channels is considered. For third-kind thermal boundary conditions, the problem is solved by separation of variables. The temperature distribution is represented as the product of an infinite Whittaker-function series in lateral coordinate and an exponential of longitudinal coordinate. Heat transfer in a variable-width annular conical channel is analyzed by stepwise approximation. Optimization of the distributing sections of extruder dies is shown to be possible.