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The paper presents an innovative computational framework for predictive solutions for simulating the spread of malaria. The structure incorporates sophisticated computing methods to improve the reliability of predicting malaria outbreaks. The study strives to provide a strong and effective tool for forecasting the propagation of malaria via the use of an AI-based recurrent neural network (RNN). The model is classified into two groups, consisting of humans and mosquitoes. To develop the model, the traditional Ross-Macdonald model is expanded upon, allowing for a more comprehensive analysis of the intricate dynamics at play. To gain a deeper understanding of the extended Ross model, we employ RNN, treating it as an initial value problem involving a system of first-order ordinary differential equations, each representing one of the seven profiles. This method enables us to obtain valuable insights and elucidate the complexities inherent in the propagation of malaria. Mosquitoes and humans constitute the two cohorts encompassed within the exposition of the mathematical dynamical model. Human dynamics are comprised of individuals who are susceptible, exposed, infectious, and in recovery. The mosquito population, on the other hand, is divided into three categories: susceptible, exposed, and infected. For RNN, we used the input of 0 to 300 days with an interval length of 3 days. The evaluation of the precision and accuracy of the methodology is conducted by superimposing the estimated solution onto the numerical solution. In addition, the outcomes obtained from the RNN are examined, including regression analysis, assessment of error autocorrelation, examination of time series response plots, mean square error, error histogram, and absolute error. A reduced mean square error signifies that the model's estimates are more accurate. The result is consistent with acquiring an approximate absolute error close to zero, revealing the efficacy of the suggested strategy. This research presents a novel approach to solving the malaria propagation model using recurrent neural networks. Additionally, it examines the behavior of various profiles under varying initial conditions of the malaria propagation model, which consists of a system of ordinary differential equations. [ABSTRACT FROM AUTHOR]

In this study, the Falkner–Skan stream (FSS) of ZnO-EG across a moving wedge is investigated using artificial neural networks backpropagated using a Bayesian regularization strategy (ANN-BRS). The PDEs of the Falkner–Skan are converted into a set of ordinary differential equations (ODEs). The reference dataset is created using the mathematical solver in Mathematica and includes moving wedge boundaries, radiation boundaries, nanoparticle volume division boundaries and Falkner–Skan power-regulation boundaries for all proposed scenarios (ANN-BRS). Examined is the effect of practical cut off points on the stream field and temperature profiles, including the radiation limit, moving wedge limit, nanoparticle volume division and Falkner–Skan power. When nanoparticles are present, viscosity and heat conductivity rise, which can be physically explained. Increases in Falkner–Skan power have both positive and negative effects. When the settings are adjusted to their highest values, the maximum rate of heat transmission is realized. The effects of radiation boundary and so on are identical due to the linear augment. As a result, as the parameters are increased, the rate of heat transmission increases. Based on the intended data points that were obtained, the estimated answer is calculated for every scenario utilizing the testing, training and validation procedures. The mean square error data (MSE), error histogram and regression analysis are used to validate the performance of (ANN-BRS). [ABSTRACT FROM AUTHOR]

Summary: A solar thermal collector collects heat by absorbing sunlight and converting this incoming radiation into useful thermal energy. The parabolic trough solar sollector (PTSC) is widely installed in concentrated solar power technology with a temperature range of 325‐700 K. The thermodynamic efficiency of the PTSC can be intensified by using nanofluids owing to their enhanced thermophysical properties. In this paper, the two‐dimensional flow over a stretched sheet in PTSC under Williamson nanofluid effects is explored. With the help of useful transformations, the partial differential equations arising from boundary layer equations of the Williamson nanofluid model are changed into nonlinear ordinary differential equations. The Keller box numerical scheme is then used to find the solution of the resulting nonlinear ordinary differential equations. Two nanofluids, copper‐engine oil (Cu‐EO) and alumina‐engine oil (Al2O3‐EO) are considered to address the performance analysis of PTSC in this study. It is observed that the parameters of the porous media reduced the heat transfer rate but increased the velocity gradient. In order to examine the effect on various performance parameters of the device, the nanoparticle concentration is also varied. With the increase in the Reynolds and Brinkman numbers, the entropy is found to increase. The thermodynamic performance of the Cu‐EO nanofluid is remarkably better than that of the Al2O3‐EO nanofluid under the same conditions. The thermal efficiency of Cu‐EO over Al2O3‐EO is seen with a minimum of 1.5% and a maximum of 9.1%. The theoretical simulations documented here may be effective in improving solar thermal energy systems. [ABSTRACT FROM AUTHOR]

In this paper, the influence of velocity slip and the Newtonian heating parameters on Williamson Nanofluid across a variable stretching sheet is studied. The basic fluid flow equations are turned into a system of coupled ordinary differential equations with appropriate conditions, which are solved numerically with the Keller-box approach. The outcomes show that, increasing Williamson parameter, due to the viscosity velocity of the fluid slowdown. As a result, it is noticed that the velocity slip parameter reduces Williamson Nanofluid velocity, while increasing shear stress, according to the results. Furthermore, it has been discovered that unlike velocity profiles, the slip influence is more pronounced on temperature and concentration profiles. Furthermore, the Newtonian heating parameter may be shown to have rising functions for velocity and dimensionless temperature. Newtonian heating has uses in the petroleum industry, heat exchangers, conjugate heat transfer around fins and solar radiation. It is discovered that the Joule heating parameter improves the thermal boundary layer thickness and slows down the velocity of the fluid, which aids in maintaining system temperature. Additionally, it has been found that the temperature profile exhibits a stronger slip effect compared with the velocity profile. To prepare toffee, chocolate and other delicacies as efficiently as possible, it is crucial to investigate the flow of Williamson fluids (such as drilling muds, clay coatings, various suspensions and some lubricating oils, thermoplastic melts, and a variety of colloids) in the incidence of heat transfer. The novelty of this paper is the effect of joule heating, Newtonian heating parameter and velocity slip on Williamson fluid velocity and temperature gradient. Furthermore, the heat and mass transfer rates are calculated for various parameters numerically and shown in tabular form. [ABSTRACT FROM AUTHOR]

The present study investigates the significance of activation energy during chemical reactions, thermal radiations and temperature gradient of 3-D steady Magnetohydrodynamic Casson nanofluid flow (MHDCNFM) in Darcy−Forchheimer medium over an oscillating disk by using an intelligent numerical-based computing solver through the Levenberg-Marquardt backpropagation neural network scheme (LMBNNS). The adjusted Buongiorno model is utilized to develop the system of partial differential equations (PDEs) for MHDCNFM, and further, by invoking Von Karman similarity transformation, the system of governing PDEs is turned out into ordinary differential equations (ODEs). First, a data set for the magnetohydrodynamic Casson nanofluid flow model (MHDNNFM) is generated for a range of sundry parameters for the radial velocity, tangential velocity, heat distribution and concentration profile by the variations of Casson parameter, magnetic parameter, Brownian motion parameter, thermophoresis parameter, Forchheimer parameter, activation energy parameter, chemical reaction parameter, stretching parameter, porosity parameter and Schmidt number through the Lobatto IIIA technique, and after this, by applying an intelligent computing algorithm through nftool training, testing and validation steps are taken into account to find out the approximate solution for various cases. The designed solver LMBNNS is used to solve the MHDCNFM through mean squared error (MSE), regression, gradient analysis and histogram studies. [ABSTRACT FROM AUTHOR]

The major purpose of this article is to exploit the strength of the Intelligent Back-propagated Neural Networks of Levenberg Marquardt Technique (IBNN-LMT) to study three-dimensional (3D) squeezed flow model of carbon nanotubes (SFM-CNTs) relying on water in a revolving network with a rigid ground wall. The impact of magnetohydrodynamic (MHD) and thermal radiation has been investigated. Similarity transformation is utilized to convert partial differential equations (PDEs) into ordinary differential equations (ODEs). For numerous nanofluids constructed of SWCNT and MWCNT, the influence of each parameter on velocity, temperature, Bejan number, and entropy production is estimated. The overall entropy optimization was also computed. The major outcome of this research is to examine the impacts of flowing parameters on CNTs when squeezing parameters are changed. Moreover, the estimated solution is evaluated for designed SFM-CNTs by using a testing method and comparing it to a standard solution that has been backed up by performance studies based on MSE convergence, error histogram, and regression studies. The velocity profile f (χ) along y-axis intensifies with the intensification in S , φ ,and A. Where Ω gives a dual performance with the increment in the function, as with the increase in M , f (χ) provides decreasing performance. The temperature function θ (χ) increase as the increment in S , Ec ,and Ec m and decrease with the increase in φ and R. The solution is accurate up to 4 to 10 decimal places which proves the worth and effectiveness of the proposed IBNN-LMT solver. [ABSTRACT FROM AUTHOR]

The current flow model is dedicated to capture the role of Dufour and Soret on heat and mass transmission of rotating flow of γ Al 2 O 3 - C 2 H 6 O 2 and γ Al 2 O 3 - water nanoparticles due to exponential stretching under the action of thermal radiation, magnetic, and Eckert numbers. The problem is modelled in terms if partial differential equations (PDEs) with associated physical conditions. The ordinary differential equations (ODEs) are obtained via suitable transformations. The reduced nonlinear ODEs set is tackled via a new scheme. We suggested significant improvements in the traditional technique and further formulated an extended version of wavelets scheme-based Chebyshev polynomials thoughts. The detailed procedure of the wavelet scheme and flow chart are provided. To validate the numerical outcomes; a comparative study with numerical technique RK (order-4) is also provided. Furthermore; numerical consequences of velocity, concentration and temperature profiles are further examined using several plots. The graphical plots, compared and convergence analyses are endorsing that our proposed modifications are worthy. Velocities profiles in view of γ Al 2 O 3 - C 2 H 6 O 2 nanofluid are lower than the γ Al 2 O 3 - H 2 O nanofluid. Temperature and concentration profiles are dominant when γ Al 2 O 3 - H 2 O nanofluid is considered. [ABSTRACT FROM AUTHOR]

The nanofluid flows play a vital role in many engineering processes owing to their notable industrial usage and excessive heat transfer abilities. Lately, an advanced form of nanofluids namely "hybrid nanofluids" has swapped the usual nanofluid flows to further augment the heat transfer capabilities. The objective of this envisaged model is to compare the performance of two renowned hybrid nanofluid models namely Hamilton–Crosser and Yamada–Ota. The hybrid nanoliquid (TiO2-SiC/DO) flow model is comprised of Titanium oxide (TiO2) and Silicon carbide (SiC) nanoparticles submerged into Diathermic oil (DO). The subject flow is considered over a stretched surface and is influenced by the magnetic dipole. The uniqueness of the fluid model is augmented by considering the modified Fourier law instead of the traditional Fourier law and slip conditions at the boundary. By applying the suitable similarity transformations, the system of ordinary differential equations obtained from the leading partial differential equations is handled by the MATLAB solver bvp4c package to determine the numerical solution. It is divulged that the Yamada–Ota model performs considerably better than the Hamilton–Crosser flow model as far as heat transfer capabilities are concerned. Further, the velocity reduces on increasing hydrodynamic interaction and slip parameters. It is also noted that both temperature profiles increase for higher hydrodynamic interaction and viscous dissipation parameters. The envisioned model is authenticated when compared with an already published result in a limiting case. [ABSTRACT FROM AUTHOR]

Chemical kinetics is a branch of chemistry that is founded on understanding chemical reaction rates. Chemical kinetics relates many aspects of cosmology, geology, and even in some cases of, psychology. There is a need for mathematical modelling of these chemical reactions. Therefore, the present research is based on chemical kinetics-based modelling and dynamics of enzyme processes. This research looks at the two-step substrate-enzyme reversible response. In the two step-reversible reactions, substrate combines with enzymes which is further converted into products with two steps. The model is displayed through the flow chart, which is then transformed into ODEs. The Atangana-Baleanu time-fractional operator and the Mittag-Leffler kernel are used to convert the original set of highly nonlinear coupled integer order ordinary differential equations into a fractional-order model. Additionally, it is shown that the solution to the investigated fractional model is unique, limited, and may be represented by its response velocity. A numerical scheme, also known as the Atangana-Toufik method, based on Newton polynomial interpolation technique via MATLAB software, is adopted to find the graphical results. The dynamics of reaction against different reaction rates are presented through various figures. It is observed that the forward reaction rates increase the reaction speed while backward reaction rates reduce it. [ABSTRACT FROM AUTHOR]

The role of non-Newtonian fluids can't be denied owing to their immense industrial and engineering applications. Taking this point in mind, the motivation of the current investigation is to examine the influence of a magnetic dipole on two-dimensional nonelectrical conducting Oldroyd-B fluid flow in the existence of thermophoretic particle deposition along a linearly stretching surface. The exponential space-based thermal source and the temperature-dependent heat source/sink are incorporated into the thermal equation. The fluid concentration is strengthened with binary activation energy and Arrhenius chemical reaction. The set of ordinary differential equations that are attained after applying the similarity transformations is resolved numerically by the bvp4c approach of MATLAB software. The impact of diverse parameters on velocity, temperature, and concentration are graphically examined. The quantities of physical importance are also computed and analyzed numerically. The results revealed that fluid velocity and temperature have opposing trends for the ferromagnetic interaction parameter. It is also witnessed that the fluid concentration arguments for the chemical reaction parameter. The validation of the model in the limiting case is also given. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids (HNF) are the advanced form of nanofluids used for improved heat transfer purposes. Taking this point in mind, the objective of the presented endeavor is to examine the Yamada–Ota HNF flow model comprising (gold–silver/engine oil) over a stretched cylindrical surface and a sheet (as a limiting case) in a permeable medium. The novelty of this research is the consideration of the surface-catalyzed reaction along with the homogeneous–heterogeneous reactions to accelerate the chemical reactions in the shortest possible time. The heat transport phenomenon is strengthened with the support of Joule heating, heat absorption/generation, and the convective heat boundary condition at the surface of the cylinder. The obtained ordinary differential equations are reduced from the partial differential equations using boundary layer theory and are numerically computed using the Keller box method. It is witnessed that for varied estimates of the magnetic parameter, the thermal profile enhances while the velocity field reduces. It is also noted that the fluid concentration is reduced when the surface-catalyzed parameter is enhanced. The validation of the envisioned model in a limiting case is also added to this investigation. [ABSTRACT FROM AUTHOR]

This article presents, for the first time, a comparative analysis of two different solution methodologies for the numerical investigation of flow and thermal behavior of Casson fluid through a channel having linearly extending lower wall while the upper wall is kept at rest. MHD Casson fluid boundary layer flow is supposed to be steady, laminar, viscous, and incompressible. We have taken into account the mixed convection effects, whereas the usual no slip condition has been imposed on both walls. The Navier–Stokes equations for the proposed model have been converted into nonlinear and coupled system of ordinary differential equations (ODEs) by employing similarity variables, which are then solved by using the differential transform method (DTM) and the quasi‐linearization method (QLM). We note that the quasi‐linearization approach is better than the DTM, as the latter becomes inappropriate for the increasing values of the parameters involved. Moreover, the variation of the different parameters for velocity and temperature profiles has been analyzed graphically. [ABSTRACT FROM AUTHOR]

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for MHD Carreau nanofluid flow model (MHDCNFM) in terms of partial differential equations (PDEs) is transformed into equivalent nonlinear ordinary differential equations (ODEs) by utilizing the similarity transformation and dimensional parameters. A reference dataset of proposed LMBNNT is made for Carreau nanofluid flow model exploiting the strength of Lobatto IIIA technique through the variations of different parameters against the velocity, temperature profile and concentration. These reference datasets are placed for validation, training and testing by LMBNNT and obtained outcomes are compared with reference results to check the accuracy of the designed methodology. The validation of the proposed solution methodology is obtained through the mean square error (MSE), error histogram error profile, regression p lot and fitness plot. MSE values' accuracy is upto 1 0 − 1 0 which establish the reliability of the LMBNNT. Moreover, due to an increase in Weissenberg number, fluid velocity decays in case of shear thinning liquid and higher values of Biot number enhance the temperature profile and improves the rate of heat transfer. Moreover, the increment in Hartman number reduces the surface drag force and large values of Prandtl number reduce the heat transfer process. These results of all these parameters are expressed in well-organized numerical and graphical forms. [ABSTRACT FROM AUTHOR]

Time delays play an important part in modeling the fact that one cannot be communicable for a long time after becoming sick. Delay can be triggered by a variety of epidemiological situations. The most egregious causes of a delay are infection latency in the vector and infection latency in the infected host. The dynamics of susceptible, infected, recovered and cross-immune (SIRC) classed-based model having cross-immune and time-delay in the transmission for spread of COVID-19 abbreviated as (SIRC-CTC-19) are investigated in this study using an intelligent numerical computing paradigm based on the Levenberg–Marquardt Method backpropagated by neural networks (LM-BPNN). The model is mathematically governed by a system of ordinary differential equations that depicts the four nodes as susceptible, infected, recovered and cross-immune ones (SIRC) nodes with cross-immune class and time-delay in transmission components for COVID-19 dissemination (CTC-19). The reference solution of the SIRC model for the spread of COVID-19 is produced by using the explicit Runge–Kutta method for the many scenarios of this model arising from altering delay with regard to time. This reference solution permits the use of evolutionary computing to solve the SIRC-CTC-19 using train, validate and test techniques. The proposed LM-BPNN method's accuracy has been proven by its results overlapping with explicit Runge–Kutta results Calculation of regression metrics, error analysis of histogram illustrations and learning curves on MSE effectively augment the LM-BPNN's accuracy, convergence and reliability in solving the SIRC-CTC-19 model. [ABSTRACT FROM AUTHOR]

This study emphasizes the performance of two-dimensional electrically non-conducting Oldroyd-B fluid flowing across a stretching sheet with thermophoretic particle deposition. The heat and mass transfer mechanisms are elaborated in the presence of a magnetic dipole, which acts as an external magnetic field. The fluid possesses magnetic characteristics due to the presence of ferrite particles. The gyrotactic microorganisms are considered to keep the suspended ferromagnetic particles stable. Cattaneo–Christov heat flux is cogitated instead of the conventional Fourier law. Further, to strengthen the heat transfer and mass transfer processes, thermal stratification and chemical reaction are employed. Appropriate similarity transformations are applied to convert highly nonlinear coupled partial differential equations into non-linear ordinary differential equations (ODEs). To numerically solve these ODEs, an excellent MATLAB bvp4c approach is used. The physical behavior of important parameters and their graphical representations are thoroughly examined. The tables are presented to address the thermophoretic particle velocity deposition, rate of heat flux, and motile microorganisms' density number. The results show that the rate of heat transfer decreases as the value of the thermal relaxation time parameter surges. Furthermore, when the thermophoretic coefficient increases, the velocity of thermophoretic deposition decreases. [ABSTRACT FROM AUTHOR]

In present study, the nano-material flow of Ree-Eyring fluid model (NF-REFM) is examined by utilizing the technique of Levenberg Marquardt with backpropagated neural networks (TLM-BNNs). The flow is examined between two disks and the impacts of porosity and velocity slip are also analyzed. The partial differential equations (PDEs) representing the NF-REFM are transformed into system of ordinary differential equations (ODEs). Homotopy analysis method (HAM) is used to solve the ODEs and interpret the reference dataset for TLM-BNN. This dataset helps to compute the approximated solution of NF-REFM in MATLAB software. Regression analysis, Error histogram and MSE results, validates the performance of TLM-BNN. The flow effects on the velocity profile, temperature distribution and concentration profile are examined for different parameters. The results for entropy generation, Bejan number, Nusselt number, Sherwood number and skin friction coefficient are also discussed in this article. [ABSTRACT FROM AUTHOR]

Prandtl–Eyring hybrid nanofluid (P-EHNF) heat transfer and entropy generation were studied in this article. A slippery heated surface is used to test the flow and thermal transport properties of P-EHNF nanofluid. This investigation will also examine the effects of nano solid tubes morphologies, porosity materials, Cattaneo–Christov heat flow, and radiative flux. Predominant flow equations are written as partial differential equations (PDE). To find the solution, the PDEs were transformed into ordinary differential equations (ODEs), then the Keller box numerical approach was used to solve the ODEs. Single-walled carbon nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT) using Engine Oil (EO) as a base fluid are studied in this work. The flow, temperature, drag force, Nusselt amount, and entropy measurement visually show significant findings for various variables. Notably, the comparison of P-EHNF's (MWCNT-SWCNT/EO) heat transfer rate with conventional nanofluid (SWCNT-EO) results in ever more significant upsurges. Spherical-shaped nano solid particles have the highest heat transport, whereas lamina-shaped nano solid particles exhibit the lowest heat transport. The model's entropy increases as the size of the nanoparticles get larger. A similar effect is seen when the radiative flow and the Prandtl–Eyring variable-II are improved. [ABSTRACT FROM AUTHOR]

The present study analyzes the comparison of the Xue and Yamada-Ota models for a hybrid nanoliquid flow in porous media occurring amidst a rotating channel with surface catalyzed reaction. Here, the hybrid nanofluid flow is studied under the effect of Cattaneo Christov (C–C) heat flux and homogenous heterogeneous (Homo-Hetero) chemical reaction with entropy generation minimization analysis. The assumptions of the viscosity of hybrid nanomaterial fluid and variable thermal conductivity are added characteristics to the inimitability of the flow model. Two kinds of nanoparticles, namely single-wall carbon nanotubes and multi-wall carbon nanotubes with ethylene glycol (EG) as the base fluid are considered. Carbon nanotubes possess diverse applications in daily life including energy storage, drug delivery, cancer treatment, tissue generation, platelet activation, magnetic force microscopy, and microwave absorption, etc. Similarity transformations are utilized to translate the modeled problem into the coupled ordinary differential equations. This system of ordinary differential equations is addressed numerically. The graphical outcomes are scrutinized by utilizing the MATLAB software bvp4c function. The results revealed that the velocity profile decreases for the higher rotation parameter while increases for the escalated slip parameter. Furthermore, the fluid concentration and temperature are on the decline for higher surface catalyzed reaction and thermal relaxation parameters respectively. [ABSTRACT FROM AUTHOR]

A numerical approach for solving second order singularly perturbed boundary value problems (SPBVPs) is introduced in this paper. This approach is based on the basis function of a 6-point interpolatory subdivision scheme. The numerical results along with the convergence, comparison and error estimation of the proposed approach are also presented. [ABSTRACT FROM AUTHOR]

In this analysis, we introduced heat convective aspects of stagnation point movement of a magnetohydrodynamic (MHD) stream on a nonlinear oscillating plane with the impacts of velocity and heat slips with variable heat reservoir. By using some appropriate transformations, the governing differential equations are switched into an ordinary differential equation. The semianalytics technique called Homotpy Analysis Method (HAM) has been applied to evaluate the ordinary differential equations. For convergence achievement, a numerical method BVPh2-midpoint method is also applied and an outstanding agreement is found. The impacts of the governing constraints on flow, motion, and temperature distributions are investigated in detail. We observed that the temperature distribution increases with nonlinear heat reservoir parameter. Our results, in some limiting situations, matched well with previously published results, which approve that our obtained results are correct. [ABSTRACT FROM AUTHOR]

This paper provides a substantial amount of study related to coupled fluid flow and heat conduction of an upper-convected-Maxwell viscoelastic liquid over a stretching plane with slip velocity. A new model, presented by Christov, for thermal convection is employed. The partial differential equations are converted to ordinary differential equations by using appropriate transformation variables. The transformed equations are solved analytically by using the Galerkin method. For the sake of soundness, a comparison is done with a numerical method, and good agreement is found. The impacts of various parameters like slip coefficient, elasticity number, the thermal relaxation time of heat flow, and the Prandtl number over the temperature and velocity fields are studied. Furthermore, the Cattaneo–Christov heat flux model is compared with Fourier's law. Additionally, the present results are also verified by associating with the published work as a limiting case. [ABSTRACT FROM AUTHOR]

In this analysis, we introduced heat convective aspects of stagnation point movement of a magnetohydrodynamic (MHD) stream on a nonlinear oscillating plane with the impacts of velocity and heat slips with variable heat reservoir. By using some appropriate transformations, the governing differential equations are switched into an ordinary differential equation. The semianalytics technique called Homotpy Analysis Method (HAM) has been applied to evaluate the ordinary differential equations. For convergence achievement, a numerical method BVPh2-midpoint method is also applied and an outstanding agreement is found. The impacts of the governing constraints on flow, motion, and temperature distributions are investigated in detail. We observed that the temperature distribution increases with nonlinear heat reservoir parameter. Our results, in some limiting situations, matched well with previously published results, which approve that our obtained results are correct. [ABSTRACT FROM AUTHOR]

In this article we observed the Darcy-Brinkman flow model in the existence of frictional heating and porous dissipation (DBFM) over a stretching sheet by employ the neural network backpropagated with Bayesian regularization technique (NNBP-BRT). NNBP-BRT has the ability to exhibit relatively complex relationships, which implies it can be used in numerical investigations to construct a robust framework. Bayesian regularization is a mathematical procedure that converts a nonlinear regression into a "well-posed" statistical equation in the ridge regression methodology. Partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) by employ appropriate similarity transformation. The resulting system of nonlinear equations was numerically solved using the fourth-order Runge–Kutta approach with velocity and thermal slip assumptions. Here we utilized ND-Solve method to solve the ordinary differential equations and clarify the reference dataset for NNBP-BRT for different scenarios of DBFM by varying parameters. To compute the approximated solutions and error analysis plots of different scenarios of DBFM the reference dataset is utilized in MATLAB software using the command 'nftool'. The performance of NNBP-BRT is observed and obtained by observing the regression curves, histograms and MSE outcomes. The solution of DBFM is obtained by testing, validation and training process. Figures depict velocity profiles and temperature profiles for different variations of parameters. The effect of different flow parameters Brinkmann parameter, porosity parameter, Prandtl number and Eckert number on velocity profile and temperature profile are discussed and the results are presented graphically. [ABSTRACT FROM AUTHOR]

In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of S c ≤ S   and   M c ≤ M ( S c > S   and   M c > M ). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised. [ABSTRACT FROM AUTHOR]

Similar to other fluids (Newtonian and non-Newtonian), micropolar fluid also exhibits symmetric flow and exact symmetric solution similar to the Navier–Stokes equation; however, it is not always realizable. In this article, the Buongiorno mathematical model of hydromagnetic micropolar nanofluid is considered. A joint phenomenon of heat and mass transfer is studied in this work. This model indeed incorporates two important effects, namely, the Brownian motion and the thermophoretic. In addition, the effects of magnetohydrodynamic (MHD) and chemical reaction are considered. The fluid is taken over a slanted, stretching surface making an inclination with the vertical one. Suitable similarity transformations are applied to develop a nonlinear transformed model in terms of ODEs (ordinary differential equations). For the numerical simulations, an efficient, stable, and reliable scheme of Keller-box is applied to the transformed model. More exactly, the governing system of equations is written in the first order system and then arranged in the forms of a matrix system using the block-tridiagonal factorization. These numerical simulations are then arranged in graphs for various parameters of interest. The physical quantities including skin friction, Nusselt number, and Sherwood number along with different effects involved in the governing equations are also justified through graphs. The consequences reveal that concentration profile increases by increasing chemical reaction parameters. In addition, the Nusselt number and Sherwood number decreases by decreasing the inclination. [ABSTRACT FROM AUTHOR]

Symmetry and fluid dynamics either advances the state-of-the-art of mathematical methods and extends the limitations of existing methodologies to new contributions in fluid. Physical scenario is modelled in terms of differential equations as mathematical models in fluid mechanics to address current challenges. In this work a physical problem to examine the unsteady flow of a third-grade non-Newtonian liquid induced through a permeable shrinking surface containing nanoliquid is considered. The model of Buongiorno is utilized comprising the thermophoresis and Brownian effects through nonlinear thermal radiation and convective condition. Based on the flow symmetry, suitable similarity transformations are employed to alter the partial differential equations into nonlinear ordinary differential equations and then these ordinary differential equations are numerically executed via three-stage Lobatto IIIa formula. The flow symmetry is discussed for interesting physical parameters and thus this work is concluded. More exactly, the impacts of pertinent constraints on the concentration, temperature and velocity profiles along together drag force, Sherwood and Nusselt numbers are explained through the aid of the tables and plots. The outcomes reveal that the dual nature of solutions is gained for a specific amount of suction and flow in the decelerating form A < 0 . However, the unique result is obtained for flow in accelerating form A ≥ 0 . In addition, the non-linear parameter declines the liquid velocity and augments the concentration and temperature fields in the first result, whereas the contrary behavior is scrutinized in the second result. [ABSTRACT FROM AUTHOR]

The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative). [ABSTRACT FROM AUTHOR]

This paper reflects the effects of velocity and thermal slip conditions on the stagnation-point mixed convective flow of Cross liquid moving over a vertical plate entrenched in a Darcy–Forchheimer porous medium. A Cross liquid is a type of non-Newtonian liquid whose viscosity depends on the shear rate. The leading partial differential equations (PDEs) are altered to nonlinear ordinary differential equations (ODEs) via feasible similarity transformations. These transmuted equations are computed numerically through the bvp4c solver. The authority of sundry parameters on the temperature and velocity distributions is examined graphically. In addition, the characteristics of heat transfer are analyzed in the presence of the impact of drag forces. The outcomes reveal that the permeability parameter decelerates the drag forces and declines the rate of heat transfer in both forms of solutions. Moreover, it is found that the drag forces decline with the growing value of the Weissenberg parameter in the upper branch solutions, while a reverse trend is revealed in the lower branch solutions. However, the rate of heat transfer shows a diminishing behavior with an increasing value of the Weissenberg parameter. [ABSTRACT FROM AUTHOR]

The principal objective of the current study is to analyze the Brownian motion and thermophoretic impacts on micropolar nanofluid flow over a nonlinear inclined stretching sheet taking into account the Soret and Dufour effects. The compatible similarity transformations are applied to obtain the nonlinear ordinary differential equations from the partial differential equations. The numerical solution of the present study obtained via the Keller-Box technique. The physical quantities of interest are skin friction, Sherwood number, and heat exchange, along with several influences of material parameters on the momentum, temperature, and concentration are elucidated and clarified with diagrams. A decent settlement can be established in the current results with previously published work in the deficiency of incorporating effects. It is found that the growth of the inclination and nonlinear stretching factor decreases the velocity profile. Moreover, the growth of the Soret effect reduces the heat flux rate and wall shear stress. [ABSTRACT FROM AUTHOR]

The prime aim of this paper is to probe the flow of micropolar nanofluid towards an inclined stretching surface adjacent to the stagnation region with Brownian motion and thermophoretic impacts. The chemical reaction and heat generation or absorption are also taken into account. The energy and mass transport of the micropolar nanofluid flow towards an inclined surface are discussed. The numerical solution is elucidated for the converted non-linear ordinary differential equation from the set of partial nonlinear differential equations via compatible similarity transformations. A converted system of ordinary differential equations is solved via the Keller-box scheme. The stretching velocity and external velocity are supposed to change linearly by the distance from the stagnation point. The impacts of involved parameters on the concerned physical quantities such as skin friction, Sherwood number, and energy exchange are discussed. These results are drawn through the graphs and presented in the tables. The energy and mass exchange rates show a direct relation with the stagnation point. In the same vein, skin friction diminishes with the growth of the stagnation factor. Heat and mass fluxes show an inverse correspondence with the inclination factor. [ABSTRACT FROM AUTHOR]

The key objective of the study under concern is to probe the impacts of Brownian motion and thermophoresis diffusion on Casson nanofluid boundary layer flow over a nonlinear inclined stretching sheet, with the effect of convective boundaries and thermal radiations. Nonlinear ordinary differential equations are obtained from governing nonlinear partial differential equations by using compatible similarity transformations. The quantities associated with engineering aspects, such as skin friction, Sherwood number, and heat exchange along with various impacts of material factors on the momentum, temperature, and concentration, are elucidated and clarified with diagrams. The numerical solution of the present study is obtained via the Keller-box technique and in limiting sense are reduced to the published results for accuracy purpose. [ABSTRACT FROM AUTHOR]

Wire coatings are necessary to provide protection from the aggressive environment and to add mechanical strength to wires and cables. In this study, we investigated the effect of radiative linear as well as non-linear heat transfer on the wire coating in response to joule heating, using a third grade fluid as the coating material. For the temperature dependent viscosity, two models namely—Reynolds' and Vogel's—were used. The non-linear ordinary differential equations were solved analytically by the Homotropy Analysis Method (HAM). Numerical technique was also applied for comparison and good agreement was found. It is interesting to note that the temperature parameter had a remarkable effect on the temperature distribution and heat transfer characteristics in the flow region within the die. It was observed that the velocity of the fluid within the die decreased as the magnetic parameter increased, while the magnetic field had an accelerating effect on the temperature distribution. Near the surface of the wire, the velocity of the coating material accelerated as the temperature parameter and radiation parameter increased. Analysis also showed that the temperature of the coating material decreased with increasing radiation and temperature parameters. [ABSTRACT FROM AUTHOR]

The aim of the present analysis is to provide local similarity solutions of Casson fluid over a non-isothermal cylinder subject to suction/blowing. The cylinder is placed inside a porous medium and stretched in a nonlinear way. Further, the impact of chemical reaction, viscous dissipation, and heat generation/absorption on flow fields is also investigated. Similarity transformations are employed to convert the nonlinear governing equations to nonlinear ordinary differential equations, and then solved via the Keller box method. Findings demonstrate that the magnitude of the friction factor and mass transfer rate are suppressed with increment in Casson parameter, whereas heat transfer rate is found to be intensified. Increase in the curvature parameter enhanced the flow field distributions. The magnitude of wall shear stress is noticed to be higher with an increase in porosity and suction/blowing parameters. [ABSTRACT FROM AUTHOR]