A novel cascade neural network with heuristic computational analysis for thermal dynamics of rectangular fin model...

The present study designs a new computational approach to study the thermal performance of a shrinking or stretching longitudinal rectangular fin under both convective and radiative conditions. A dimensionless mathematical model is developed to describe the thermal behavior of the fin, including parameters such as Peclet number, convective and radiative coefficients, temperature ratios, and stretching/shrinking parameters. The hybrid neurocomputing method used to solve the nonlinear system of differential equations consists of Cascaded Neural Networks (CNN) along with Genetic Algorithm hybridized with Sequential Quadratic Programming (GA-SQP). CNN modeling offers an approximate solution through a piecewise continuous representation, whereas GA-SQP improves convergence by optimal network weights. A detailed parametric study is done in six scenarios to assess the fin's temperature distribution and tip characteristics. The accuracy and stability of the solver are validated using statistical metrics such as RMSE, MAE, E-VAF, and E-NSE. The outcome shows that the Peclet number increases enhance the fin tip temperature up-to 15% as the temperature ratio increases, the fin tip temperature increases by 7-10%. The increase in the the radiation coefficient reduces the temperature by 8%. Various statistical measures confirm its reliability and effectiveness, making it a strong tool for handling complex ODEs and PDEs. Histogram and boxplot analysis show accuracy ranges up to 10^- 9, indicating that almost 90% of total iterations achieved the required accuracy tolerance range. Fitness evaluation attains high rate of convergence shows that CNN-GA-SQP scheme is a fast-converging and accurate computational intelligence approach for solving stiff nonlinear fin heat transfer models.