Search

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 ( R d ). 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 ( C f x , N u x , and S h x ) 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., λ c = − 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. [ABSTRACT FROM AUTHOR]

In this article, we discuss the increase in Reiner--Philippoff liquid thermal energy and mass transfer through a perpendicular plane in the presence of the magnetizing field. Characterizations regarding mass dissipation and heat energy are improved using non-Fourier's analysis with the existence of a thermal source. Three kinds of nanoparticles, i.e., titanium dioxide, silicon dioxide, and aluminum oxide, are introduced in engine lubricants to create thermal energy. Darcy--Forchheimer analysis is adopted to examine the effects of flow and thermal energy. Furthermore, the Dufour and Soret effects are also discussed. A developing model is converted into a system of ordinary differential equations using similarity variables and solved using the finite element method. It is observed that the heat energy of the fluid increased as opposed to a higher rate of time relaxation number. Moreover, the fluid concentration declined as opposed to changes in the Schmidt number and chemical reaction parameters. [ABSTRACT FROM AUTHOR]

We have generalized, in the current study, the results of research presented earlier with the aim of obtaining an approximate solution for the creeping, plane-parallel flow of viscoplastic non-Newtonian fluid where the focus is on the study of rivulet fluid flows on an inclined surface. Namely, profiles of velocity of flow have been considered to be given in the same form as previously (i.e., Gaussian-like, non-stationary solutions) but with a novel type of pressure field p. The latter has been chosen for solutions correlated explicitly with the critical maximal non-zero level of stress τs in the shared plane layer of rivulet flow, when it begins to move as viscous flow (therefore, we have considered here the purely non-Newtonian case of viscoplastic flow). Correlating phenomena such as the above stem from the equations of motion of viscoplastic non-Newtonian fluid considered along with the continuity equation. We have obtained a governing sub-system of two partial differential equations of the first order for two functions, p and τs. As a result, a set of new semi-analytical solutions are presented and graphically plotted. [ABSTRACT FROM AUTHOR]

This article provides a comparison among the generalized Second Grade fluid flow described by three recently proposed fractional derivatives i.e. Atangana Baleanu fractional derivative in Caputo sense (ABC), Caputo Fabrizio (CF) and Constant Proportional-Caputo hybrid (CPC) fractional derivative. The heat mass transfer is observed during the flow past a vertical porous plate that is accelerated exponentially under the effects of the Magneto hydro dynamics. The effects of the heat generation and exponential heating in the temperature boundary layer and chemical reaction at the concentration boundary layer are also analyzed in this article. The flow model is described by three partial differential equations and the set of non-dimensional PDE's is transformed into ODE's by utilization of the integral transform technique (Laplace transform). For the better understanding of the rheological properties of the Second Grade fluid we used the CF, ABC and CPC operators to describe the memory effects. The analytical exact solution of the problem is obtained in the form of G-functions and Mittag Leffler functions. For the physical significance of flow parameters, different parameters are graphed. From this analysis it is concluded that the CPC is the most suitable operator to describe the memory effects. [ABSTRACT FROM AUTHOR]

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery. In contrast to water, polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening, polymer convection, diffusion, adsorption retention, inaccessible pore volume and reduced effective permeability. Meanwhile, the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution, formation damage, and proppant breakage. In this paper, we present an oil-water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior, and non-uniform fracture characteristics in fractured polymer flooding. The hydraulic fracture is firstly divided into two parts: high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section. A hybrid grid system, including perpendicular bisection (PEBI) and Cartesian grid, is applied to discrete the partial differential flow equations, and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution. The combination of polymer behavior characterizations and numerical flow simulations are applied, resulting in the calculation for the distribution of water saturation, polymer concentration and reservoir pressure. Compared with the polymer flooding well with uniform fracture conductivity, this non-uniform fracture conductivity model exhibits the larger pressure difference, and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section. The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately, and yields fracture half-lengths that better match engineering reality, enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity. The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology, as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves. [ABSTRACT FROM AUTHOR]

3D Concrete Printing (3DCP) is a rapidly evolving technology that allows for the efficient and accurate construction of complex concrete objects. In this paper, a numerical modelling approach is presented for the simulation of the printing process of cementitious materials, based on the homogeneous fluid assumption. To cope with the large deformations of the domain and the nonlinearity resulting from the use of a non-Newtonian rheological law, the Navier–Stokes equations are solved in the framework of the Particle Finite Element Method (PFEM). Furthermore, tailored solutions have been formulated and implemented for the time-dependent moving boundary conditions at the nozzle outlet and for the efficient handling of the inter-layer contact in the same PFEM framework. The overall computational cost is decreased by the implementation of an adaptive de-refinement technique, which drastically reduces the number of degrees of freedom in time. The proposed modelling approach is finally validated by simulating the printing process of six rectilinear layers and one multi-layer "wall". The results show good agreement with the experimental data and provide valuable insights into the printing process, paving the way for the use of numerical modelling tools for the optimization of materials and processes in the field of 3D Concrete Printing. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of the existence of trajectory and global attractors in the Kelvin–Voigt fluid model, taking into account memory along the trajectories of fluid motion. For the model under study, the concept of a weak solution on a finite segment and semi-axis is introduced and the existence of their solutions is proved. The necessary exponential estimates for the solutions are established. Then, based on these estimates, the existence of trajectory and global attractors in the problem under study is proved. [ABSTRACT FROM AUTHOR]

A study has been made of the flow of a non-Newtonian polymer medium in a plane channel and of heat transfer in it with boundary conditions of the first kind for small Reynolds numbers and a large Péclet number with the Ellis rheological model with a viscosity dependent on the temperature, pressure, and degree of chemical conversion of the medium. Consideration was given to the flow of a high-viscosity medium with chemical reactions leading to an abrupt increase in its viscosity for whose mathematical description the authors used a model that included the kinetic chemical-reaction equation and the energy equation with a dissipative term. Significant influence of various factors on the formation and rate of growth of the solidified wall layer in such flow has been shown. The problem has been solved numerically by the finite-diff erence method according to the iterative scheme. [ABSTRACT FROM AUTHOR]

The dynamics of non-Newtonian shear-thinning (carboxymethyl cellulose-CMC solution) droplet splitting with permanent and partial obstructions are experimentally investigated using a high-speed experimental framework in a microfluidic T-junction divergence. Four sequential stages of shear-thinning droplet splitting are found: squeezing, transition, pinch-off, and rupture. The role of various flow and fluid parameters (CMC concentrations, flow ratio, and droplet size) on the splitting dynamics is investigated with the help of flow regime maps. The dynamics of droplet neck thinning and the intriguing phenomenon of satellite droplet formation are further investigated at distinct CMC concentrations. The present study aims to enhance comprehension of the phenomenon of rapid droplet splitting, which has greater outreach in biofluids-based applications. [ABSTRACT FROM AUTHOR]

This research aims to propose a numerical scheme for solving boundary value problems. It is a two-stage, third-order accurate scheme known as a predictorcorrector scheme. The two main results are finding the region of the scheme where it is stable and determining the stability criterion for a set of linearized first-order differential equations. In addition, a mathematical model for heat and mass transfer of Darcy-Forchheimer flow of non-Newtonian nanofluid over the sheet is presented. The similarity transformations reduce PDE into a system of ODE for easier manipulation. The results are compared with the past research and those obtained by MATLAB SOLVER BVP4C. The results show that the velocity profile slightly decays by enhancing the Weisenberg number. [ABSTRACT FROM AUTHOR]

Multi-layer fabrics are commonly used in ballistics shields with a lower bulletproof class to protect against pistol and revolver bullets. In order to additionally limit the dynamic deflection of the samples, layers reinforced with additional materials, including non-Newtonian fluids compacted by shear, are additionally used. Performing a wide range of tests in each case can be very problematic; therefore, there are many calculation methods that allow, with better or worse results, mapping of the behavior of the material in the case of impact loads. The search for simplified methods is very important in order to simplify the complexity of numerical fabric models while maintaining the accuracy of the results obtained. In this article, multi-layer composites were tested. Two samples were included in the elements subjected to shelling. In the first sample, the outer layers consisted of aramid fabrics in a laminate with a thermoplastic polymer matrix. The middle layer contained a non-Newtonian shear-thickening fluid enclosed in hexagonal (honeycomb) cells. The fluid was produced using polypropylene glycol and colloidal silica powder with a diameter of 14 µm in the proportions of 60/40. The backing plate was made using a 12-layer composite made of Twaron® para-aramid fabrics with a DCPD matrix—not yet used in a wide range of ballistics. Then, numerical simulations were carried out in the Abaqus/Explicit dynamic analysis. The Johnson–Cook constitutive strength model was used to describe the behavior of elastic–plastic materials constituting the elements of the projectiles. For the non-Newtonian fluid, a Up-Us EOS was used. The inner layers of the fabric were treated as an orthotropic material. Complete homogenization of the sample layers was carried out, thanks to which each layer was treated as a homogeneous continuum. As a parameter of fracture mechanics for shield components, the strain criterion was used with the smooth particles hydrodynamics method (SPH). Then, the results of simulations were compared with the results of the ballistic test for both samples placed next to each other, which resulted in the formation of a multi-layer composite in one ballistic test subjected to impact loads during firing with a 9 × 19 mm Parabellum FMJ projectile with an initial velocity of 370 ± 10 m/s. The results of numerical tests are very similar to the ballistic tests, which indicates the correct mapping of the process and the correct conduct of layer homogenization. The applied proportions of the components in the non-Newtonian fluid allowed a reduction in the deflection compared to previous studies. Additionally, the proposal to use a DCPD matrix allowed to obtain a much lower deflection value compared to other materials, which is a novelty in the field of production of ballistic shields. [ABSTRACT FROM AUTHOR]

To compensate for the decrease of velocity and pressure of waxy crude oil flow in a pipeline under the conditions that it exhibits non-Newtonian behavior, engineers would have to optimize the transmission power. This objective requires correct modeling of the rheological behavior and estimating the distributions of velocity, pressure, and temperature in the fluid along the pipeline. The rheological behavior of crude oil is highly dependent on wax content, shear rate, and temperature. In this work, to study the influence of wax content, two types of crude oils with different paraffin contents, referred to as reference crude oils, were studied. The results of shear-rotary tests using an Anton Paar MCR 302 indicate that in a specific range of shear rates, the reference crude oils are non-Newtonian at the studied temperatures of pipe wall and inlet. Considering the Power-law model for describing the rheological behaviors of these fluids, two dimensionless numerical models are proposed. Using Computational Fluid Dynamics (CFD) technique, the velocity, pressure, and temperature of each reference crude oil were modeled. The accuracy of the model and input data were successfully evaluated against results reported in the literature. [ABSTRACT FROM AUTHOR]

The rheological behavior of aqueous solutions of polyvinyl alcohol at 4, 6, 8 and 10% by weight has been studied and evaluated at temperatures of 20, 25, 30 and 35 °C, using five non-Newtonian fluid models independent of time: Ferrys, Robertson-Stiff, Williamson, Sisko, and Ellis de Haven. The classical method consists in carrying out regression analysis. Using a comparative procedure of determination coefficients and variances, the model that most appropriately adjusts the experimental data to said model is selected. From the statistical point of view, the Sisko and Robertson-Stiff models present better regression parameters; to better specify the choice of the respective rheological model, a new factor has been proposed in the literature, the viscosity factor (VF), which expresses the relationship between apparent and dynamic viscosity. The analysis of this factor for the five models confirms the greater stability of the Ellis de Haven model in terms of the coefficient of variation of the VF. The value of VF fluctuates between 1 and 2 for all ranges of temperature and concentration experienced for vinyl alcohol solutions. As a consequence of the above, for the choice of the non-Newtonian fluid model associated with the rheology of the aqueous solution of polyvinyl alcohol, it is necessary to analyze the statistical parameters and the VF factor simultaneously. [ABSTRACT FROM AUTHOR]

This work is an attempt to study the behaviour of fluid in the mixing vessel with a two-bladed or four-bladed impeller. The working fluid is complex, of a shear-thinning type and the Oswald model is used to describe the fluid viscosity. The study was accomplishedby numerically solving the governing equations of momentum and continuity. These equations were solved for the following range of conditions: 50-1000 for the Reynolds number, 0-0.15 for the baffle length ratio, and the number of impeller blades 2 and 4. The simulations were done for the steady state and laminar regime. The results show that the increase in baffle length (by increasing the ratio baffle length ratio) decreases the fluid velocity in the vessel. Increasing the speed of rotation of the impeller and/or increasing the number of blades improves the mixing process. Also, the length of the baffles does not affect the consumed power. [ABSTRACT FROM AUTHOR]

In this paper melting of a carreau non-Newtonian PCM in the space between two concentric horizontal tubes, which is partially filled with porous material with different shapes but same area, is investigated numerically. A magnetic source is located in the center of the geometry for melting process of PCM to occur in the presence of ferro-hydrodynamic effects. Porous material is made of Cu that covers the cross-section of the inner tube. In addition, the space between inner and outer tubes is saturated with paraffin-wax PCM. Flow of melted paraffin-wax is considered as a Carreau non-Newtonian, laminar and incompressible flow with viscous dissipation that is evaluated in a specific time interval. Boussinesq approximation is valid for the PCM. Also local thermal equilibrium condition is assumed between the porous and the PCM. Galerkin finite element method has been utilized to solve the problem. Results showed that melting rate is higher for the third model in comparison other models. Also effects of the magnetic number depends on the shape of the porous medium. Therefore, that increase in the magnetic number, increasingly enhances the progress of the melting front in the second case. Moreover, effects of Carreau index, Stefan number, and porosity on the melting process are studied. Key words: PCM, porous media, magnetic field. [ABSTRACT FROM AUTHOR]

This article reports on the emission of H2S (hydrogen sulfide) during the excavation of disturbed material covering a former ocean shoreline. Operators of the excavators expressed concerns about the strong odors of H2S, the insensitivity of workplace instruments, and the safety of the work. This situation demanded an immediate and appropriate response. The literature contains no information concerning worker exposure to H2S in these situations. Levels detected by the Jerome 631-X ranged from 1 ppb (part per billion) to 25 ppb in 1-min samples during various activities. Levels decreased to zero when activity ceased. Unpredicted excursions peaking at 2500 ppb superimposed onto background levels immediately followed exposure to material containing H2S. Excursion levels rose abruptly, peaked, and decreased rapidly to the background. Excursions occurred once per day and lasted about 10 min. These emissions share characteristics of shear-thinning, pseudoplastic non-Newtonian fluids. A very conservative estimation of exposure during this work compared to the Threshold Limit Value-Time-Weighted Average of 1 part per million (ppm = 1000 ppb) suggested that this was considerably less than the lowest level of regulatory concern and that work under these conditions can proceed without overexposure to H2S. This work has relevance and application in similar situations occurring globally. [ABSTRACT FROM AUTHOR]

Stochastic simulations enable researchers to incorporate uncertainties beyond numerical discretization errors in computational fluid dynamics (CFD). Here, the authors provide examples of stochastic simulations of incompressible flows and numerical solutions for validating these newly emerging stochastic modeling methods. A numerical scheme is constructed for finding solutions to stochastic parabolic equations. The scheme is second-order accurate in time for the constant coefficient of the Wiener process term. The stability analysis of the scheme is also provided. The scheme is applied to the dimensionless heat and mass transfer model of mixed convective non-Newtonian nanofluid flow over oscillatory sheets. Both the deterministic and stochastic energy equations use temperature-dependent thermal conductivity. The stochastic model is more general than the deterministic model. The results are calculated for both flat and oscillatory plates. Casson parameter, mixed convective parameter, thermophoresis, Brownian motion parameter, Prandtl number, Schmidt number, and reaction rate parameter all impact the velocities, temperatures, and concentrations shown in the graphs. Under the influence of the oscillating plate, the results reveal that the concentration profile decreases with increasing Brownian motion parameters and increases with increasing thermophoresis parameters. The behavior of the velocity profile for the deterministic and stochastic models is provided, and contour plots for the stochastic model are also displayed. This article aims to provide a state-of-the-art overview of recent achievements in the field of stochastic computational fluid dynamics (SCFD) while also pointing out potential future avenues and unresolved challenges for the computational mathematics community to investigate. [ABSTRACT FROM AUTHOR]

This work examined the thermodynamics of the MHD rotating dusty Maxwell water-based nanofluid with suspended dust particles. This study examines the importance of increasing the volume fraction of tiny particles of TiO2 and dust on fluid dynamics. With appropriate similarity transformations, the governing PDEs for both fluid and dusty-phase models are transformed into non-linear linked non-dimensional ODEs. To acquire graphical consequences, the bvp4c technique is implemented in MATLAB scripts. The primary and secondary velocities' magnitude in both phases decreases with an increase in the dust particle volume concentration, Lorentz force, rotating, and Maxwell fluid parameters. The growing strength of tiny particles of dust and TiO2 is responsible for the upshot of temperature in both dust and nanofluid phases. A visual representation of the Nusselt number and skin friction coefficients are is provided. [ABSTRACT FROM AUTHOR]

In this paper, a two-dimensional, steady, laminar boundary layer analysis is presented to analyze numerically the internal heat generation and Soret–Dufour effects on mixed convection flows of power-law fluids adjacent to a vertical flat plate maintained at variable heat flux and variable mass flux conditions in a Darcy porous medium. The Ostwald–de Waele power-law model is utilized here. The transformed governing equations are solved by the Keller box method. After performing comparisons with previously published results, good agreement is obtained. [ABSTRACT FROM AUTHOR]

We have examined the magnetized stagnation point flow of non-Newtonian fluid towards an inclined cylindrical surface. The mixed convection, thermal radiation, viscous dissipation, heat generation, first-order chemical reaction, and temperature-dependent thermal conductivity are the physical effects being carried for better novelty. Mathematical equations are constructed for four different flow regimes. The shooting method is used to evaluate the heat transfer coefficient at the cylindrical surface with and without heat generation/thermal radiation effects. For better examination, we have constructed artificial neural networking models with the aid of the Levenberg–Marquardt training technique and Purelin and Tan-Sig transfer functions. The Nusselt number strength is greater for fluctuations in the Casson fluid parameter, Prandtl number, heat generation, curvature, and Eckert number when thermal radiations are present. [ABSTRACT FROM AUTHOR]

A model of two-phase flow involving non-Newtonian fluid is described to be more reliable to present the fluid that involves industrial applications due to the special characteristics in its behavior. Many models of non-Newtonian fluid were discovered in the last few decades but the model that captured the most attention is the Williamson model. The consideration of the existing particles in the Williamson flow (two-phase Williamson fluid) will make the model more interesting to investigate. Hence, this paper is aimed to explore the flow of two-phase Williamson fluid model in the presence of MHD and thermal radiation circumstances. The obtained ordinary differential equations after the transformations are solved using the Runge-Kutta Fehlberg (RKF45) method. The flow is considered asymmetric since it moves over a vertical stretching sheet with external stimuli. The result displays variation in dust phases compared to the fluid phase under distribution of velocity and temperature. It can be concluded that the fluid–particle interaction (FPI) parameter lessening the motion of fluid and heating characteristics. In addition, the upsurges on skin friction and heat transfer are resulting from the rising FPI. Furthermore, the presence of Williamson parameter increases the skin friction while causing degenerations on heat transfer of flow. [ABSTRACT FROM AUTHOR]

Roland Glowinski published 8 books and more than 300 articles. He was also an editor of many very well cited proceedings. Hence this attempt to summarize his scientific work is not likely to do justice to his work. Nevertheless, we will try to extract his major contributions, such as the augmented Lagrangian algorithm, various domain decomposition and fictitious methods and their performance on the Navier--Stokes equations in a moving domain. Roland has created a school of applied mathematicians remarkable by their rigor and efficiency for industrial applications. He marked his time and his books will be authorities as long as computer architectures are similar to their present structures. [ABSTRACT FROM AUTHOR]

In the study of polymer flooding, researchers usually ignore the genetic stress properties of viscoelastic fluids. In this paper, we investigate the process of viscoelastic fluid flooding the remaining oil in the dead end. This work uses the fractional-order Maxwell in the traditional momentum equation. Furthermore, a semi-analytic solution of the flow control equation for fractional-order viscoelastic fluids is derived, and the oil-repelling process of viscoelastic fluids is simulated by a secondary development of OpenFOAM. The results show that velocity fractional-order derivative α significantly affects polymer solution characteristics, and increasing the elasticity of the fluid can significantly improve the oil repelling efficiency. Compared to the Newtonian fluid flow model, the fractional order derivative a and relaxation time b in the two-parameter instanton equation can accurately characterize the degree of elasticity of the fluid. The smaller the a, the more elastic the fluid is and the higher the oil-repelling efficiency. The larger the b, the less elastic the fluid is and the lower the cancellation efficiency. Moreover, the disturbance of the polymer solution to the dead end is divided into two elastic perturbation areas. The stronger the elasticity of the polymer solution, the higher the peak value of the area in the dead end and the higher the final oil displacement efficiency. [ABSTRACT FROM AUTHOR]

An invariant solution is derived using the Lie symmetry technique for steady laminar twodimensional and axisymmetric boundary layer jet flow of incompressible power-law fluids with appropriate boundary conditions. Using symmetry, the nonlinear partial differential equation of the jet flow problem is transformed into a nonlinear ordinary differential equation. The resultant nonlinear ordinary differential equation with boundary conditions is converted to an initial value problem using the Lie symmetry technique. A numerical solution for the resulting initial value problem is derived using Fehlberg’s fourth-fifth order Runge-Kutta method through Maple software. The graphical representation of the characteristics of the velocity field for different physical parameters is also discussed. [ABSTRACT FROM AUTHOR]

Nanoparticles play an essential role in biomedical applications. A most promising area in nanomedicine is drug targeting which is done with the aid of magnetized nanoparticles. In this study, the hemodynamics of hybrid nanofluid flow with gold and copper nanoparticles suspended in it is investigated. This research primarily focuses on magnetic drug delivery which is propagated through a tapered stenosed artery under three situations, including converging, diverging, and non-tapering arteries. To explore the rheological characteristics of blood, a Sutterby fluid, which is a non-Newtonian fluid, is postulated. The energy equation also incorporates the effects of the magnetic field and joule heating, as well as the viscous dissipation function. Lubrication theory provides a mathematical framework for model formulation. The hypothesized modeling is simplified to a set of nonlinear differential equations that are then solved using a perturbation method up to the second order of approximation. Graphs are used to describe the outcomes of different evolving parameters. The Sutterby fluid parameter opposes the flow negligibly, whereas the Hartmann number and thermal Grashof number strengthen the flow field. Copper nanoparticles (in the absence of gold nanoparticles) are observed to deplete the thermal profile substantially more than gold nanoparticles. Nevertheless, the thermal profile is enhanced by the presence of both nanoparticles (hybrid nanofluids). For greater values of the Sutterby fluid parameter, the wall shear stress has been observed to rise considerably, whereas the inverse is true for the Hartmann number and the thermal Grashof number. The present results have been improved to give significant information for biomedical scientists who are striving to study blood flow in stenosis situations, as well as for those who will find the knowledge valuable in the treatment of different diseases. [ABSTRACT FROM AUTHOR]

The effect of elasticity on the peristaltic flow of a micropolar fluid containing nanoparticles in a cylindrical tube is investigated using a mathematical model. The expressions for velocity and flux flow rate are determined by using Homotopy Perturbation method, under long wave length and low Reynold's number approximations. The variation of flux is calculated by Rubinow and Keller, Muzumdar methods. Different parameters' effects on velocity and flow have been discussed. For various settings, the trapping phenomenon is demonstrated. The flux increases as the elasticity parameters, micropolar parameter, thermophoresis parameter, and coupling number increase. The flux similarly reduces as the Brownian motion parameter is increased. The obtained results are same when we apply Rubinow and Keller, Muzumdar methods. [ABSTRACT FROM AUTHOR]

The dynamics of MHD non-Newtonian fluid flow past a cylinder with slip boundary condition and magnetic field is addressed in this study. The non-Newtonian fluid (tangent hyperbolic) considered in this study are nail polish and whipped cream. This article investigates the statistical analysis of two-dimensional MHD tangent hyperbolic fluid flow over a cylinder with slip condition. The partial differential equations describing the problem are later transformed into the ordinary differential equation by similarity variables. The derived model is solved by the spectral homotopy analysis method (SHAM). The characteristics of the parameters of the flow are demonstrated by the velocity of the flow. The skin friction coefficient is computed and presented with the aid of a tables. The slope of the linear regression is obtained through the data points while bar charts for engineering quantities of interest are presented. The findings indicated that an increase in magnetic parameters builds a resistance to the flow. Also, it was discovered that the radius of curvature decreases when the curvature parameter increases. [ABSTRACT FROM AUTHOR]

In this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal) fluid is depicted as a continuum in a noninteger dimensional space. Involving vector calculus for the instance of a noninteger dimensional space, we determine an analytical solution of the Cauchy equation for the instance of a non-Newtonian self-similar fluid flow in a cylindrical pipe. The plot of the velocity profile obtained shows that the rheological behavior of a non-Newtonian power-law fluid is essentially impacted by its self-similar structure. A self-similar shear thinning fluid and a self-similar Newtonian fluid take on a shear-thickening way of behaving, and a self-similar shear-thickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology. [ABSTRACT FROM AUTHOR]

For propulsion systems using gel fuels, reducing the gel fuel viscosity is essential for achieving better atomization and combustion. In this paper, we investigate the flow and heat transfer in a water-gel with a temperature and shear dependent viscosity. We consider several different channels, mimicking the transport of gelled fuels in propulsion systems, and we also look at corrugation, which is a way of enhancing fluid mixing and thus improving the heat transfer characteristics. The rheological parameters in the constitutive model of the gel are fitted with experimental data. The influence of different corrugation profiles, corrugation configuration parameters and the Reynolds number on the mean apparent viscosity and the pressure drop are investigated. It was found that the flow recirculation formed in the valley of the corrugations enhances the heat transfer and thus the temperature of the main flow. We also noticed an increase in the pressure drop due to the stronger viscous dissipation. Furthermore, it was observed that the sinusoidal corrugation can achieve lower viscosity with a lower pressure drop compared with triangular and trapezoidal corrugations. A shorter wavelength and a deeper wave amplitude of the corrugation seemed to be better for reducing the gel fuel viscosity, while we must consider the adverse consequence of increased pressure drop. A larger Reynolds number was helpful for both lowering the pressure drop and for reducing the viscosity. In addition, compared with a smooth straight pipe, a Y-shape corrugated channel with a constant inlet velocity reduced the mean apparent viscosity by 70.8%, and this value increased to 72.6% by further applying a pulsed inlet velocity, which can greatly enhance the gel fuel atomization and thus improve the combustion efficiency. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to investigate the solvability of the steady-state flow model for low-concentrated aqueous polymer solutions with a damping term in a bounded domain under the no-slip boundary condition. Mathematically, the model under consideration is a boundary value problem for the system of strongly nonlinear partial differential equations of third order with the zero Dirichlet boundary condition. We propose the concept of a full weak solution (velocity–pressure pair) in the distributions sense. Using the method of introduction of auxiliary viscosity, the acute angle theorem for generalized monotone nonlinear operators, and the Krasnoselskii theorem on the continuity of the superposition operator in Lebesgue spaces, we obtain sufficient conditions for the existence of a full weak solution satisfying some energy inequality. Moreover, it is shown that the obtained solutions of the original problem converge to a solution of the steady-state damped Navier–Stokes system as the relaxation viscosity tends to zero. [ABSTRACT FROM AUTHOR]

In the present study, a novel body-armor-like abrasive tool (BAAT) was designed with the "particle cluster" effect to realize a high-shear and low-pressure grinding. The finite element method (FEM) was utilized to analyze the interplay of the abrasive layer and the micro convex peak (MCP) of the workpiece during the grinding process with the BAAT. An experimental platform was established to explore the high-shear and low-pressure grinding phenomenon and verify the simulation results. The simulation results showed that the BAAT formed a "particle cluster" effect when contacting MCP. The ratio of the tangential force and the normal force was greater than 0.33, which was identical to the experimental results. The BAAT demonstrated the strongest hindrance to the MCP. In the absence of Kevlar, the degree of energy dissipation was lower compared to the BAAT. The kinetic energy dissipation of the MCP was the smallest without abrasive particles. The maximum displacement of the Kevlar in the case of Kevlar was only 4.85 mm. The displacement of Kevlar in the BAAT was 1.81 mm. The degree of decline had been reduced by 62.6%. Comparing the speed of the MCP, the speed least dropped when only Kevlar existed. The trend of speed variation coincided well with that of kinetic energy. [ABSTRACT FROM AUTHOR]

We study a feedback optimal control problem for a three-dimensional model of a stationary flow of a non-Newtonian fluid (with variable viscosity) in a pipeline network with complex geometry. The control parameter is the dynamic pressure on connection surfaces of pipes to nodes. The flow model is a mixed boundary-value problem for a system of strongly nonlinear partial differential equations in a netlike domain with Kirchhoff-type transmission conditions at interior nodes of the network. The solvability of the optimization problem in the weak formulation is proved; namely, we establish sufficient conditions for the existence of a weak solution which minimizes a lower semicontinuous cost functional. [ABSTRACT FROM AUTHOR]

The main objective of this investigation to examine the momentum and thermal transportation of rotating dusty micropolar fluid flux with suspension of conducting dust particles across the stretched sheet. The novelty of the flow model is the exploration of the significance of boosting the volume concentration of dust particles in fluid dynamics. The governing PDEs of the problem for both phase models are transmuted into nonlinear coupled non-dimensional ODEs by utilizing suitable similarity modifications. The bvp4c technique was utilized in MATLAB script to acquire a graphical representation of the experimental results. This study illustrates the analysis of repercussions of pertinent parameters on non-Newtonian fluid and the dusty phase of fluid. By improving the volume concentration of dust particles and rotating parameters, the axial velocity for both phases depreciates, whereas temperature and transverse velocity for both phases have the opposite behavior. The micro-rotation distribution rises with higher contributions of rotating and material parameters, whereas it decreases against larger inputs of volume concentration of dust particles. The growing strength of the dust volume fraction ( ϕ d ) caused the coefficient of skin friction to decrease along the x direction, and the skin friction coefficient is raised along the y direction. [ABSTRACT FROM AUTHOR]

To investigate the unsteady flow field generated by magnetorheological (MR) fluid of a high-speed unsteady laminar boundary layer flow in a narrow-long gap of the magnetorheological absorber (MRA), a new unsteady numerical model is proposed. The gap has magnetic-field-activated and inactivated regions, with MR fluid flowing as bi-viscous (non-Newtonian) and Newtonian fluid. The unsteady flow field is described by the unsteady incompressible governing partial differential equation (PDE) and initial-boundary conditions with the moving boundary. The space-time solution domain is discretized using the finite difference method, and the governing PDE is transformed into implicit partial difference equations. The volume flow rate function is constructed to solve numerical solutions of pressure gradient and fluid velocity based on mass conservation, the continuity equation, and the bisection method. The accuracy of unsteady numerical model is validated by the experiment data. The results show that the fluid acceleration profiles along the gap's height are non-uniform distribution. Further, the volume flow rate and excitation current has a significant impact on the dynamic distribution of fluid velocity profiles, and the moving boundary makes the flow field asymmetric about the central plane. Furthermore, as the transition stress increases, the thickness of the pre-yield region in the activated region increases. There is also a transition flow phenomenon in the activated region as the volume flow rate increases. Finally, the unsteady numerical model has good stability and convergence. [ABSTRACT FROM AUTHOR]

This paper studied the evolution of NaAlg solution micro-droplet in a coaxial microchannel. The Bird–Carreau model was used to characterize the flow properties of NaAlg solution. As the mass fraction decreased, the flow behavior index n also decreased, indicating that the NaAlg solution was increasingly shear-thinning. There were three stages during the micro-droplet evolution, which were the growth stage, the squeezing stage, and the pinch-off stage. This paper led the flow behavior index n to estimate the effects of rheological property on the breakup dynamics of micro-droplet. We proposed two new prediction models of the minimum neck width wm which were affected by |n| in the squeezing and pinch-off stages for the non-Newtonian fluids. In addition, this paper indicated the rate ratio Qd/Qc was another factor on the wm model in the squeezing stage and the H(λ) of Stokes mechanism was a function governed by |n|2 in the pinch-off stage. [ABSTRACT FROM AUTHOR]

The recent study was concerned with employing the finite element method for heat and mass transfer of MHD Maxwell nanofluid flow over the stretching sheet under the effects of radiations and chemical reactions. Moreover, the effects of viscous dissipation and porous plate were considered. The mathematical model of the flow was described in the form of a set of partial differential equations (PDEs). Further, these PDEs were transformed into a set of nonlinear ordinary differential equations (ODEs) using similarity transformations. Rather than analytical integrations, numerical integration was used to compute integrals obtained by applying the finite element method. The mesh-free analysis and comparison of the finite element method with the finite difference method are also provided to justify the calculated results. The effect of different parameters on velocity, temperature and concentration profile is shown in graphs, and numerical values for physical quantities of interest are also given in a tabular form. In addition, simulations were carried out by employing software that applies the finite element method for solving PDEs. The calculated results are also portrayed in graphs with varying sheet velocities. The results show that the second-order finite difference method is more accurate than the finite element method with linear interpolation polynomial. However, the finite element method requires less number of iterations than the finite difference method in a considered particular case. We had high hopes that this work would act as a roadmap for future researchers entrusted with resolving outstanding challenges in the realm of enclosures utilized in industry and engineering. [ABSTRACT FROM AUTHOR]

The processes of hydrodynamics and heat transfer during the flow of a non-Newtonian polymeric medium in a plane channel have been investigated with boundary conditions of the first kind. Consideration was given to a steady-state nonisothermal process with low values of the Reynolds number and high values of the Péclet number, which made it possible to neglect gravity and inertial forces, and also longitudinal thermal conductivity. The Ellis model with a viscosity dependent on temperature, pressure, and the degree of chemical transformation was used as the rheological model. A high-viscosity medium was investigated. Therefore, it is the dissipative term that was taken account of in the energy equation. With the above rheological model, an expression in explicit form was obtained from the equation of motion of such a medium for the velocity profile of its flow. It has been established that the dependence of the viscosity of a medium on its temperature, pressure, and the degree of transformation has an appreciable effect on the distribution of the temperature of the medium and the velocity of its flow along the channel's length. Taking account of the temperature dependence of the viscosity of the medium leads to a decline in the role of dissipation in the process of its warmup. The dependence of the medium's viscosity on pressure, conversely, considerably enhances the dissipative effect, which appreciably accelerates the course of a chemical reaction. [ABSTRACT FROM AUTHOR]

The main purpose of this study is to compare a semi-analytical method and numerical method namely the homotopy perturbation method (HPM) and finite difference method (FDM) respectively. These methods were employed for solving the nonlinear problem of the magnetohydrodynamic (MHD) couette flow of third-grade fluid between the two parallel plates. The comparison was made between a solution of HPM and FDM against a solution obtained from regular perturbation and the results are tabulated. From a computational viewpoint, it is revealed that the HPM is more reliable and efficient than FDM. Also, the results show that the FDM requires slightly more computational effort than the HPM, although the HPM yields more accurate results than the FDM. [ABSTRACT FROM AUTHOR]

In the modern day science and medics, scholars are focusing on the behavioral study of non-Newtonian fluid and its relevance with ciliated motion in human body. This would offer advanced avenues of research to mitigate the risks of new and contagious diseases relating to various systems in human body. This manuscript focuses on the behaviour of metachronal wave in Prandtl fluid generated by ciliated movement through a horizontal tapering channel once magnetic field is applied to the fluid. The theoretical approach raises mathematical calculations and results obtained presented highly nonlinear system of PDEs. Latterly, ODEs are developed which accrue the accurate results by using scaling group of transformations. Second, approximation of long wavelength and low Reynold's number used to analyze the flow motion caused by metachronal waves. The emerging equations achieved are further solved numerically using the bvp4c method. Results are engendered through graphical attempt of velocity, temperature, pressure gradient, pressure rise and wall shear stress graphs in relation to various factors. It can be inferred that theoretical impact of velocity profile for magnetic parameter decreases near the walls of the ciliated channel while increases in the middle of channel. It concludes that magnetic field opposes the strength of the flow close to the walls. Another observation is the flow of temperature across the subject domain is accelerated by the Brinkman number. Thus, the flow of heat transfer may be increased by the fast metachronal wave and fixed initial temperature. While streamlines are also fabricated to exhibit the flow phenomenon of ciliary motion. [ABSTRACT FROM AUTHOR]

In this work, a numerical study of polymer flow behaviors in a lid-driven cavity, which is inspired by the coating process, at a broad range of Oldroyd numbers ( 0 ≤ Od ≤ 50 ), is carried out. The Reynolds number is height-based and kept at Re = 0.001 . The fluid investigated is of Carbopol gel possessing yield stress and shear-thinning properties. To express rheological characteristics, the Herschel–Bulkley model cooperated with Papanastasiou's regularization scheme is utilized. Results show that the polymer flow characteristics, i.e., velocity, viscosity, and vortex distributions, are considerably influenced by viscoplastic behaviors. Additionally, there exist solid-like regions which can be of either moving rigid or static dead types in the flow patterns; they become greater and tend to merge together to construct larger ones when Od increases. Furthermore, various polymer flow aspects in different cavity configurations are discussed and analyzed; the cavity width/aspect ratio and skewed angle are found to have significant impacts on the vortex structures and the formation of solid-like regions. Moreover, results for the critical aspect ratio at which the static dead zone is broken into two parts and the characteristic height of this zone are also reported in detail. [ABSTRACT FROM AUTHOR]

This paper investigates the mobility of cilia in a non-uniform tapered channel in the presence of an induced magnetic field and heat transfer. Thermal radiation effects are included in the heat transfer analysis. The Jeffrey model is a simpler linear model that uses time derivatives rather than convected derivatives as the Oldroyd-B model does; it depicts rheology other than Newtonian. The Jeffrey fluid model is used to investigate the rheology of a fluid with cilia motion. The proposed model examines the behavior of physiological fluids passing through non-uniform channels, which is responsible for symmetrical wave propagation and is commonly perceived between the contraction and expansion of concentric muscles. To formulate the mathematical modeling, the lubrication approach is used for momentum, energy, and magnetic field equations. The formulated linear but coupled differential equations have been solved analytically. Graphs for velocity profile, magnetic force function, induced magnetic field, current density, pressure rise, and heat profile are presented to describe the physical mechanisms of significant parameters. It is found that the eccentricity parameter of the cilia equations opposes the velocity and the magnetic force functions. The thermal radiation decreases the temperature profile while it increases for Prandtl and Eckert numbers. A promising impact of the magnetic Reynolds number and electric field on the current density profile is also observed. [ABSTRACT FROM AUTHOR]

Hemodynamic performance of the Celect Platinum vena cava filter and the revised forms of it with helical flow inducer strut were studied with computational fluid dynamic software Ansys Fluent 18. The central velocity and shear stress increased but overall flow disturbance has been observed minimal level. Central velocity increases to 9.72% with Celect filter, by the single helical flow inducer strut the rate reaches to 14.69%, and with doubled form it reaches to 19.73%. The filter surface shear rate increases to 8.29% with the single helical flow inducer strut and increases 13.31% with doubled attachment. Increased velocity and shear stress on the filter may eliminate short term thrombus build-up problems by breaking the big size particulates with the high shearing forces. The new struts may also contribute to the ability of the filter to capture smaller clots, as well as to dissolve them from being bigger. Shear stress in the vein wall increases approximately 6.63% with the filter placement. It raises to 8.06% and 9.45% with single and double helical flow inducer strut attachment. Increased vein wall shear may reduce the recirculation and clotting in the vein wall and it may prevent the accumulation of clots. The increased shear stress on the filter may cause the migration problem, design improvements can minimize this risk. Helical flow inducer strut attachment can cause efficacy increase, and the flow are normalized. [ABSTRACT FROM AUTHOR]

The finite difference schemes for equations depicting the fluid flow, heat and mass transfer of viscoelastic fluid in porous media based on fractional constitutive model are analyzed, when Soret and Dufour effects are taken into account. Different from the conventional fractional partial differential equations, the governing momentum equation of this system not only contains convection terms, but also a term: D t β 0 (∂ 2 u / ∂ y 2) , which are great challenges when we do the stability analysis. In addition, the temperature equation and concentration equation are coupled with each other, which increases the difficulty of numerical analysis. By using the energy method, the stability and convergence of the finite difference schemes employed for the governing equations are obtained. The accuracy of the scheme for momentum equation is O (τ + h x 2 + h y 2) , while the one for temperature and concentration equations is O (τ 2 + h x 2 + h y). Finally, numerical examples are presented to verify methods and demonstrate the analysis effectiveness. [ABSTRACT FROM AUTHOR]

This paper deals with the MHD peristaltic flow of Williamson fluids through a porous medium between two joint cylinders. The fluid flow was considered to be that of a non-Newtonian fluid, i.e., a Williamson fluid. The inner tube was uniform, while the flexible outer tube had a Sine wave moving down its wall. The analytical solutions for velocity and temperature were obtained as functions (Bessell functions of the first and second types). The solution for velocity profile, temperature, and concentration distribution were obtained as functions of the physical parameters of the problem (Darcy number, magnetic parameter, Grasoff thermal number, Reynolds number, Prantl number, and Schmidt number) along with other physical parameters. The effect of the physical parameters was discussed graphically. A comparison with previously published graphical results was also carried out. The ambition of the present paper is to contribute to practical applications in geographical and physiological fluid dynamics, such as on sandstone, in the human lungs, on beach sand, on limestone, and in the bile duct. This study is based on theoretical research and can be helpful in the fields of fluid mechanics and mathematics. [ABSTRACT FROM AUTHOR]

This study deals with the influence of a wavy interface separating two layers filled with power law fluid and porous media, respectively. The governing equations are solved using the Finite Element Method (FEM) and the numerical model is validated by comparing with experimental findings. The parameters governing the studied configuration are varied as: Rayleigh number (103 ≤ Ra ≤ 106), power law index (0.6 ≤ n ≤ 1.4), Darcy number (10−2 ≤ Da ≤ 10−6), buoyancy ratio (0.1 ≤ N ≤ 10) and Lewis number (1 ≤ Le ≤ 10). It is inferred that the temperature gradient increases by augmenting the Rayleigh number, as the flow is observed from the vertical to horizontal direction in both layers. Constant enhancement in the heat and mass transfer is also observed by enriching the buoyancy effect. Moreover, the average Nusselt and Sherwood numbers decline by increasing the width of the porous layer. [ABSTRACT FROM AUTHOR]

Porous materials are used in thermal devices such as heat exchangers to improvement the heat transfer. The heat transfer of a non-Newtonian fluid flow in an annular pipe with porous discs is numerically investigated in this paper. The flow regime in both porous medium and clear region are considered to be turbulent. The effects of power-law index of the non-Newtonian fluid and porous discs pitch variationson the heat transfer rate, friction coefficient are studied and compared to each other for two porous layer thicknesses. Finally, the thermal performance is defined which determines the optimum porous media and non-Newtonian fluid characteristics in the annular pipe. [ABSTRACT FROM AUTHOR]

[Display omitted] Shear thickening fluids (STFs) have been the research focus for decades because of the prospect as a damping ingredient. However, their inherent liquid character confines their practical applications. In this work, inspired by the assembly engineering, novel gelatinous shear thickening fluids (GSTFs) are fabricated by integrating low molecular weight gelators (LMWGs) into STFs and investigated by rheological experiments. The results show that the apparent performances of GSTFs are determined by the LMWGs content. LMWGs inside GSTFs can assemble into three-dimensional network that can constraint the flowability of liquid molecular and their content dominate the density and strength of assembly network. At a moderate content, GSTFs exhibit desired properties with restricted quasi-static flowability and almost undamaged dynamic shear thickening character. While a higher content will disappear shear thickening and a lower content cannot gelate STFs. Besides, three different LMWGs are employed to gelate STFs and all they can gelate STFs in spite of the distinct minimum gelation concentration, indicating the universality for GSTFs preparation and the superiority of a reasonable molecular structure of LMWGs. Further, the temperature sweep experiments suggest that GSTFs can endure higher temperature without flowing due to its higher gel-sol transition temperature. Basing on these advanced mechanical properties, we believe that the GSTFs with more expected characters have significance for the study of non-Newtonian fluids and will broaden the special application field of STFs. [ABSTRACT FROM AUTHOR]

Hydraulic fracturing fracture propagation is the main factor affecting the fracturing effect. In view of the more diversified selection of fracturing fluid, the problem of fracture propagation in non‐Newtonian fluid fracturing is often encountered in fracturing. In this paper, the influencing factors of fracture propagation of non‐Newtonian fluid fracturing fluid are analyzed. Based on PKN model, a three‐dimensional fracture propagation model considering the rheology and filtration of fracturing fluid is established, the better fracture shape simulation results are given, and the effects of fluid properties, rock physical properties, and injection parameters on fracture propagation are analyzed in detail. The research shows that (1) in the process of fracture propagation, the fracture length and width gradually increase, and the corresponding pressure in the fracture also increases. The overall increase trend is that the growth is rapid in the initial stage of fracturing and gradually slows down in the later stage. (2) The greater the consistency coefficient and rheological index, the greater the fracture width and pressure in the fracture, and the easier it is to form wide fracture. The larger the filtration coefficient is, the weaker the fracture forming ability is, and the fracture width, length, and pressure in the fracture are reduced. (3) Rock physical properties have a certain influence on fracture propagation, Young's modulus has a great influence on fracture propagation, while Poisson's ratio has little influence on it. However, the larger the Young's modulus, the more difficult the fracture is to expand, and the smaller the corresponding fracture width. (4) The larger the pump injection rate, the larger the fracture size and the higher the pressure in the fracture. The model can provide a theoretical basis for fracturing design and fracture shape prediction. [ABSTRACT FROM AUTHOR]

In this paper, the mathematical models for flow and heat-transfer analysis of a non-Newtonian fluid with axisymmetric channels and porous walls are analyzed. The governing equations of the problem are derived by using the basic concepts of continuity and momentum equations. Furthermore, artificial intelligence-based feedforward neural networks (ANNs) are utilized with hybridization of a generalized normal-distribution optimization (GNDO) algorithm and sequential quadratic programming (SQP) to study the heat-transfer equations and calculate the approximate solutions for the momentum of a non-Newtonian fluid. Legendre polynomials based Legendre neural networks (LNN) are used to develop a mathematical model for the governing equations, which are further exploited by the global search ability of GNDO and SQP for rapid localization convergence. The proposed technique is applied to study the effect of variations in Reynolds number Re on the velocity profile (f ′) and the temperature profile (q) . The results obtained by the LeNN-GNDO-SQP algorithm are compared with the differential transformation method (DTM), which shows the stability of the results and the correctness of the technique. Extensive graphical and statistical analyses are conducted in terms of minimum, mean, and standard deviation based on fitness value, absolute errors, mean absolute deviation (MAD), error in the Nash–Sutcliffe efficiency (NSE), and root mean square error (RMSE). [ABSTRACT FROM AUTHOR]