Numerical investigation for rotating flow of MHD hybrid nanofluid with thermal radiation over a stretching sheet

Thermal performance of Joule heating in radiative Eyring-Powell nanofluid with Arrhenius activation energy and gyrotactic motile microorganisms

Background

Bioconvection is the term for macroscopic convection of particles accompanied by a variable density gradient and a cluster of swimming microorganisms. The accumulation of gyrotactic microbes in the nanoparticles is important to exaggerate the thermal efficacy of various structures for instance, germs powered micro-churns, microbial fuel cubicles, micro-fluidics policies, and chip-designed micro plans like bio-microstructures.

Purpose

Here approach in the current effort is to present an innovative study of bio-convection owing to gyrotactic microbes in a nanofluid comprising non-uniform heat source/sink, space and temperature-dependent viscosity and Joule dissipation. The physical constraints such as convective-surface and new mass flux conditions are examined for 3D Eyring-Powell magneto-radiative nanofluid via porous stretched sheet.

Method

ology: Over suitable similarity alterations, the related non-linear flow, temperature, and concentration phenomena, equations are altered into non-linear equations. By combining the shooting methodology with the Runge-Kutta fourth-order technique is applied to get numerical solutions. A thorough investigation for the impact of important non-dimensional thermophysical parameters regulating flow characteristics is carried out.

Motivation

Lots of the studies on nanofluids realize their performance therefore that they can be exploited where conventional heat transport development is paramount as in numerous engineering uses, micro-electronics, transportation in addition to foodstuff and bio-medicine. The gyrotactic microbes flow in nanofluids has attained great devotion amongst researchers and the scientist community because of its works in numerous areas of bio-technology. The benefits of counting nanoparticles in mobile microbe's deferral can be established in micro-scale involvement and stability of nanofluid.

Significant results

For a few chosen parameters, the computed results for friction factor and transport for motile microorganism values are shown. The computed numerical results for parameters of engineering interest are given using tables. Furthermore, the recent solutions are stable with the former stated results and excellent association is found. The temperature of the fluid exaggerates for higher values of thermo-Biot and radiation parameter; however, Peclet and bio-convective Lewis's factor decay the motile microorganisms' field of Eyring-Powell fluid. The concentration field also enhances the activation energy parameter.

Channelized water driven flow of MHD carbon-nanotube nanofluid influenced by rotation, heat source and thermal radiation

The efficiency enhancements of thermal energy systems are made with advancements made in the effective use of thermal solar collectors, operating fluid and the introduction of curved and transparent solar panels. In this paper, we present a prototype theoretical/mathematical model for the carbon nanotube-based curved solar panels combined with the solar thermal collector and the porous rotating channel. The analysis is carried out to study the effect of transversely applied magnetic, rotation of the porous channel, linear thermal radiation and the uniformly distributed heat source on the heat transfer characteristics of the single-walled (SWCNT) and multi-walled carbon nanotubes (MWCNT). Due to the nonlinearity of the governing momentum and the heat transport equations and the limitation of the exact methods, numerical similarity solutions are obtained for the boundary value problem using the MATLAB function bvp4c. Influences of different parameters are observed through graphs on the nanofluid flow and temperature profiles. The velocity profile exhibits dual behavior for rising the nanoparticles' volume fraction, the magnetic parameter, rotation, and the Reynolds number. The temperature profile increases with increasing nanoparticles and heat source parameters and decreases for increasing suction, rotation, Reynolds number, and thermal radiation. In some cases, flow profiles for SWCNT exceed those of MWCNT.

Intelligent computing for MHD radiative Von Kármán Casson nanofluid along Darcy-Fochheimer medium with activation energy

The impact of activation energy in chemical processes, heat radiations, and temperature gradients on non-Darcian steady MHD convective Casson nanofluid flows (NMHD-CCNF) over a radial elongated circular cylinder is investigated in this study. The network of partial differential equations (PDEs) for NMHD-CCNF is developed using the modified Buongiorno framework, and the network of controlling PDEs is then transformed into ordinary differential equations (ODEs) utilizing the Von Karman method. Finally, the resulting non-linear ODEs are computed using the ND-solve approach to produce sets of data to assess the proposed model's skills, which can then be handled using the Bayesian Regularization technique of artificial neural networks (BRT-ANN). A novel stochastic computing-based application is being developed to evaluate the importance of NMHD-CCNF across a spinning disc that is radially stretched. The novelty and significance of results for better understanding, clarity, and highlighting the innovative contributions and significance of the proposed scheme. Further, to check the validity of the defined results for NMHD-CCNF, error charts, validation, and mean squared error suggestions are employed. The impact of multiple physical parameters on concentration, radial and tangential velocities, and temperature profiles is shown via tables and figures. Additionally, the results demonstrate that as the Forchheimer number, Casson nanofluid parameter, magnetic parameter, and porosity parameter are strengthened, the radial and rotational nanofluid mobility drops dramatically. The stretching parameter, on the other hand, has a parallel developmental trend. The heat generation parameter, the thermophoresis process, the thermal radiation parameter, and the Brownian motion of nanoparticles can all be increased to give thermal enhancement. On the other side, with larger estimates in thermophoresis parameters and the activation energy, there is a noticeable increase in the concentration profile.

The impacts of shape factor and heat transfer on two-phase flow of nano and hybrid nanofluid in a saturated porous medium

The focus of this article is to obtain the effect of shape factor of the hybrid nanoparticles on the convective heat and mass transference of two immiscible fluids in an inclined duct by employing the perturbation technique. The hybrid nanoparticle of Carbon Nanotube & Sodium alginate is being used with Silicon oil as the base fluid to study the heat and mass phenomena due to the soret effect, viscous dissipation, Darcy and Thermal diffusion. The physical flow problem is then modelled into a set of differential equations. The system of equations is solved analytically to obtain various graphical and numerical results for analyzing the impact of various material parameters on velocity and thermal field. The heat transfer rate and skin friction analysis for the flow dynamics are also investigated. It is observed that the shape factor enhances the fluid flow and temperature distribution. In specific lamina shape particles have better performance comparatively, significance of the soret number can also be observed.

Transportation of thermal and velocity slip factors on three-dimensional dual phase nanomaterials liquid flow towards an exponentially stretchable surface

The fundamental purpose of this research is to elaborate on slip boundary conditions and the flow of three-dimensional, stable, incompressible, rotating movements of nanoparticles lying across a stretchable sheet. The mathematical model for fluid flow is created using the assumptions stated above. The partial differentials are produced after utilizing boundary layer estimates. The partial differential governing equations are reduced into three coupled ordinary differential equations by using similarity transformations. After, applying transformations the system is solved numerically. Numerical results are approved with the help of the MATLAB bvp4c algorithm. The analysis shows that velocity and temperature are strongly dependent on essential parameters like stretching ratio, velocity slip, rotation, thermal slip parameter, and Prandtl number. Numerical values of distinct parameters on heat flux and skin friction factors are shown in a tabulated form. Partial velocity and thermal slip are applied to the temperature surface. The comparison among the nano-sized particles copper oxide and silver with water base nanofluid affecting velocity and temperature fields are used for analysis. Moreover, the Graphical depiction designates that the velocity and temperature spreading of the thermal slip parameter is increasing. It is observed that Ag-water is the best heat carrier as compared to CuO-water nanofluid.

Investigation of 3D flow of magnetized hybrid nanofluid with heat source/sink over a stretching sheet

The thermal processes with inclusion of nanomaterials provide a wide range of applications pertaining to heat exchangers and cooling of compact heat density devices. The current research investigates the three-dimension flow of hybrid nanofluid comprising TC4(Ti-6A-14V) and Nichrome 80% Ni and 20% Cr nanoparticles mixed within engine oil as the base fluid for the enhancement of heat and mass transfer rate. The effects of homogeneous-heterogeneous processes and thermal radiation are incorporated. The heat transfer occurs due to a rotating inclined stretched sheet is discussed against prominent factors such as thermal radiation, inclined angle parameter, rotation parameter, and heat source/sink. The leading mathematical formulation consists of a set of PDEs, which are then transmuted into ordinary differential equations using suitable similarity transformation. The numerical solutions are obtained by using MATLAB's built-in function bvp4c. The results for velocity profile, temperature profile and concentration distribution are evaluated for suitable ranges of the controlling parameters. The graphical result shows that when the angle of inclination, magnetic parameter, and the volumetric concentration of hybrid nanomaterials increase the axial flow profile of the hybrid nanofluid is reduced. However, the rotation parameter reveals the opposite response. The temperature is intensified with an increment of heat source/sink, shape factors, and magnetic field parameter. For enhanced nanoparticle volumetric concentration, the temperature of the fluid rises up. The graphical validation is also illustrated using streamlines and statistical plots for hybrid nanofluid.

Analysis of entropy production in a bi-convective magnetized and radiative hybrid nanofluid flow using temperature-sensitive base fluid (water) properties

The heat transport characteristics, flow features, and entropy-production of bi-convection buoyancy induced, radiation-assisted hydro-magnetic hybrid nanofluid flow with thermal sink/source effects are inspected in this study. The physical characteristics of hybrid nanofluids (water-hosted) are inherited from the base liquid (water) and none has considered the physical characteristics of base liquid (water) in the study of temperature-sensorial hybrid nanofluid investigations, though the water physical characteristics are not constants in temperature variations. So, the temperature-sensorial attributes of base liquid (water) are taken into account for this hybrid nanofluid ([Formula: see text]) flow analysis. The mathematical forms of the flow configuration (i.e., the set of coupled, nonlinear PDE form of governing equations) are solved by utilizing the subsequent tasks: (i) congenial transformation; (ii) quasilinearization; (iii) methods of finite differences to form block matrix system, and (iv) Varga's iterative algorithm. The preciseness of the whole numerical procedure is ensured by restricting the computation to follow strict convergence conditions. Finally, the numerically extracted results representing the impacts of various salient parameters on different profiles ([Formula: see text]), gradients, and entropy production are exhibited in physical figures for better perception. A few noticeable results are highlighted as: velocity graph shows contrast behaviour under assisting and opposing buoyancy; temperature ([Formula: see text]) is dropping for heightening heat source ([Formula: see text]) surface friction remarkably declines with the outlying magnetic field ([Formula: see text]); thermal transport confronts drastic abatement under radiation ([Formula: see text]), and [Formula: see text]; the characteristics Reynolds and Brinkman numbers promote entropy. Furthermore, the bounding surface acts as a strong source of [Formula: see text]-production. Summarizations are listed at the end to quantify percentage variations.

Entropy Generation and Statistical Analysis of MHD Hybrid Nanofluid Unsteady Squeezing Flow between Two Parallel Rotating Plates with Activation Energy

Squeezing flow is a flow where the material is squeezed out or disfigured within two parallel plates. Such flow is beneficial in various fields, for instance, in welding engineering and rheometry. The current study investigates the squeezing flow of a hybrid nanofluid (propylene glycol–water mixture combined with paraffin wax–sand) between two parallel plates with activation energy and entropy generation. The governing equations are converted into ordinary differential equations using appropriate similarity transformations. The shooting strategy (combined with Runge–Kutta fourth order method) is applied to solve these transformed equations. The results of the conducted parametric study are explained and revealed in graphs. This study uses a statistical tool (correlation coefficient) to illustrate the impact of the relevant parameters on the engineering parameters of interest, such as the surface friction factor at both plates. This study concludes that the squeezing number intensifies the velocity profiles, and the rotating parameter decreases the fluid velocity. In addition, the magnetic field, rotation parameter, and nanoparticle volumetric parameter have a strong negative relationship with the friction factor at the lower plate. Furthermore, heat source has a strong negative relationship with heat transfer rate near the lower plate, and a strong positive correlation with the same phenomena near the upper plate. In conclusion, the current study reveals that the entropy generation is increased with the Brinkman number and reduced with the squeezing parameter. Moreover, the results of the current study verify and show a decent agreement with the data from earlier published research outcomes.

Entropy generation optimization of unsteady radiative hybrid nanofluid flow over a slippery spinning disk

Entropy generation investigation of hybrid nanofluidic transport over an unsteady spinning disk is reported in this analysis. The magnetic influence, velocity slips, and thermal radiative effects are included within the flow. Ferrous oxide (Fe3O4) and graphene oxide (GO) are used as tiny nano ingredients, and water (H2O) is the base medium. The dimensional leading equations are settled to dimensionless nonlinear ordinary differential equations (ODEs) by significant similarity transformations. Then, classical RK-4 scheme with a shooting process has been initiated to execute the numerical simulation. The software MAPLE-18 is used to run the entire simulation with an indispensable accuracy rate. Several streamlines, graphs, and requisite tables are executed to divulge the parametric impact on the nanofluidic stream. Entropy generation–related figures are depicted for diverse parameters, and parametric effects on Bejan number are also analyzed. Moreover, the corresponding physical consignments like the measure of the frictional hindrance, heat transport are calculated and reviewed. The entropy generation augments for higher magnetic value but reduces for velocity slip, radiation, and nanoparticle concentration. Hybrid nanofluid gives a lower magnitude in entropy production as compared to the usual nanofluid. Magnetic parameter reduces the Bejan number, while slip factor and nanoparticle concentration amplify such effects. Heat transfer ultimately seems to increase for nanoparticle volume fraction, and the increase rate is 4.01685 for usual nanofluid, but it is 6.7557 for hybrid nanofluid. Also, the numerical fallouts address the possibility of using magnetized spinning disks in space engines and nuclear propulsion, and such a model conveys significant applications in heat transport improvement in so many industrial thermal management equipment and renewable energy systems.

Computational Analysis for Bioconvection of Microorganisms in Prandtl Nanofluid Darcy-Forchheimer Flow across an Inclined Sheet

The two-dimensional boundary layer flow of a Prandtl nanofluid was explored in the presence of an aligned magnetic field over an inclined stretching/shrinking sheet in a non-Darcy permeable medium. To transform the PDEs of the leading equations into ODEs, a coupled boundary value problem was formed and suitable similarity functions were used. To obtain numerical answers, an efficient code for the Runge–Kutta technique with a shooting tool was constructed with a MATLAB script. This procedure is widely used for the solution of such problems as it is efficient and cost-effective with a fifth-order accuracy. The significance of immersed parameters on the velocity, temperature, concentration, and bioconvection is shown through figures. Furthermore, the physical parameters of the skin friction coefficient and the Nusselt numbers are demonstrated in tables. The declining behavior of the flow velocity against the porosity parameter Kp and the local inertia co-efficient Fr is shown, and the both parameters of the Darcy resistance and Darcy–Forchheimer resistance are responsible for slowing the fluid speed. The increasing values of the Schmidt number Sc decrease the concentration of the nano entities.

Heat Transfer Attributes of Gold-Silver-Blood Hybrid Nanomaterial Flow in an EMHD Peristaltic Channel with Activation Energy

The heat enhancement in hybrid nanofluid flow through the peristaltic mechanism has received great attention due to its occurrence in many engineering and biomedical systems, such as flow through canals, the cavity flow model and biomedicine. Therefore, the aim of the current study was to discuss the hybrid nanofluid flow in a symmetric peristaltic channel with diverse effects, such as electromagnetohydrodynamics (EMHD), activation energy, gyrotactic microorganisms and solar radiation. The equations governing this motion were simplified under the approximations of a low Reynolds number (LRN), a long wavelength (LWL) and Debye–Hückel linearization (DHL). The numerical solutions for the non-dimensional system of equations were tackled using the computational software Mathematica. The influences of diverse physical parameters on the flow and thermal characteristics were computed through pictorial interpretations. It was concluded from the results that the thermophoresis parameter and Grashof number increased the hybrid nanofluid velocity near the right wall. The nanoparticle temperature decreased with the radiation parameter and Schmidt number. The activation energy and radiation enhanced the nanoparticle volume fraction, and motile microorganisms decreased with an increase in the Peclet number and Schmidt number. The applications of the current investigation include chyme flow in the gastrointestinal tract, the control of blood flow during surgery by altering the magnetic field and novel drug delivery systems in pharmacological engineering.

Effect of Thermal Radiation on Three-Dimensional Magnetized Rotating Flow of a Hybrid Nanofluid

The effect of thermal radiation on the three-dimensional magnetized rotating flow of a hybrid nanofluid has been numerically investigated. Enhancing heat transmission is a contemporary engineering challenge in a range of sectors, including heat exchangers, electronics, chemical and biological reactors, and medical detectors. The main goal of the current study is to investigate the effect of magnetic parameter, solid volume fraction of copper, Eckert number, and radiation parameter on velocity and temperature distributions, and the consequence of solid volume fraction on declined skin friction and heat transfer against suction and a stretching/shrinking surface. A hybrid nanofluid is a contemporary type of nanofluid that is used to increase heat transfer performance. A linear similarity variable is−applied to convert the governing partial differential equations (PDEs) into corresponding ordinary differential equations (ODEs). Using the three-stage Labatto III-A method included in the MATLAB software’s bvp4c solver, the ODE system is solved numerically. In certain ranges of involved parameters, two solutions are received. The temperature profile θη upsurges in both solutions with growing values of EC and Rd. Moreover, the conclusion is that solution duality exists when the suction parameter S≥Sci, while no flow of fluid is possible when S<Sci. Finally, stability analysis has been performed and it has been found that only the first solution is the stable one between both solutions.

Dynamics of ethylene glycol-based graphene and molybdenum disulfide hybrid nanofluid over a stretchable surface with slip conditions

In this research study, numerical and statistical explorations are accomplished to capture the flow features of the dynamics of ethylene glycol-based hybrid nanofluid flow over an exponentially stretchable sheet with velocity and thermal slip conditions. Physical insight of viscous dissipation, heat absorption and thermal radiation on the flow-field is scrutinized by dissolving the nanoparticles of molybdenum disulfide (MoS2) and graphene into ethylene glycol. The governing mathematical model is transformed into the system of similarity equations by utilizing the apt similarity variables. The numerical solution of resulting similarity equations with associated conditions are obtained employing three-stages Lobatto-IIIa-bvp4c-solver based on a finite difference scheme in MATLAB. The effects of emerging flow parameters on the flow-field are enumerated through various graphical and tabulated results. Additionally, to comprehend the connection between heat transport rate and emerging flow parameters, a quadratic regression approximation analysis on the numerical entities of local Nusselt numbers and skin friction coefficients is accomplished. The findings disclose that the suction and thermal radiation have an adverse influence on the skin friction coefficients and heat transport rate. Further, a slight augmentation in the thermal slip factor causes a considerable variation in the heat transport rate in comparison to the radiation effect.

Novel Adaptive Bayesian Regularization Networks for Peristaltic Motion of a Third-Grade Fluid in a Planar Channel

In this presented communication, a novel design of intelligent Bayesian regularization backpropagation networks (IBRBNs) based on stochastic numerical computing is presented. The dynamics of peristaltic motion of a third-grade fluid in a planar channel is examined by IBRBNs using multilayer structure modeling competency of neural networks trained with efficient optimization ability of Bayesian regularization method. The reference dataset used as inputs and targets parameters of IBRBN has been obtained via the state-of-the-art Adams numerical method. The data of solution dynamics is created for multiple scenarios of the peristaltic transport model by varying the volume flow rate, material parametric of a third-grade fluid model, wave amplitude, and inclination angles. The designed integrated IBRBNs are constructed by exploiting training, testing, and validation operations at each epoch via optimization of a figure of merit on mean square error sense. Exhaustive simulation of IBRBNs with comparison on mean square error, histograms, and regression index substantiated the precision, stability, and reliability to solve the peristaltic transport model.

MHD Hybrid Nanofluid Flow Due to Rotating Disk with Heat Absorption and Thermal Slip Effects: An Application of Intelligent Computing

The objective of this study is to explore the flow features and heat transfer properties of an MHD hybrid nanofluid between two parallel plates under the effects of joule heating and heat absorption/generation (MHD-HFRHT) by utilizing the computational strength of Levenberg–Marquardt Supervised Neural Networks (LM-SNNs). Similarity equations are utilized to reduce the governing PDEs into non-linear ODEs. A reference solution in the form of data sets for MHD-HFRHT flow is obtained by creating different scenarios by varying involved governing parameters such as the Hartman number, rotation parameter, Reynolds number, velocity slip parameter, thermal slip parameter and Prandtl number. These reference data sets for all scenarios are placed for training, validation and testing through LM-SNNs and the obtained results are then compared with reference output to validate the accuracy of the proposed solution methodology. AI-based computational strength with the applicability of LM-SNNs provides an accurate and reliable source for the analysis of the presented fluid-flow system, which has been tested and incorporated for the first time. The stability, performance and convergence of the proposed solution methodology are validated through the numerical and graphical results presented, based on mean square error, error histogram, regression plots and an error-correlation measurement. MSE values of up to the accuracy level of 1 × 10−11 established the worth and reliability of the computational technique. Due to an increase in the Hartmann number, a resistance was observed, resulting in a reduction in the velocity profile. This occurs as the Hartmann number measures the relative implication of drag force that derives from magnetic induction of the velocity of the fluid flow system. However, the Reynolds number accelerates in the velocity profile due to the dominating impact of inertial force.

Heat transfer analysis of the mixed convective flow of magnetohydrodynamic hybrid nanofluid past a stretching sheet with velocity and thermal slip conditions

The present study is related to the analytical investigation of the magnetohydrodynamic flow of Ag − MgO/ water hybrid nanoliquid with slip conditions via an extending surface. The thermal radiation and Joule heating effects are incorporated within the existing hybrid nanofluid model. The system of higher-order partial differential equations is converted to the nonlinear system of ordinary differential equations by interpreting the similarity transformations. With the implementation of a strong analytical method called HAM, the solution of resulting higher-order ordinary differential equations is obtained. The results of the skin friction coefficient, Nusselt number, velocity profile, and temperature profile of the hybrid nanofluid for varying different flow parameters are attained in the form of graphs and tables. Some important outcomes showed that the Nusselt number and skin friction are increased with the enhancement in Eckert number, stretching parameter, heat generation parameter and radiation parameter for both slip and no-slip conditions. The thermal profile of the hybrid nanofluid is higher for suction effect but lower for Eckert number, stretching parameter, magnetic field, heat generation and radiation parameter. For both slip and no-slip conditions, the hybrid nanofluid velocity shows an upward trend for both the stretching and mixed convection parameters.

Impact of Bioconvection and Chemical Reaction on MHD Nanofluid Flow Due to Exponential Stretching Sheet

Thermal management is a crucial task in the present era of miniatures and other gadgets of compact heat density. This communication presents the momentum and thermal transportation of nanofluid flow over a sheet that stretches exponentially. The fluid moves through a porous matrix in the presence of a magnetic field that is perpendicular to the flow direction. To achieve the main objective of efficient thermal transportation with increased thermal conductivity, the possible settling of nano entities is avoided with the bioconvection of microorganisms. Furthermore, thermal radiation, heat source dissipation, and activation energy are also considered. The formulation in the form of a partial differential equation is transmuted into an ordinary differential form with the implementation of appropriate similarity variables. Numerical treatment involving Runge–Kutta along with the shooting technique method was chosen to resolve the boundary values problem. To elucidate the physical insights of the problem, computational code was run for suitable ranges of the involved parameters. The fluid temperature directly rose with the buoyancy ratio parameter, Rayleigh number, Brownian motion parameter, and thermophoresis parameter. Thus, thermal transportation enhances with the inclusion of nano entities and the bioconvection of microorganisms. The findings are useful for heat exchangers working in various technological processors. The validation of the obtained results is also assured through comparison with the existing result. The satisfactory concurrence was also observed while comparing the present symmetrical results with the existing literature.

Numerical Investigation of Heat Transfer on Unsteady Hiemenz Cu-Water and Ag-Water Nanofluid Flow over a Porous Wedge Due to Solar Radiation

Nanoparticles are generally used to scatter and absorb solar radiations in nanofluid-based direct solar receivers to efficiently transport and store the heat. However, solar energy absorption in nanofluid can be enhanced by using differential materials and tuning nanofluid parameter. In this regard, theoretical investigations of unsteady homogeneous Hiemenz flow of an incompressible nanofluid having copper and silver nanoparticles over a porous wedge is carried out by using optimal homotopy asymptotic method (OHAM). Hence, a semi-analytical solver is applied to the transformed system to study the significance of magnetic field along with Prandtl number. In this work, impacts of conductive radiations, heat sink/source, unsteadiness, and flow parameters have been investigated for velocity and temperature profiles of copper and silver nanoparticles-based nanofluid. The effects of magnetic strength, volume fraction of nanoparticles, thermal conductivity, and flow parameters have also been studied on the considered nanofluids.

Intelligent computing technique based supervised learning for squeezing flow model

In this study, the unsteady squeezing flow between circular parallel plates (USF-CPP) is investigated through the intelligent computing paradigm of Levenberg–Marquard backpropagation neural networks (LMBNN). Similarity transformation introduces the fluidic system of the governing partial differential equations into nonlinear ordinary differential equations. A dataset is generated based on squeezing fluid flow system USF-CPP for the LMBNN through the Runge–Kutta method by the suitable variations of Reynolds number and volume flow rate. To attain approximation solutions for USF-CPP to different scenarios and cases of LMBNN, the operations of training, testing, and validation are prepared and then the outcomes are compared with the reference data set to ensure the suggested model’s accuracy. The output of LMBNN is discussed by the mean square error, dynamics of state transition, analysis of error histograms, and regression illustrations.

Intelligent Computing with Levenberg-Marquardt Backpropagation Neural Networks for Third-Grade Nanofluid Over a Stretched Sheet with Convective Conditions

This article discussed the influence of activation energy on MHD flow of third-grade nanofluid model (MHD-TGNFM) along with the convective conditions and used the technique of backpropagation in artificial neural network using Levenberg–Marquardt technique (BANN-LMT). The PDEs representing (MHD-TGNFM) transformed into the system of ODEs. The dataset for BANN-LMT is computed for the six scenarios by using the Adam numerical method by varying the local Hartman number (Ha), Prandtl number (Pr), local chemical reaction parameter (σ), Schmidt number (Sc), concentration Biot number (γ₂) and thermal Biot number (γ₁). By testing, validation and training process of (BANN-LMT), the estimated solutions are interpreted for (MHD-TGNFM). The validation of the performance of (BANN-LMT) is done through the MSE, error histogram and regression analysis. The concentration profile increases when there is an increase in Biot number and the local Hartmann number; meanwhile, it decreases for the higher values of Schmidt number and the local chemical reaction parameter.

Supervised Learning Algorithm to Study the Magnetohydrodynamic Flow of a Third Grade Fluid for the Analysis of Wire Coating

In the present study, modeling of intelligent numerical computing through Levenberg-Marquardt back propagation-based supervised neural network (LMB-SNN) is incorporated to analyze the magnetohydrodynamic flow of a third grade fluid for wire coating analysis (MHD-TGFWCA). The original mathematical formulations in terms of partial differential equations for MHD-TGFWCA are converted into a system of ordinary differential equations through dimensionless parameters and a suitable transformation mechanism. A reference dataset for the LMB-SNNs scheme is created with Adam's numerical technique for various scenarios by variation of different physical quantities such as third grade fluid parameter, magnetic parameter, and the velocity ratio parameter. To compute the approximate solution for MHD-TGFWCA in terms of various scenarios, the training, testing, and validation operations are carried out in parallel to adjust neural networks by developing the mean square error function (MSEF) through Levenberg-Marquardt back-propagation. The comparative analyses and performance studies through outputs of MSEF, regression illustrations, and error histograms validate the effectiveness of the suggested solver LMB-SNNs. The method's precision is verified by the closest numerical outputs of both built and dataset values with similar levels 10 - 5 to 10 - 9 .

MHD Williamson Nanofluid Flow over a Slender Elastic Sheet of Irregular Thickness in the Presence of Bioconvection

Bioconvection phenomena for MHD Williamson nanofluid flow over an extending sheet of irregular thickness are investigated theoretically, and non-uniform viscosity and thermal conductivity depending on temperature are taken into account. The magnetic field of uniform strength creates a magnetohydrodynamics effect. The basic formulation of the model developed in partial differential equations which are later transmuted into ordinary differential equations by employing similarity variables. To elucidate the influences of controlling parameters on dependent quantities of physical significance, a computational procedure based on the Runge–Kutta method along shooting technique is coded in MATLAB platform. This is a widely used procedure for the solution of such problems because it is efficient with fifth-order accuracy and cost-effectiveness. The enumeration of the results reveals that Williamson fluid parameter λ, variable viscosity parameter Λμ and wall thickness parameter ς impart reciprocally decreasing effect on fluid velocity whereas these parameters directly enhance the fluid temperature. The fluid temperature is also improved with Brownian motion parameter Nb and thermophoresis parameter Nt. The boosted value of Brownian motion Nb and Lewis number Le reduce the concentration of nanoparticles. The higher inputs of Peclet number Pe and bioconvection Lewis number Lb decline the bioconvection distribution. The velocity of non-Newtonian (Williamson nanofluid) is less than the viscous nanofluid but temperature behaves oppositely.

Intelligent computing through neural networks for numerical treatment of non-Newtonian wire coating analysis model

In the current study, a modern implementation of intelligent numerical computational solver introduced using the Levenberg Marquardt algorithm based trained neural networks (LMA-TNN) to analyze the wire coating system (WCS) for the elastic-viscous non-Newtonian Eyring-Powell fluid (EPF) with the impacts of Joule heating, magnetic parameter and heat transfer scenarios in the permeable medium. The nonlinear PDEs describing the WCS-EPF are converted into dimensionless nonlinear ODEs containing the heat and viscosity parameters. The reference data for the designed LMA-TNN is produced for various scenarios of WCS-EPF representing with porosity parameter, non-Newtonian parameter, heat transfer parameter and magnetic parameter for the proposed analysis using the state of the art explicit Runge-Kutta technique. The training, validation, and testing operations of LMA-TNN are carried out to obtain the numerical solution of WCS-EPF for various cases and their comparison with the approximate outcomes certifying the reasonable accuracy and precision of LMA-TNN approach. The outcomes of LMA-TNN solver in terms of state transition (ST) index, error-histograms (EH) illustration, mean square error, and regression (R) studies further established the worth for stochastic numerical solution of the WCS-EPF. The strong correlation between the suggested and the reference outcomes indicates the structure's validity, for all four cases of WCS-EPF, fitting of the precision [Formula: see text] to [Formula: see text] is also accomplished.