Mathematics, Vol. 11, Pages 2401: Stochastic Levenberg–Marquardt Neural Network Implementation for Analyzing the Convective Heat Transfer in a Wavy Fin
Mathematics doi: 10.3390/math11102401
R. S. Varun Kumar
M. D. Alsulami
I. E. Sarris
The present research examines the steady, one-dimensional thermal distribution and heat transfer of a wavy fin. This heat transfer analysis considers convective effects as well as temperature-dependent thermal conductivity. Furthermore, a novel implementation of a neural network with backpropagated Levenberg&ndash;Marquardt algorithm (NN-BLMA)-based machine learning intelligent strategies is provided to interpret the heat transfer analysis of a convective wavy fin. The non-linear ordinary differential equation (ODE) of the study problem is converted into its non-dimensional form using the similarity transformation technique. The dimensionless equation obtained is then numerically explored via the Runge&ndash;Kutta&ndash;Fehlberg scheme. A data set for varying the pertinent parameters is generated, and an artificial neural network model is designed to estimate the heat transfer behavior of the wavy fin. The effectiveness of the proposed NN-BLMA is subsequently endorsed by analyses using a regression model, mean square error, and histograms. The findings of comprehensive computational parametric studies illustrate that the presented technique, NN-BLMA is an effective convergent stochastic numerical solver employed for the heat transfer model of the convective wavy fin. The wavy fin&rsquo;s temperature dispersion optimizes as the thermal conductivity parameter rises. Heat transfer rate is higher in wavy fin compared to rectangular fin.
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