A Reliable Numerical Algorithm For Treatment Of Fractional Model Of Convective Straight Fins With Temperature Dependent Thermal Conductivity

Fins serve the purpose of enhancing heat transfer between their surroundings and the underlying surface, resembling the function of heat exchangers in various scientific domains. This research undertakes an investigation into the temperature distribution within convective straight fins, considering the impact of both constant and thermally conductive temperature-dependent properties. The chosen approach utilizes a numerical technique known as the Laguerre operational matrix collocation method, which relies on the Laguerre operational matrix and Laguerre collocation method for Caputo fractional derivatives of arbitrary orders. This methodology effectively converts the issue into a set of nonlinear algebraic equations (NLAEs). To evaluate this arbitrary order model, we employed the collocation method to obtain an approximate solution. The numerical results obtained through this approach demonstrate its ease of application and computational efficiency. In addition, we performed a comparative analysis with the Homotopy Perturbation Sumudu Transform Method (HPSTM) and the Variational Iteration Method (VIM). The numerical and graphical presentation of the results underscores the efficacy and precision of the methodologies employed within the scope of this investigation.