Study on motion of rigid rod on a circular surface using MHPM

In this paper motion of rigid rod on a circular surface is studied analytically. A new analytical method called modified homotopy perturbation method (MHPM) is applied for solving this problem in different initial conditions to show capability of this method. The governing equation for motion of a rigid rod on the circular surface without slipping have been solved using MHPM. The efficacy of MHPM for handling nonlinear oscillation systems with various small and large oscillation amplitudes are presented in comparison with numerical benchmarks. Outcomes reveal that MHPM has an excellent agreement with numerical solution. The results show that by decreasing the oscillation amplitude, the velocity of rigid rod decreases and for A=π/3 the velocity profile is maximum

Thermal analysis of convective fin with temperature-dependent thermal conductivity and heat generation

In this study, a simple and highly accurate semi-analytical method called the Differential Transformation Method (DTM) is used for solving the nonlinear temperature distribution equation in a longitudinal fin with temperature dependent internal heat generation and thermal conductivity. The problem is solved for two main cases. In the first case, heat generation is assumed variable by fin temperature and in the second case, both thermal conductivity and heat generation vary with temperature. Results are presented for the temperature distribution for a range of values of parameters appeared in the mathematical formulation (e.g. N, εG, and G). Results reveal that DTM is very effective and convenient. Also, it is found that this method can achieve more suitable results compared to numerical methods