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In this study, an advanced computational artificial neural network (ANN) procedure is designed using the novel characteristics of the Levenberg–Marquardt backpropagation (LBMBP), i.e., ANN-LBMBP, for solving the waste plastic management in the ocean system that plays an important role in the economy of any country. The nonlinear mathematical form of the waste plastic management in the ocean system is categorized into three groups: waste plastic material W(χ), marine debris M(χ), and reprocess or recycle R(χ). The learning based on the stochastic ANN-LBMBP procedures for solving mathematical waste plastic management in the ocean is used to authenticate the sample statics, testing, certification, and training. Three different statistics for the model are considered as training 70%, while for both validation and testing are 15%. To observe the performances of the mathematical model, a reference dataset using the Adams method is designed. To reduce the mean square error (MSE) values, the numerical performances through the ANN-LBMBP procedures are obtained. The accuracy of the designed ANN-LBMBP procedures is observed using the absolute error. The capability, precision, steadfastness, and aptitude of the ANN-LBMBP procedures are accomplished based on the multiple topographies of the correlation and MSE.

The main theme of the present communication is to analyze the flow of micropolar Casson fluid with the influence of dissipation effects and inclined magnetic field upon a stretching surface by incorporating the Lobatto IIIA based numerical solver. In the presented study, the Navier–Stokes theory is exploited to model the governing fluidic system and similarity variables are used to reduce the system of governing partial differential equations into the equivalent ordinary differential equation-based model. A graphical and tabular illustration of the result of the system using the Lobatto IIIA method for the study of influential effects of various sundry parameters against the velocity profile, temperature, and microrotation are presented with brief interpretations. Results show that the increment of the inclination angle diminishes the velocity and upsurges the temperature, while, the Eckert number reduces the rate of heat transfer and shear stress, however, on the other hand, enhances the temperature and velocity profiles.

This study investigates the transportation of mass and heat in the 3D flow of hybrid nanofluids over a rotating disk in the presence of uniform magnetic field acting along the transverse direction to the flow. Water is being used as a base fluid mixed with nanoparticles of aluminum oxide and copper. The mathematical model of the nano-fluidic problem in terms of partial differential equations (PDEs) is formulated by considering the velocity slip at the boundary and heat transport mechanism due to thermal convection and radiation effects. Suitable similarity transformations are being used to transform the governing system of PDEs into a system of nonlinear ordinary differential equations. The transformed model is then analyzed by employing the competency of the Lobatto IIIA technique. Numerical and graphical illustrations are presented for the analysis of different flow parameters by varying velocities and temperature profiles. The behavior of heat transfer rate and coefficient skin friction is also studied numerically for the presented flow model.

A theoretical investigation on heat transfer of nanofluid transport in a ciliated channel is presented. A mathematical model for cilia oriented nanofluid transport through the human male reproductive tract is exhibited. Considering the structure of tubules, the Reynolds number is considered very small. The concept of a long wavelength approximation is incorporated to model the nanofluid flow problem. The exact analytical expressions for the x-component of velocity, temperature, nanoparticle concentration, stream function, volume flow rate, and pressure gradient are calculated. The solution for the transverse component of velocity, pressure rise per wavelength, and friction force on the wall of the channel is explored numerically, while variations in crucial flow parameters are examined graphically.

In this study, numerical treatment with the Lobatto IIIA technique is presented to analyze the dynamics of Darcy–Forchheimer flow for carbon nanotubes (CNTs) in a revolving frame. Stretching the surface causes fluid flow and the model is implemented for the transport of hybrid nanofluids. The governing partial differential system is simplified with the involvement of the boundary layer approximation. Similarity variables are used for the transformation of governing partial differential equations into a system of nonlinear ordinary differential equations. The results for single and multiwalled CNTs are attained by the Lobatto IIIA technique for the analysis of the resulting system. Adequate numerical and graphical illustrations are presented to investigate and understand how different flow parameters affect the velocities and temperature fields. Furthermore, the coefficients of the skin friction and the local Nusselt number are inspected numerically.

A novel theoretical model for unsteady, non-isothermal flow with temperature variant viscosity for the Newtonian fluid in the presence of transverse magnetic field is studied in the ductus efferentes of human male reproductive tract. Importance of cilia for the fluid transport through ductus efferente is elaborated in this study. To investigate the flow, we considered a channel and constant temperature difference is imposed between the wall of channel. A mathematical model is developed and analytical solution is achieved with the help of Adomian decomposition method (ADM) for MHD heat and fluid flow with temperature dependent viscosity. Flow is modeled by considering assumptions that Reynolds number is small, so that inertial forces are insignificant and wavelength to diameter ratio is maximum, so that pressure can be assumed uniform in the channel. Solutions are presented for the exponential dependent viscosity on temperature. Effect of different flow parameters on the axial and transverse component of velocity are analyzed graphically. Pumping characteristic due to ciliary beat from one row of cilia to another are investigated. Lastly variation of different flow parameters on the trapped bolus and pressure are examined graphically.

Scraped surface heat exchangers (SSHEs) diversely used in various industries for different settings when continuous processing of fluid and related material is required. In this work, heat transfer for steady incompressible flow of a Newtonian fluid in the presence of high magnetic field with temperature variant viscosity in a small gap of SSHE is studied for a fixed temperature difference narrow gaps between rotor and stator. The fluidic system is modeled mathematically in terms of PDEs for non-isothermal megnetohydrodynamic (MHD) flow with temperature dependent viscosity for linear blade shape. The solution of modeled PDEs are obtained analytically by exploiting the strength of Adomian decomposition method (ADM). The effects of different flow parameters of the systems are studied and their results are presented with analytical expressions and graphical illustrations.

A novel application of Lobatto IIIA computing solver is presented for the solution of nanofluidic Buongiorno model in the porous space. Incompressible electrically conducting fluid mixed with nanomaterial is considered. Flow expression is modelled via nonlinear mixed convection and Navier’s slip condition. Activation energy, Joule heating and non-liner thermal radiation characterise the heat/mass transport. The governing PDEs of the considered problem are transformed into an equivalent system of ODEs using similarity variables. The resulting system is solved numerically by exploiting the strength of Lobatto IIIA computing solver. Numerical and graphical illustrations are utilized to interpret the behaviour of sundry physical parameters on velocity, concentration and temperature profiles. Skin friction, temperature and concentration gradients for different scenarios of embedding variables are tabulated and analysed. Furthermore, numerical data for mesh points, error analysis, ODEs and boundary conditions evaluation are also displayed. Our computed analysis indicates that velocity of nanofluid increases for large value of slip parameter while it decreases with the increase of porosity parameter. In addition, concentration distribution is decaying and increasing functions of chemical reaction and activation energy parameters respectively.

In this article, nanofluid rheology with slip effects over a convective wall is staggeringly examined. The simultaneous effects of non-linear thermal radiations and internal heat generation/absorption properties are taken into the account. The hydro-magnetic flow in the presence of a porous medium, thermophoresis and Brownian motion effects are analyzed. Mathematical modelling of the fluid dynamic system has been performed in order to obtain the governing relations of the problem. Numerical solutions for the velocity, temperature and mass fraction profiles have been determined using the finite-difference method (FDM) based numerical computing. Various graphical and numerical illustrations for several parameters have been presented in order to investigate physics behind the mathematical equations.

This article explores the Jeffery-Hamel flow of an incompressible non-Newtonian fluid inside non-parallel walls and observes the influence of heat transfer in the flow field. The fluid is considered to be micropolar fluid that flows in a convergent/divergent channel. The governing nonlinear partial differential equations (PDEs) are converted to nonlinear coupled ordinary differential equations (ODEs) with the help of a suitable similarity transformation. The resulting nonlinear analysis is determined analytically with the utilization of the Taylor optimization method based on differential evolution (DE) algorithm. In order to understand the flow field, the effects of pertinent parameters such as the coupling parameter, spin gradient viscosity parameter and the Reynolds number have been examined on velocity and temperature profiles. It concedes that the good results can be attained by an implementation of the proposed method. Ultimately, the accuracy of the method is confirmed by comparing the present results with the results obtained by Runge-Kutta method.