A New Truly Meshless Method for Heat Conduction in Solid Structures

In this study a new meshless method is presented for the analysis of heat transfer in heterogeneous solid structures. The presented meshless method is based on the integral form of energy equation for the sub-particles in the domain of the material. A micromechanical model based on the presented meshless method is presented for analysis of heat transfer, temperature distribution and steady-state effective thermal conductivities of fiber-matrix type of composite materials. Because the domain integration is eliminated in the presented meshless formulation, the computational efforts in presented method are decreased substantially. A small area of the composite system called the representative volume element (RVE) is considered as the solution domain. The fully bonded fiber-matrix interface is considered and contact thermal resistant is neglected in the fiber-matrix interface and so the continuity of temperature and reciprocity of heat flux is satisfied in the fiber-matrix interface. A direct interpolation method is employed for enforcement the appropriate boundary conditions to the RVE. Numerical results are presented for temperature distribution, heat flux and thermal conductivity. Numerical results show that presented meshless method is simple, effective, accurate and less costly method in micromechanical modeling of heat conduction in heterogeneous materials.