Nonlinear dynamics of porous fin temperature profile: The extended simplest equation approach

This paper discusses the extended simplest equation method for analyzing the behavior of a porous fin while taking into account the porous and convection parameters. This method helps in obtaining exact solutions and understanding the temperature distribution and heat transfer characteristics of the fin. Furthermore, the equation is transformed into a planar dynamical system using the Galilean transformation. Under dynamic and quasiperiodic conditions, the behavior of the equation is extensively discussed. The bifurcation of the planar system of dynamics described by the transformed equation is studied using bifurcation theory and phase portrait analysis. Additionally, a perturbed force is introduced to the dynamical system, and the RK4 method is employed to identify periodic or quasiperiodic patterns in the system. Sensitivity and multistability analysis are applied to the porous fin equation, considering different initial conditions to investigate its quasiperiodic and periodic behavior. The chaotic structure of the perturbed dynamical system using Lyapunov exponent analysis has also been discussed. Through a comparison between numerical solutions and graphical representations, the validity and applicability of the exact technique are demonstrated. The reported findings contribute novel insights into understanding the behavior of nonlinear equations encountered in mathematical physics.