Numerical investigation of the temperature profile in a rectangular longitudinal fin

In this paper we consider a model describing the temperature profile in a longitudinal fin with a rectangular profile attached to a stationary base surface. The heat transfer coefficient is given as a nonlinear function and the thermal conductivity as a linear function, allowing both to be temperature-dependent. Numerical solutions for the relevant energy balance equation for a longitudinal fin in dimensionless variables are obtained through the implementation of an in-built function, bvp4c, in MATLAB. Solutions are considered and compared for various values of the thermo-geometric parameter MM and the exponent nn, providing some useful insights into the problem at hand with regard to the thermal stability. A dynamical systems analysis is performed for the case n=1n=1 as a means of investigating the stability of the numerical solutions obtained.