The current article performs heat transfer analysis on the annular fin of different profiles. This nonlinear analysis considers temperature-dependent thermal conductivity, variable heat transfer coefficient, and surface radiation. The meshless local Petrov–Galerkin (MLPG) method, regarded as a truly meshfree method is applied to create discrete equations. The function approximation is done using moving least square (MLS) scheme and essential boundary condition is imposed with the penalty method. The nonlinearity of the problem is handled with a simple iterative method. The performance of different profiles based on their respective volume in nonlinear cases is evaluated and compared.