Method of additional boundary conditions in the problem of heat transfer for non-Newtonian fluid moving in laminar mode in circular pipe

Taking into account the dissipation of mechanical energy the problem of heat transfer is formulated for non-Newtonian fluid moving in stable laminar mode in circular pipe. Two variants were considered: 1) non-stationary problem taking into account the diffusion component of heat transfer along the pipe; 2) the stationary problem without taking into account the longitudinal diffusion component of heat transfer in fluids. The synthesis of method of initial functions and method of complementary boundary conditions were used for the approximate solving of problems that was possible to reduce by one the dimensionality of the problem by spatial variables. In the stationary case, due to the additional boundary conditions it was able to obtain a higher degree of approximation of the temperature field than in the non-stationary case. Different methods of approximation of boundary conditions for the temperature of the liquid were studied at the entrance to the pipe with coordination and without coordination for the wall temperature. Calculations of temperature fields were conducted for melting of high-pressure polyethylene in accounting and neglect of dissipation of mechanical energy in the polymer. Comparison with calculations on the basis of other approximate method, previously developed, different from the one proposed in this study, was performed.