Abstract
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.
Highlights
In mechanical engineering, light industry, other areas of the economy, as well as in nature, processes of pressing particles from soft materials into porous layers, in particular, into fabric, are often found
It is known that the process of indentation of particles significantly depends on their mechanical properties, which, in turn, are significantly affected by the temperature of the particle material
The lower surface of the fabric with a thickness of hm is assumed to be thermally insulated; the cylinder isolated from the material of the roller extends indefinitely, in the areas of contact of the roller and fabric with the material of the particle there is an ideal thermal contact [4-9]
Summary
Light industry, other areas of the economy, as well as in nature, processes of pressing particles from soft materials into porous layers, in particular, into fabric, are often found. The assessment of the temperature of particles in contact with the tool (roller) is of practical interest [1-3]. The aim of this work is to simulate the heat transfer of an instrument (roller) with particles when they are pressed into the fabric. Assessment of the dynamics of the average temperature of the material of the particles during the preload time, taking into account their deformation; 4. The solution in the engineering approximation of the mathematical problem of contact heat transfer between a roller and fabric with deformable particles located between them 1. analysis of the main stages of indentation of the polymer particle material into the tissue (Fig. 1); 2. analysis of the thermal interaction of the polymer particle with the roller and fabric; 3. assessment of the dynamics of the average temperature of the material of the particles during the preload time, taking into account their deformation; 4. the solution in the engineering approximation of the mathematical problem of contact heat transfer between a roller and fabric with deformable particles located between them
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