Heat exchange of a roller with a particle from polymeric material when it is pressed into tissue

We study the heat transfer of polymer particles with a roller that presses the material of the particles into the fabric. Provided that the speed of movement of the tissue with the particles relative to the roller is small, the heat exchange of the pressed particles with the environment is not taken into account, a mathematical model of conductive heat transfer in the contacting roller, polymer particle and reinforcing fabric is proposed. This model includes heat conservation equations written with respect to average temperatures of the roller, particles, fabric, as well as boundary and initial conditions. Assuming that there is perfect thermal contact between the polymer particles and the fabric, in the direction of heat propagation the average thickness of the pressed tissue particle is small, the layer of material of particles and fabric is considered thermally thin, the temperature in it varies slightly in thickness. As a result, the initial system of three equations is reduced to one equation with respect to the temperature of the roller, which is supplemented by the corresponding boundary and initial conditions. In the case when the temperature along the radius of the roller varies along its radius linearly, the specific heat flux on the surface of the roller is estimated. After that, this expression is substituted into the heat balance equation of a thermally thin layer consisting of particle material and tissue, which is integrated after certain transformations