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In the present article, the intelligence based numerical investigation by Levenberg–Marquardt algorithm with Back‐propagated Artificial Neural Networks (LMA–BANN) is exploited to analyze the nonlinear radiative stagnation point flow of cross nanofluid system (NRS‐CNFS) past a stretching surface. The designed NRS‐CNFS, initially represented by system of partial differential equations (PDEs), is converted into system of non‐linear ODEs through the applicability of mathematical conversion analysis. The desired reference solution in the form of a dataset for LMA–BANN is achieved from the Adam method for NRS‐CNFS's different scenarios by varying the magnetic parameter (Ha), Prandlt number (Pr), thermal radiation parameter(R), Eckert number (Ec), thermophoresis diffusion coefficients (Nt), and non‐dimensional activation energy (E). The obtained results are construed for the NRS‐CNFS through the performances of the testing, validation, and training. In addition, the comparison is provided using the LMA ‐BANN analysis, which is validated in terms of regression, fitness estimations, and histograms along with MSE performances. Hence, the article provides an impeccable innovative approach to problem‐solving by implementing a soft computation paradigm. It promotes the use of an effective and dependable alternative framework that is based on soft computing environments and emphasizes descriptive analysis to successfully handle the problems brought on by varied physical features. [ABSTRACT FROM AUTHOR]

This study explores the Entropy generation in the Flow of Jeffery Nanomaterial Model (EFJNM) past a variable thicked surface by considering joule heating effect, convectively heated surface, nonlinear radiative heat flux, and convective boundary conditions via Artificial Back Propagated Levenberg Marquardt Neural Networks (ABP-LMNNs). The ODEs system is obtained by implementing suitable transformation on PDEs for EFJNM. Applying homotopy analysis method (HAM) to create dataset for ABP-LMNNs by the variation of physical parameters of EFJNM. The reference datasets are then segmented in validation/training/testing process to scrutinize the approximated solution for EFJNM and further to compare it with standard solution. The better performance is further investigated by MSE based curves, regression fitting, absolute error, error histogram analysis. Results reveals that performance in form of MSE is in ranges of 10−9, 10−11, 10−9, 10−9, 10−10, 10−9, 10−10, 10−9, and 10−10 with 494, 285, 496, 219, 71, 167, 194, 121, 179, and 738, respectively, for all scenarios. The impact of variants of EFJNM on velocity, entropy production rate, temperature, and concentration are also analyzed. As the entropy generation increase with the increment in Deborah number and Brinkman number. The velocity increases with the escalation in Deborah number and wall thickness variable whereas decreases with the increase in relaxation to retardation ratio. The absolute errors of effective parameters for velocity are 10−7-10−4, 10−7-10−3, 10−7-10−4, and 10−6-10−3, the absolute errors for temperature are 10−7-10−3, 10−7-10−3, and 10−7-10−4 whereas the absolute errors for concentration are 10−8-10−4, 10−8-10−3, and 10−8-10−4, which show the accuracy of proposed ABP-LMNNs. Abbreviations: ABP-LMNNs, Artificial back propagated Levenberg Marquardt Neural Networks; EFJNM, Entropy generation in the Flow of Jeffery Nanomaterial Model; HAM, Homotopy analysis method [ABSTRACT FROM AUTHOR]

This article addressed entropy generation of Nonlinear Electro-Magneto Mixed Convective nanofluid model (NEM-MCNM) with second-order velocity slip flow over a stretched surface via artificial backpropagated neural networks with Levenberg–Marquardt scheme (ABPNN-LMS). The ODEs are formed by applying suitable similarity transformation on system of PDEs for NEM-MCNM. The reference dataset is obtained by the variation of different parameters from homotopy analysis method (HAM) for all scenarios of proposed ABPNN-LMS. The reference data samples for training, testing and validation sets are used to find the approximate solution of proposed ABPNN-LMS and to compare it with reference HAM outcomes. The worthy and consistent performance of ABPNN-LMS is certified through MSE convergence, and the error histogram and regression index in terms of ABPNN-LMS are also analyzed. The impact of all variants on velocity, thermal gradient, concentration, skin friction, Bejan number, entropy generation, Sherwood and Nusselt number is discussed by conducting graphics and numerical studies. Results reveal that the decrease in motion of the fluid is seen for higher slip parameters. The temperature acts as an increasing function of Eckert number and thermophoresis parameter. The augmentation in activation energy enhances the concentration of the fluid, whereas reverse trend is noticed for reaction parameter. The absolute error results are obtained as 10–07–10–03 and 10–07–10–04 for velocity, 10–07–10–04 and 10–07–10–03 for temperature and 10–09–10–03 and 10–06–10–03 which determine the accuracy of ABPNN-LMS. The best performance is accomplished at, 265, 250, 636, 346, 299 and 182 epochs with MSE around E - 09 , E - 10 , E - 09 , E - 09 , E - 09 and E - 08 . [ABSTRACT FROM AUTHOR]

[Display omitted] • Concepts and definitions. • Fluid dynamics. • Non-viscous flow. • Conservation of mass and energy. • Darcy-Forchheimer Flow. • Entropy generation. • Artificial neural networks with Levenberg-Marquardt backpropagation • Molybdenum disulfide and silicon dioxide nanoparticles • Thermal radiation • Heat generation • Numerical solutions The work in hand examines the entropy generation of magnetohydrodynamic Darcy-Forchheimer nanofluid flow model (MHD-DFNM) over a stretched surface via Artificial back propagated neural networks with Levenberg Marquardt Algorithm (ABNN-LMA). Two types of nanoparticles i.e Silicon dioxide (SiO 2) and Molybdenum disulfide (MoS 2) and continuous phase liquid i.e propylene glycol is considered. The PDEs of MHD-DFNM are transformed into coupled ODEs via appropriate (similarity) transformations. The reference dataset is obtained by the variation of 1st and 2nd order slip parameters (γ 1 and γ 2), porosity parameter (β), viscosity parameter (λ), radiation parameter(R), volume friction coefficient(ϕ), heat generation/absorption parameter(Q), Biot number (B 1) and Eckert number (Ec) from Homotopy Analysis Method (HAM). The reference data is executed in training/testing/validation sets to find and analyze the approximated solution of designed ABNN-LMA as well as it's comparison with reference data solution. The better performance is consistently certified with Mean Squared Error (MSE) curves, regression index and error histogram study. Results reveal that, increase in values of porosity parameter declines the velocity profile for both SiO 2 and MoS 2 nanoparticles suspended in propylene glycol nanofluids. The thermal profile improves for both SiO 2 − propylene glycol and MoS 2 − propylene glycol nanofluids when heat generation parameter increases. [ABSTRACT FROM AUTHOR]