Abstract

In this study, a new computing model is developed using the strength of feedforward neural networks with the Levenberg–Marquardt method- (NN-BLMM-) based backpropagation technique. It is used to find a solution for the nonlinear system obtained from the governing equations of Falkner–Skan with heat transfer (FSE-HT). Moreover, the partial differential equations (PDEs) for the unsteady squeezing flow of heat and mass transfer of the viscous fluid are converted into ordinary differential equations (ODEs) with the help of similarity transformation. A dataset for the proposed NN-BLMM-based model is generated in different scenarios by a variation of various embedding parameters, Deborah number ( β ) and Prandtl number (Pr). The training (TR), testing (TS), and validation (VD) of the NN-BLMM model are evaluated in the generated scenarios to compare the obtained results with the reference results. For the fluidic system convergence analysis, a number of metrics such as the mean square error (MSE), error histogram (EH), and regression (RG) plots are utilized for measuring the effectiveness and performance of the NN-BLMM infrastructure model. The experiments showed that comparisons between the results of the proposed model and the reference results match in terms of convergence up to E-05 to E-10. This proves the validity of the NN-BLMM model. Furthermore, the results demonstrated that there is an increase in the velocity profile and a decrease in the thickness of the thermal boundary layer by increasing the Deborah number. Also, the thickness of the thermal boundary layer is decreased by increasing the Prandtl number.

Highlights

  • Research ArticleA dataset for the proposed NN-BLMM-based model is generated in different scenarios by a variation of various embedding parameters, Deborah number (β) and Prandtl number (Pr)

  • Imran Khan,1 Hakeem Ullah,1 Hussain AlSalman,2 Mehreen Fiza,1 Saeed Islam,1 Asif Zahoor Raja,3 Mohammad Shoaib,4 and Abdu H

  • For the fluidic system convergence analysis, a number of metrics such as the mean square error (MSE), error histogram (EH), and regression (RG) plots are utilized for measuring the effectiveness and performance of the NN-BLMM infrastructure model. e experiments showed that comparisons between the results of the proposed model and the reference results match in terms of convergence up to E-05 to E-10. is proves the validity of the NN-BLMM model

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Summary

Research Article

A dataset for the proposed NN-BLMM-based model is generated in different scenarios by a variation of various embedding parameters, Deborah number (β) and Prandtl number (Pr). E training (TR), testing (TS), and validation (VD) of the NN-BLMM model are evaluated in the generated scenarios to compare the obtained results with the reference results. The thickness of the thermal boundary layer is decreased by increasing the Prandtl number. 1. Introduction e boundary layer flow of an incompressible liquid through a stretching sheet is commonly used in many industrial and engineering processes. Sakiadis [4, 5] experimented with new work in this area, and many researchers in the field have investigated the flow of the boundary layer into the ongoing stretching sheet at an increasing speed. Gupta and Gupta [7] studied the same effects as given in [6] by Mathematical Problems in Engineering β/2

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