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This study aims to propose a central composite design (CCD) combined with response surface methodology (RSM) to create a statistical experimental design. A new parametric optimization of entropy generation is presented. The flow behavior of magnetohydrodynamic hybrid nanofluid (HNF) flow through two flat contracting expanding plates of channel alongside radiative heat transmission was considered. The lower fixed plate was externally heated whereas the upper porous plate was cooled by injecting a coolant fluid with a uniform velocity inside the channel. The resulting equations were solved by the Homotopic Analysis Method using MATHEMATICA 10 and Minitab 17.1. The design consists of several input factors, namely a magnetic field parameter (M), radiation parameter (N) and group parameter (Br/A1). To obtain the values of flow response parameters, numerical experiments were used. Variables, especially the entropy generation (Ne), were considered for each combination of design. The resulting RSM empirical model obtained a high coefficient of determination, reaching 99.97% for the entropy generation number (Ne). These values show an excellent fit of the model to the data.

The main idea of this investigation is to introduce an integrated intelligence approach that investigates the chemically reacting flow of non-Newtonian fluid with a backpropagation neural network (LMS-BPNN). The AI-based LMS-BPNN approach is utilized to obtain the optimal solution of an MHD flow of Eyring–Powell over a porous shrinking wedge with a heat source and nonlinear thermal radiation (Rd). The partial differential equations (PDEs) that define flow problems are transformed into a system of ordinary differential equations (ODEs) through efficient similarity variables. The reference solution is obtained with the bvp4c function by changing parameters as displayed in Scenarios 1–7. The label data are divided into three portions, i.e., 80% for training, 10% for testing, and 10% for validation. The label data are used to obtain the approximate solution using the activation function in LMS-BPNN within the MATLAB built-in command ‘nftool’. The consistency and uniformity of LMS-BPNN are supported by fitness curves based on the MSE, correlation index (R), regression analysis, and function fit. The best validation performance of LMS-BPNN is obtained at 462, 369, 642, 542, 215, 209, and 286 epochs with MSE values of 8.67 × 10−10, 1.64 × 10−9, 1.03 × 10−9, 302 9.35 × 10−10, 8.56 × 10−10, 1.08 × 10−9, and 6.97 × 10−10, respectively. It is noted that f′(η), θ(η), and ϕ(η) satisfy the boundary conditions asymptotically for Scenarios 1–7 with LMS-BPNN. The dual solutions for flow performance outcomes (Cfx, Nux, and Shx) are investigated with LMS-BPNN. It is concluded that when the magnetohydrodynamics increase (M=0.01, 0.05, 0.1), then the solution bifurcates at different critical values, i.e., λc=−1.06329,−1.097,−1.17694. The stability analysis is conducted using an LMS-BPNN approximation, involving the computation of eigenvalues for the flow problem. The deduction drawn is that the upper (first) branch solution remains stable, while the lower branch solution causes a disturbance in the flow and leads to instability. It is observed that the boundary layer thickness for the lower branch (second) solution is greater than the first solution. A comparison of numerical results and predicted solutions with LMS-BPNN is provided and they are found to be in good agreement.

The primary goal of this research is to present a novel computational intelligence approach of the AI-based Levenberg–Marquardt scheme under the influence of backpropagated neural network (LMS-BPNN) for optimizing MHD ternary hybrid nanofluid using Casson fluid over a porous shrinking sheet in the existence of thermal radiation (Rd) effects. The governing partial differential equations (PDEs) showing the Casson ternary hybrid nanofluid are converted into a system of ordinary differential equations (ODEs) with suitable transformations. The numerical data is constructed as a reference with bvp4c (MATLAB built-in function used to solve a system of ODEs) by varying Casson fluid parameters (β), magnetic field (M), porosity (S), nanoparticle concentrations (ϕ1=ϕ2=ϕ3), and thermal radiation (Rd) effects across all LMS-BPNN scenarios. The numerical data-sheet is divided into 80% of training, 10% of testing, and 10% of validation for LMS-BPNN are used to analyze the estimated solution and its assessment with a numerical solution using bvp4c is discussed. The efficiency and consistency of LMS-BPNN are confirmed via mean squared error (MSE) based fitness curves, regression analysis, correlation index (R) and error histogram. The results show that velocity decreases as β grows, whereas velocity increase as M increases. The concentrations of nanoparticles and thermal radiations have increasing effects on θ0. To comprehend the dependability and correctness of the data gained from numerical simulations, error analysis is a key stage in every scientific inquiry. Error analysis is presented in terms of absolute error and it is noticed that the error between the numerical values and predicted values with AI is approximately 10−6. The error analysis reveals that the developed AI algorithm is consistent and reliable.

Climate change impacts on temperatures, precipitations, streamflows, and recharges were studied across eastern, central, and western Prince Edward Island (PEI) between climate normals in 1991–2020, 2021–2050, and 2051–2080 using observed and projected data, and SWAT modeling. Average annual temperature can significantly rise from the existing 5.90–6.86 °C to 8.26–11.09 °C in different parts during the next 30–60 years under different RCP scenarios. Average annual precipitations would not significantly change except in western PEI where a 17% likely increase would offset further warming impact; therefore, current streamflows (~650 mm/year) and recharges (~320 mm/year) would not be much affected there. However, warming and increased pumping together in its Wilmot River watershed could reduce streamflows up to 9%, and 13% during 2021–2050, and 2051–2080, respectively. In the eastern forest-dominated Bear River watershed, no significant reductions in current streamflows (~692 mm/year) or recharges (~597 mm/year) are expected. Nevertheless, near constant precipitation and warming could cumulatively reduce streamflows/recharges up to 8% there, as pumping will be negligible. In the central zone, precipitation could insignificantly increase up to 5%, but current streamflows (~737 mm/year) and recharges (~446 mm/year) would not be significantly affected, except for RCP8.5 under which streamflows could reduce by ~16% during 2051–2080. Overall, more attenuated streamflows and recharges are likely with higher quantities in late winter and early spring, and somewhat lesser ones in summer, which could reduce water supplies during the growing season. Besides, precipitation uncertainty of ~300 mm/year between dry and wet years continues to be a major water management challenge. Adapting policies and regulations to the changing environment would ensure sustainable water management in PEI.

This article deals with steady-state laminar, electrically conducting immiscible fluids. The Newtonian fluid considered passes between two parallel vertical plates in a porous medium. The channel consists of two regions, one of them filled with engine-oil-based carbon nanotubes (CNTs) and the second region filled with water through a porous medium. The assumptions for the channel walls are electrically non-conducting and are at two different temperatures. Mathematical formulation is formed using rules for the conservation of mass, momentum and energy in both regions. Continuous conditions are used for velocity, temperature and also for shear pressure at the crossing area. The governing equations are first transformed in a non-dimensional form by using appropriate transformations, and then the subsequent differential equations are solved using a topological approach by means of the homotopy analysis method. It is found that the impact of the actual boundaries utilized in the issue is directed, and the outcomes are introduced graphically and discussed. It is noted that the engine-oil SWCNTs experience a significant increase in temperature profiles as compared to the engine-oil MWCNTs, while the movement of fluid slowdown in the nanofluid region due to the concentration of nanoparticles and the thickness of the thermal boundary layer increases by increasing the volume fraction of the carbon nanotubes.

This article deals with the unsteady flow in rotating circular plates located at a finite distance filled with Reiner-Rivlin nanofluid. The Reiner-Rivlin nanofluid is electrically conducting and incompressible. Furthermore, the nanofluid also accommodates motile gyrotactic microorganisms under the effect of activation energy and thermal radiation. The mathematical formulation is performed by employing the transformation variables. The finalized formulated equations are solved using a semi-numerical technique entitled Differential Transformation Method (DTM). Padé approximation is also used with DTM to present the solution of nonlinear coupled ordinary differential equations. Padé approximation helps to improve the accuracy and convergence of the obtained results. The impact of several physical parameters is discussed and gives analysis on velocity (axial and tangential), magnetic, temperature, concentration field, and motile gyrotactic microorganism functions. The impact of torque on the lower and upper plates are deliberated and presented through the tabular method. Furthermore, numerical values of Nusselt number, motile density number, and Sherwood number are given through tabular forms. It is worth mentioning here that the DTM-Padé is found to be a stable and accurate method. From a practical point of view, these flows can model cases arising in geophysics, oceanography, and in many industrial applications like turbomachinery.

The multiphase fluid flow under the influence of electro-magnetohydrodynamics (EHD) is investigated in this study. The base fluid contains hafnium particles. Two illustrative models namely fluid phase and particulate phase are considered for three different geometries having great importance in both industrial and mechanical usage. The impact of pertinent parameters from different aspects is illustrated graphically with requisite discussion keeping in view their physical aspects. The stream lines are also erected to highlight their physical importance regarding the flow patterns. In addition, the paper is terminated by making a comparison with the existing literature as a limiting case of considered problem to confirm the validations of achieved results and hence found in excellent agreement. This model can be used to design and engineer for nozzle or diffuser type of injectors in the latest models of automobiles to improve their performance and reduce the consumption of fuel.