Analysis of the convective heat transfer through straight fin by using the Riemann-Liouville type fractional derivative: Probed by machine learning

This work aims to analyze the transfer of heat through new fractional-order convective straight fins by using the Riemann-Liouville type fractional derivatives. The convection through the fins is considered in such a way that the thermal conductivity depends on the temperature. The transformed fractional-order problems are constituted through an optimization problem in such a way that the $L_2$ norm remains minimal. The objective functions are further analyzed with the hybrid Cuckoo search (HCS) algorithm that use the artificial neural network (ANN) mechanism. The impacts of the fractional parameter β, the thermo-geometric parameter of fin ψ, and dimensionless thermal conductivity α are explained through figures and tables. The fin efficiency during the whole process is explained with larger values of ψ. It is found that the larger values of ψ decline the fin efficacy. The fractional parameter declines the thermal profile as we approach the integer order. The convergence of HCS algorithm is performed in each case study. The residual error touches $E-14$ for the integer order of α. The present results are validated through Table 6 by comparing with HPM, VIM and LHPM, while the error for HCS-ANN touches $E-13$. This proves that the proposed HCS is efficient.