Numerical investigation of the Space-Fractional Straight Fin Model with temperature-dependent properties using the Shooting Method

Traditionally, models based on physical phenomena are represented by integer-order differential equations. The extension to non-integer (fractional) orders represents a significant advancement in modeling highly nonlinear systems. However, fractional differential models introduce greater complexity compared to integer-order models. This study aims to analyze the physical parameters and evaluate the influence of fractional orders on the temperature and efficiency profiles of fins. To achieve this, the original two-point boundary value problem is transformed into an equivalent single-point problem using the Shooting Method. The resulting system is then solved using the Fractional Adams Predictor–Corrector Method. To validate the proposed approach, two straight fins with temperature-dependent properties are considered. The results demonstrate that the proposed methodology is a promising strategy for solving both integer and fractional order problems. The change in the fractional order influences the model parameters and, consequently, the temperature profiles and fin efficiency. Furthermore, depending on the fractional order, the temperature profile may be distorted in relation to the integer-order model, and the heat transfer process may be faster (or slower) in fractional order models compared to those with an integer order. Regarding the integer-order model, the fin efficiency can be maximized by choosing an appropriate fractional order.