A new general analytical PBEM for solving three-dimensional transient nonlinear heat conduction problems with spatially-varying heat generation

•A new general analytical polygonal boundary element method (PBEM) is proposed.•The PBEM is developed to solve transient nonlinear heat conduction problems for the first time.•The radial integrals concerning arbitrary temperature-dependent thermal physical properties can be analytically integrated.•Compared with numerical PBEM, the proposed method can save more than 50% computational cost.•The same level of accuracy can be acquired with much fewer nodes and elements than FEM.