Abstract
In this paper, the 3D Darcy–Forchheimer flow model (TDDF-FM) is discussed by utilizing the artificial intelligence-based backpropagated neural networks with the algorithm of Levenberg–Marquardt (BNN-ALM) along with the convective conditions. The effects of Brownian diffusion and thermophoresis are also examined. The governing partial differential equations are transformed into a system of ODEs. Lobatto IIIA method is used to interpret the reference dataset of BNN-ALM for different scenarios of TDDF-FM by variation of porosity parameter, Forchheimer parameter, ratio parameter, Prandtl number, Biot number, Brownian motion parameter, Schmidt number, strength parameter of homogeneous reaction and thermophoresis parameter. The solutions are computed for the designed TDDF-FM by testing, training and validation processes of BNN-ALM. The performance analysis of the designed BNN-ALM is validated by histogram analysis, regression studies and the results of mean square error (MSE). Graphs are presented for temperature profile, concentration profile and concentration rate profile. The increasing values of porosity parameter, Forchheimer parameter and Biot number enhance the temperature distribution, whereas the temperature profile shows a decreasing behavior with the increase in Prandtl number and ratio parameter. The concentration profile increases with the increase in porosity parameter, Forchheimer parameter and thermophoresis parameter and it decreases with the increasing behavior of Brownian motion parameter, ratio parameter and Schmidt number. The concentration rate profile decreases with the increase in porosity parameter, Forchheimer parameter and strength parameter of homogeneous reaction and it increases with the ratio parameter. The best performance values for different cases of scenarios are 1.42E−08, 1.70E−08, 1.78E−08, 1.61E−08, 2.43E−08, 1.05E−08, 1.30E−08, 1.59E−08 and 2.31E−08, attained at 215, 186, 178, 99, 125, 213, 187, 190 and 191 epochs. The values for the Gradient factor are 9.93E−08, 9.86E−08, 9.99E−08, 2.97E−07, 1.23E−07, 9.94E−08, 9.94E−08, 9.87E−08 and 9.94E−08, where the value of regression is [Formula: see text] for the training, testing and validation data.
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