Boundary element methods for nonlinear heat conduction in solids - Raghavan, Raghuraman (Nanyang Technological University, 2020)
This report is concerned with the development of a boundary element method based on radial basis function approximation for solving numerically boundary value problems for non-linear heat conduction in solids. The boundary element method has evolved to become a widely used numerical technique to solve many engineering problems. This is because of the reduced computational load required to process just the boundary discretization of the body and not the entire body itself. In the present report, heat conduction problems for solids with temperature-dependent thermal conductivity are formulated in terms. of non-linear partial differential equations. The formulation is carried out using concepts such as boundary integral equation and radial basis function approximation. The unknown temperature required can be ascertained by determining numerically the temperature at selected collocated points first and then approximating the temperature at the arbitrary points using radial basis functions. The programming software used for computation of the numerical solution is MATLAB. The code is used to generate results for a steady-state heat conduction problem in homogeneous solids with varying boundary conditions and geometries. An intensive numerical analysis is performed to study specific cases of heat propagation in solids with temperature-dependent thermal conductivity. For some cases, the numerical solution can be verified by comparing it with the exact solution. For cases with no analytical solution, a boundary element method based on Kirchhoff’s transformation, which is well established in the literature, is used to obtain numerical solutions for comparison.