Distribution of temperature field strength on the surface of graphene inclusions in a matrix composite

Objectives . The study sets out to obtain an analytical expression for the distribution of the temperature field strength on the surfaces of anisotropic graphene inclusions taking the form of thin disks in the matrix composite and to use the obtained expressions to predict the strength of the temperature field on the surface of inclusions from the matrix side. Methods . An inclusion taking the form of a thin circular disk represents a special limit case of an ellipsoidal inclusion. To obtain the corresponding analytical expressions, the authors use their previously derived more general expression for the operator of the concentration of the electric field strength on the surface of ellipsoidal inclusion. The approach is justified by the mathematical equivalence of problems of finding the electrostatic and temperature field in the stationary case. The operator relates the field strength on the inclusion surface from the matrix side to the average field strength in the composite sample; the corresponding expression is obtained in a generalized singular approximation. Results . Analytical expressions were obtained for the operator of the concentration of the temperature field strength on the surface of the inclusion taking the form of a thin disk of multilayer graphene in a matrix composite. The expressions take into account inclusion anisotropy, the position of the point on the inclusion surface, the volume fraction of inclusions in the material, and the inclusion orientation. Two types of inclusion orientation distributions were considered: equally oriented inclusions and uniform distribution of inclusion orientations. Model calculations of the value for the temperature field strength at the points of the inclusion disk edge as a function of the angle between the radius vector of this point and the direction of the applied field strength were carried out. Conclusions. In the case of graphene multilayer inclusions, it is shown that the field strength at points on their edges can exceed the applied field strength by several orders of magnitude.