Application of Legendre polynomials based neural networks for the analysis of heat and mass transfer of a non-Newtonian fluid in a porous channel

Abstract In this paper, the mathematical models for flow and heat-transfer analysis of a non-Newtonian fluid with axisymmetric channels porous walls are analyzed. The governing equations problem derived by using basic concepts continuity momentum equations. Furthermore, artificial intelligence-based feedforward neural networks (ANNs) utilized hybridization generalized normal-distribution optimization (GNDO) algorithm sequential quadratic programming (SQP) to study calculate approximate solutions fluid. Legendre polynomials based (LNN) used develop model equations, which further exploited global search ability GNDO SQP rapid localization convergence. proposed technique is applied effect variations in Reynolds number Re on velocity profile $(f^{\prime })$ ( f ′ ) temperature $(q)$ q . results obtained LeNN-GNDO-SQP compared differential transformation method (DTM), shows stability correctness technique. Extensive graphical statistical analyses conducted terms minimum, mean, standard deviation fitness value, absolute errors, mean (MAD), error Nash–Sutcliffe efficiency (NSE), root square (RMSE).