Abstract
In this paper, the mathematical models for flow and heat-transfer analysis of a non-Newtonian fluid with axisymmetric channels and porous walls are analyzed. The governing equations of the problem are derived by using the basic concepts of continuity and momentum equations. Furthermore, artificial intelligence-based feedforward neural networks (ANNs) are utilized with hybridization of a generalized normal-distribution optimization (GNDO) algorithm and sequential quadratic programming (SQP) to study the heat-transfer equations and calculate the approximate solutions for the momentum of a non-Newtonian fluid. Legendre polynomials based Legendre neural networks (LNN) are used to develop a mathematical model for the governing equations, which are further exploited by the global search ability of GNDO and SQP for rapid localization convergence. The proposed technique is applied to study the effect of variations in Reynolds number Re on the velocity profile (f^{prime }) and the temperature profile (q). The results obtained by the LeNN-GNDO-SQP algorithm are compared with the differential transformation method (DTM), which shows the stability of the results and the correctness of the technique. Extensive graphical and statistical analyses are conducted in terms of minimum, mean, and standard deviation based on fitness value, absolute errors, mean absolute deviation (MAD), error in the Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE).
Highlights
In recent years, the problems of non-Newtonian fluid flow have been a topic of discussion for many researchers
6 Conclusion This paper investigates a mathematical model for flow and heat analysis of a nonNewtonian fluid with an axisymmetric channel and porous wall
A novel evolutionary algorithm is proposed in which we combine the strength of Legendre neural networks (LeNNs) with a generalized normal-distribution algorithm and sequential quadratic programming
Summary
The problems of non-Newtonian fluid flow have been a topic of discussion for many researchers. The fundamental reason for this high level of interest was its numerous applications in various engineering domains, the interest in nonNewtonian fluid-flow and heat-transfer problems such as cooling, hot rolling, lubrication, and drag reduction. The Adomain decomposition method (ADM) [17, 18], the Hyers–Ulam stability approach [19], the B-spline collocation method [20, 21] and optimal homoptopy perturbation (OHAM) [22, 23] methods were developed to study the numerical solutions of heat and mass transfer of the fluid models. The basic idea of DTM has been presented in previous papers [24,25,26] Analysis of these numerical methods demonstrates that they are deterministic and require prior information about the problem [27,28,29]
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