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This study aims to develop a supervised learning artificial recurrent neural network algorithm supported by Bayesian regularization called (ARNN‐BR) to analyze the impact of physical parameters, including radius of curvature (κ$\kappa $), Casson parameter (β$\beta $), heat generation parameter (λ$\lambda $) and radiation parameter (Rd${{R}_d}$) on velocity fʹ(η), and temperature profiles θ(η) in Casson nanofluid consisting of carbon nanotubes (CNTs‐CNF) model for single and multiwalled CNTs across a curved stretched surface. The numerical dataset of the proposed model has been constructed by varying various parameters for five scenarios that are used in a Bayesian regularization‐based intelligent computing method to build networks for approximating the numerical solutions of CNTs‐CNF model. It is observed that increment in the dimensionless radius of curvature (κ$\kappa $) causes to rise an increase in the velocity profile fʹ(η) for both SWCNTs and MWCNTs. However, a contrasting trend is observed when the Casson parameter (β$\beta $) is increased to higher values. The temperature θ(η) of fluid increases as the heat generation parameter (λ$\lambda $) and radiation parameter (Rd${{R}_d}$) increase. However, an opposite behavior is noticed when the dimensionless radius of curvature (κ$\kappa $) varies. The effectiveness and significance of designed Bayesian regularization based artificial recurrent neural networks (ARNN‐BR) is demonstrated through regression index measurements, error histogram studies, auto‐correlation analysis and convergence curves showing a minimal level of mean square error (E‐11 to E‐04) for the comprehensive simulations of CNTs‐CNF model. The designed ARNN‐BR algorithm is employed in many domains such as voice recognition, machine translation, identification of neurological brain illnesses as well as for automated translation of texts across different languages. [ABSTRACT FROM AUTHOR]

In this study, a novel neuro heuristic approach is designed to investigate the flow properties of magnetohydrodynamic (MHD) nanofluid along an exponentially extending sheet with a permeable medium with the impact of radiation as well as fluctuating heat source/sink. The designed scheme to handle the suggested problem is established through the well‐known biologically inspired neural networks (BINNs) by exploiting the inverse multiquadric kernel (IMQK), that is, BINNs‐IMQK which is quite a new approach. The partial differential equations (PDEs) which govern the fluidic flow are reformed into a nonlinear system of ordinary differential equations (ODEs) using the most fitted similarity transformations rules and numerically solved by varying the parametric values including unsteady parameter, Brownian motion parameter, suction/injection parameter, radiation parameter, Schmidt number together with Prandtl number to visualize the velocity, thermal gradient, and mass transfer in the suggested fluid problem. It is noticed that nanofluid temperature hikes by uplifting the value of the Brownian motion parameter but this effect is reversed in case of unsteady parameter. The obtained numerical results are verified through reference solution using the well‐known Adams method and the efficacy of the suggested solver is endorsed using a variety of statistical operators. [ABSTRACT FROM AUTHOR]

Purpose: The present study aims to encompass the bidirectional magnetized flowing of a hybrid-nanofluid over an unsteady stretching device with the inclusion of thermal radiation and entropy generation. Brick-shaped nanoparticles (zinc-oxide and ceria) are suspended in water, serving as the base-fluid to observe the performance of the hybrid mixture. The Maxwell thermal conductivity relation is employed to link the thermophysical attributes of the hybrid mixture with the host liquid. Additionally, a heat source/sink term is incorporated in the energy balance to enhance the impact of the investigation. Both prescribed-surface-temperature (PST) and prescribed-heat-flux (PHF) conditions are applied to inspect the thermal performance of the hybrid nanofluid. Design/methodology/approach: The transport equations in Cartesian configuration are transformed into ordinary differential equations (ODEs), and an efficient method, namely the Keller-Box method (KBM), is utilized to solve the transformed system. Postprocessing is conducted to visually represent the velocity profile, thermal distribution, skin-friction coefficients, Bejan number, Nusselt number and entropy generation function against the variations of the involved parameters. Findings: It is observed that more entropy is generated due to the increases in temperature difference and radiation parameters. The Bejan number initially declines but then improves with higher estimations of unsteadiness and Hartmann number. Overall, the thermal performance of the system is developed for the PST scenario than the PHF scenario for different estimations of the involved constraints. Originality/value: To the best of the authors' knowledge, no investigation has been reported yet that explains the bidirectional flow of a CeO2-ZnO/water hybrid nanofluid with the combined effects of prescribed thermal aspects (PST and PHF) and entropy generation. [ABSTRACT FROM AUTHOR]

In this investigative study, the electro-magneto hydrodynamic (EMHD) influence on a nano viscous fluid model is scrutinized by designing an artificial neural network (ANN) paradigm using a neuro-heuristic approach (NHA) through the combination of GAs (genetic algorithms) and one of the most efficient locally searching solver SQP (sequential quadratic programming), i.e., NHA-GA-SQP. The fluid flow for the proposed problem is initially interpreted in the form of PDEs and then utilization of suitable similarity transformation on these PDEs yields in terms of a stiff nonlinear system of ODEs. The numerical results of the suggested fluidic model based on the variation of its physically existing parameters are calculated through the NHA-GA-SQP solver to detect the variation in velocity, thermal gradient, and concentration during the fluid flow. A detailed analysis of obtained outcomes through the NHA-GA-SQP algorithm and their comparison with the reference results estimated via the Adams method are presented. The calculation of the proposed solver's accuracy, stability, and consistency through various statistical operators is also involved in the current inspection. [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 present research, a numerical approach to examine magnetohydrodynamics (MHD) Casson nanofluid flow in a porous medium along a stretchable surface with different slips using artificial neural networks (ANNs) by taking inverse multiquadric (IMQ) radial basis function (RBF) as an activation function. i.e. ANNs-IMQ-RBF. The hybridization of genetic algorithms (GAs) and sequential quadratic programming (SQP) is used for learning in ANNs-IMQ-RBF. The PDEs representing the fluid flow are converted into a nonlinear system of dimensionless form of ODEs through an appropriate transformation while effects of variation in the values of Casson parameter (β), Brownian motion parameter (Nb), Prandtl number (Pr), stretching parameter (n), porosity parameter (P), Lewis number (Le) along with temperature slip parameter (λ 2) on velocity, temperature and nanofluid concentration are depicted through graphs. The effectiveness, convergence and accuracy of the proposed solver are validated evidently through boxplot analysis, histograms and cumulative distribution function (CDF) plots. [Display omitted] • A new ANNs-IMQ-RBF solver is designed for MHD Casson nanofluid problem in the shape of a system of nonlinear ODEs. • Velocity, temperature and concentration profiles are calculated for sundry cases of physical parameters of the interest. • Results are compared with the reference solutions of Adams numerical technique to analyze the accuracy and convergence. • Statistical operators via box plot, CDF and histograms analyses are used to verify the effectiveness and stability. [ABSTRACT FROM AUTHOR]

The nanoparticles convey noteworthy applications in many engineering and industrial systems like cooling and heat processes, thermal extrusion systems, heat exchangers, as an energy source, treatment of various diseases and chemotherapy. Owing to such importance of nanomaterials, various studies are presented for nanofluids with diverse flow features. This investigation discloses an unsteady flow of Cross nanofluid over periodically accelerated imbedded in porous space. The combined heat and mass transportation aspects of nanomaterials are entertained with applications of Buongiorno's model. Further, Cattaneo–Christov fluxes are mathematically implemented for investigating the diffusion aspect of heating and mass pattern. Additionally, the nonlinear on set of radiative distribution is followed. Referred to the suitable transformations, the independent variable in the governing system is reduced. The homotopy-based analytical expressions are obtained for set of flow parameters. The complete graphical exploration is visualized, for governing parameters, and scrutinized. The mass and heat transfer pattern has been inspected in the form of numerical data. It is perceived that velocity profile has decreasing tendency for enhancement in Weissenberg number and magneto-porous constant. The temperature and concentration profiles diminish with increase of thermal and solutal relaxation constants, respectively. [ABSTRACT FROM AUTHOR]

Investigation of expanding sheet flow in the existence of tiny particles is an interesting field of research and this type of mathematical model is usually expressed in the form of partial differential equations. Present exploration has been made to describe the unsteady 3D dynamics of MHD tangent-hyperbolic fluid impinging over an expanded sheet with the characteristics of haphazard movement and thermo migration of nanoparticles. Moreover, securitization has been accomplished in the environment of prescribed temperature and prescribed concentration restrictions at the stretchable surface. Novel combination of scaling transformations has been accustomed to exchange the governing equations into complicated system of ordinary differential equation and then solved by an innovative analytical scheme, namely, homotopy analysis method. The significance of involved scientific factors on temperature phase, concentration phase, condensed Nusslet number and condensed Sherwood number has been explained through various contours. It has been noticed that increasing choices of random movement 0 ≤ N b ≤ 1.0 and thermo-migration of nanoparticles 0 ≤ N t ≤ 3.0 reduce the estimate of heat transaction along with the estimate of mass transaction. Moreover, temperature and concentration circulations have improved with the advanced choices of Weissenberg number 0 ≤ W e x ≤ 10.0 and flow behavior index 0 ≤ n ≤ 2.1. [ABSTRACT FROM AUTHOR]

In the field of nano-composites, hybrid nano-fluids have noteworthy applications in aerospace, energy materials, thermal sensors, antifouling, etc. because of their ability to produce higher thermal conductivity than conventional nanofluids. Different combinations of nanocomposites have been found in the literature to develop the suitable hybrid-mixture, but no study has been found yet about the combined influence of ceria and zinc-oxide nanocomposites in the host liquid. In this article, unsteady 3 D transport of water driven hybrid nano-fluid with the consequences of brick shaped nanocomposites (ceria; Ce O 2 and zinc oxide; ZnO) has deliberated with the thermal link of heat source/sink. Variable thermal conditions have been supplied at the surface with the effect of a magnetic environment. Similarity relations have been used to articulate the transport equations into solvable forms and then solved numerically via Keller-Box method. Nusselt number and skin-friction coefficients have also plotted with the wide ranges of involved parameters. Thermal setup has also briefly been discussed with the non-uniformity of surface temperature. Rate of heat transfer has significantly improved with the amounts of ceria (1 wt% to 10 wt%) and zinc-oxide (1 wt% to 10 wt%) nanocomposites. The Nusselt number is reported in the range of 4.0 to 4.8 with the increasing amount of γ from −0.6 to −0.2, whereas it is reported in the range of 3.1 to 3.9 with the varying amount of γ from 0.2 to 0.6. Rate of heat transfer is observed higher for zinc-oxide nanoparticles as compared to ceria nanoparticles. [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]

The present mathematical model discloses the effects of Boussinesq and Rosseland approximations on unsteady 3D dynamics of water-driven hybridized nanomaterial with the movements of nanoplatelets (molybdenum disulfide, MoS 2 and graphene oxide, GO). Variable thermal conditions, namely, VST (variable surface temperature) and VHF (variable heat flux), are opted to provide temperature to the surface. MHD effects have also been used additionally to make the study more versatile. In order to transmute the transportation equations into nondimensionlized forms, similarity transformations have been adopted. The Keller-Box technique has been applied to obtain a numerical simulation of the modeled problem. The convergence of the solution for both VST and VHF cases is presented via the grid independence tactic. Thermal setup against escalating choices of power indices and nonlinear thermal radiation parameter is discussed via graphical illustrations. The rate of heat transaction has been discussed with the growing choices of mixed convection, thermal radiation, and unsteady parameters through various tabular arrangements. It is observed through the present analysis that mixed convection parameter, radiation parameter, temperature maintaining indices r , s , and unsteady parameter magnify the rate of heat transference under the control of platelet-shaped nanoparticles. [ABSTRACT FROM AUTHOR]

In this exploration, we decided to investigate the significance of prescribed thermal conditions on unsteady 3D dynamics of water-based radiative hybrid nanofluid with the impact of cylindrical-shaped nanosized particles (alumina ( Al 2 O 3 ) and titania (Ti O 2 )). For physical relevancy, the impact of the Lorentz force is also included. The combination of suitable variables has been used to transform the transport equations into the system of ordinary differential equations and then numerically solved via the Keller-Box approach. Graphical illustrations have been used to predict the impact of the involved parameters on the thermal setup. Convergence analysis is presented via the grid independence approach. Skin frictions and local Nusselt numbers against various choices of involved parameters are plotted and arranged in tabular forms. It is observed through the present investigation that temperature distribution is increased with the higher choices of radiation parameter 0.0 ≤ R d ≤ 2.0 and decreased with the improvement in the choices of temperature maintaining indices (i.e., − 2.0 ≤ r , s ≤ 2.0). Moreover, the thermophysical properties except specific heat for hybrid nanofluid are improved with the involvement of cylindrical-shaped nanoparticles. The temperature of the hybrid nanofluid is observed to be higher for variable thermal conditions as compared to uniform thermal conditions. Outfalls for a limited version of the report have been compared with a previous published paper. [ABSTRACT FROM AUTHOR]

An investigation of the thermal performance of water-conveying nanospheres (magnetite ( Fe 3 O 4 ) and silver (Ag)) subject to variable thermal controls, namely, variable surface temperature and variable surface normal heat flux, has been made. A bidirectionally elongating surface is used to generate an unsteady flow mechanism with the action of the Lorentz force. Derived equations of basic laws are firstly nondimensionalized and then numerically solved by applying the Keller-Box method. The local Nusselt number for both the thermal cases is calculated and discussed. Percent-wise enhancement in the rate of heat transport has also been included in the analysis. It was concluded through the present exploration that at lower volume fractions of magnetite and silver, the rate of heat transport is observed to be dominant. The rate of heat transference has attained identical values for both the provided thermal conditions at the surface. Moreover, intensities of velocity and thermal profiles diminish with the appreciation of the choice of unsteadiness. The temperature-controlling indices also affect the thermal profile, and it is reduced with the intensification in the considerations of these indices. The values of thermal conductivity, density, and electrical conductivity have been improved with the inclusion of nanospheres (magnetite ( Fe 3 O 4 ) and silver (Ag)), whereas the value of specific heat is reduced with the mixture of these nanospheres. The Nusselt number is increased up to 5% with the involvement of magnetite nanospheres, and it is enhanced up to 4% with the involvement of silver nanospheres. [ABSTRACT FROM AUTHOR]

The ultra-high significances of thermal radiation, magnetic field and activation energy in thermal enhancement processes allow significant applications in chemical and mechanical engineering, modern technology and various thermal engineering eras. The improvement in energy resources and production became one of the major challenges for researchers and scientists for sustained development in industrial growths. Beside this, the bioconvection assessment in nanomaterials conveys prestigious applications in biotechnology like bio-sensors, enzymes, petroleum industry, bio-fuels and many more. In view of such renewable applications, present exploration discloses unsteady two-dimensional flow of third-grade nanomaterial accommodating gyrotactic microorganisms induced by unsteady stretched Riga sheet in porous medium. The formulated flow problem is further scrutinized by utilizing the chemical reaction, activation energy, thermal radiation and magnetic aspects. The convective Nield constraints are further subjected in the current investigation. Apposite transformations are used to condense the nonlinear developed problem into dimensionless ordinary form. The numerical solution of such similar flow problem is presented via shooting technique. The detailed graphical illustrations of the dimensionless temperature, nanoparticles concentration, velocity and motile microorganisms for physical significance of diverse relevant parameters are deliberated. Furthermore, numerical data of local Sherwood, Nusselt and motile density numbers is designated in tabular form. Study accentuated that velocity increases for higher modified Hartmann and material constants, while the effects of buoyancy ratio and bioconvected Rayleigh numbers are rather opposite. The temperature, microorganism and concentration distributions were enhanced for unsteady parameter. It is also acknowledged that the concentration distribution is enhanced for activating the energy number. Moreover, the microorganism distribution enhances for concentration difference and magneto-porous constants, while bioconvected Lewis and Peclet numbers show conflicting trend. [ABSTRACT FROM AUTHOR]

Little is known in the literature about the concept of nonuniform heat source/sink and higher-order chemical reaction for the dynamics of Oldroyd-B nanoparticles. Therefore, the present article addresses the nonuniform heat source/sink and higher-order chemical reaction features in nonlinear mixed convection bidirectional MHD dynamics of Oldroyd-B nanoparticles with thermal radiation aspects through porous space. Stratification effects for both the temperature and concentration setups are also used in the mathematical model with the significance of random movement and thermodiffusion of nanoparticles. Shape-preserving transformations have been employed to convert the transport equations into solvable forms. An innovative analytical tactic, namely, homotopy analysis method, has been adopted to find the solution of the modeled problem. Behaviors of pertinent parameters on thermal and concentration profiles have been discussed through various graphs. Inspection of heat/mass transport against appropriate varieties of pertinent parameters has been made and explained physically. Thermal profile is augmented with the higher estimations of space and temperature-dependent heat source/sink links. Concentration profile is diminished with the augmentation of higher-order chemical reaction parameter. Sherwood number is improved with the estimation of 0 ≤ β t ≤ 100 and is reduced with the growth of 0 ≤ β c ≤ 100. Nusselt number is declined with the upgraded amounts of 0 ≤ N b ≤ 3 and 0 ≤ N t ≤ 5. [ABSTRACT FROM AUTHOR]

This study analyzes Hall current and Joule heating effects on the ferro‐nanofluid flow by the rotation of the disk incorporated with generalized slip condition. By using the well‐known Von Karman transformation, formulated flow equations are modeled into ordinary differential equations. Numerical solutions of the governing flow equations are attained by utilizing the shooting method consolidated with the fourth‐order Runge–Kutta scheme. The impacts of different parameters on skin friction coefficient, velocity, temperature, and Nusselt number are given in graphs and tables and investigated in detail. Furthermore, an association with formerly published articles is given and met in remarkable correspondence. [ABSTRACT FROM AUTHOR]

In the recent advancement in growing nano-technology, the dynamic scientists have shown their interest toward the thermal aspects of nanoparticles due to their prestigious industrial, engineering, medical and modern sciences applications. The current exertion discloses unsteady three-dimensional chemically reactive couple stress nanofluid flow induced by bidirectional oscillatory stretching surface. The heat transfer analysis is explored by utilizing heat generation/absorption and thermal radiation features. Additionally, the mixed convection and magnetic effects are also encountered as novelty. The flow has been generated by bidirectional periodically accelerated surface. Apposite transformations are engaged to reduce formulated nonlinear problem into dimensionless form, and then analytic series solution is computed via homotopic technique. The physical aspect of involved flow parameters is graphically entertained. A complete graphical investigation for profiles of dimensionless velocities, temperature, concentration and skin friction coefficients is deliberated for various prominent flow parameters. Furthermore, the numerical calculations for local Nusselt and Sherwood numbers are presented and discussed. The results perceived that amplitude of oscillation increases in both components of velocities and skin friction coefficients for higher couple stress parameter. It is further reported that temperature distribution enhanced for higher values of Brownian motion parameter, thermophoresis constant and radiation parameter. Moreover, the concentration distribution decreases for enhancement of Brownian motion parameter and chemical reaction parameter. [ABSTRACT FROM AUTHOR]

The growing interest in emerging nanotechnologies has led the scientists towards to investigate the interaction of nanoparticles with fluids. Current continuation endeavors the rheological analysis for the Oldroyd-B nanomaterial across periodically accelerated and heated surface. The interesting features of thermophoresis and Brownian motions are presented by following famous Buongiorno nanofluid model. Further, Cattaneo–Christov heat and mass flux expressions are exploited to determine the characteristics of thermal and mass diffusions. As a novelty, the variable thermal conductivity and heat absorption/generation consequences are also utilizing the energy equation. The flow model has been developed by using concerning boundary layer equations which are converted into dimensionless forms by using appropriate variables. The analytical solution of such transmuted equations is computed by using homotopy analytic method. Various physical parameters of interest are scrutinized through various graphs. The observations from analysis convey a declining change in nanofluid concentration and temperature with variation of thermal and solutal relaxation parameters, respectively. Moreover, thermophoresis parameter causes an enhancement of concentration profile while a retarded concentration profile results with increment of Schmidt number. The obtained theoretical results reflect significant applications in cooling and heating systems, thermal sciences, manufacturing processes, extrusion systems, enhancement of transport of energy and heat resources. [ABSTRACT FROM AUTHOR]

Motivated by the significant role of nanofluid in pollution cleaning and energy recovery, we decided to explore the unsteady three-dimensional rotating flow of nanofluid driven by the movement of a flat surface with the potencies of prescribed heat distributions. The modeling of the physical model is completed with the help of Buongiorno nanofluid model. Suitable arrangement of similarity variables is implemented to transform the model equations into strongly nonlinear ordinary differential equations. Numerical inspection of the model is made by employing Keller–Box algorithm. Influences of involved parameters on the distributions of heat and mass are discussed graphically, while the potencies of influential parameters on reduced Nusselt and reduced Sherwood numbers are physically discussed through tabular arrangements. It is deduced that increasing the values of Prandtl factor and heat controlling indices diminishes the temperature and concentration distributions, whereas intensification in the amount of rotation factor enhances the temperature as well as concentration distribution. Moreover, negative trends in the amounts of reduced Nusselt and Sherwood numbers are achieved with the escalations in the values of rotation and thermophoresis factors, whereas opposite trend is achieved with the intensification in the choice of Prandtl factor. [ABSTRACT FROM AUTHOR]

The present investigation aims to explore the influence of a mixed convection and nonuniform heat source/sink on unsteady flow of a chemically reactive nanofluid driven by a bidirectionally expandable surface. Convective heat transport phenomenon is used to maintain the temperature of the surface. Moreover, zero mass flux is also accounted at the surface such that the fraction of nanomaterial maintains itself on strong retardation. The governing nonlinear set of partial differential equations is transformed into a set of ordinary differential equations via a suitable combination of variables. The Keller‐Box scheme has been incorporated to make a numerical inspection of the transformed problem. The spectacular impacts of the pertinent constraints on thermal and concentration distributions are elucidated through various plots. Graphical outcomes indicate that the thermal state of nanomaterial and nanoparticles concentration are escalated for elevated amounts of Biot number, porosity parameter and nonuniform heat source/sink constraints. Furthermore, it is also seen that escalating amounts of unsteady parameter, temperature controlling indices, Prandtl number, and expansion ratio parameter reduce the thermal and concentration distributions. Numerical results for the rate of heat transference have been reported in tabular form. The grid independence approach is used to verify the convergence of the numerical solution and the CPU run time is also obtained to check the efficiency of the numerical scheme adopted for finding the solution. [ABSTRACT FROM AUTHOR]

The present contribution determines the impacts of viscous dissipation and Ohmic heating with magnetic coating on Prandtl nanofluid flow driven by an unsteady bidirectionally moveable surface. Random motion of nanoparticles and thermophoretic diffusion are elaborated through a two-phase nanofluid model. The novelty of the investigation is fortified by prescribed heat flux and prescribed mass flux mechanisms. The appropriate combination of variables leads to a system of strong nonlinear ordinary differential equations. The formulated nonlinear system is then tackled by an efficient numerical scheme, namely, the Keller-Box method. Nanoliquidtemperature and mass-concentration distributions are conferred through various plots with the impacts of miscellaneous-arising parameters. The rates of heat and mass transferences are also discussed through tables. The thermal states of the nanomaterial and mass concentration are reduced for incremental amounts of the unsteady factor, ratio parameter, elastic parameter, and Prandtl fluid parameter. Moreover, escalating amounts of the Brownian parameter, Eckert number, magnetic factor, and thermophoresis parameter enhances the temperature of the nanoliquid. An error analysis is also presented to predict the efficiency of the method used for the computational work. [ABSTRACT FROM AUTHOR]

Current continuation describes the computational study concerning with the unsteady flow of Eyring–Powell magneto nanoliquid over a bidirectionally deformable surface. Transference of activation energy is used in the improvement of binary chemical reaction. Nonlinear significance of thermal radiation is also incorporated in the energy equation. Investigation has been carried out through convective Nield's boundary restrictions. Firstly, useful combination of variables has been implemented to alter the governing PDEs into ODEs. Later on, Keller-Box approach has been adopted to obtain the numerical solution of the physical problem. Physical interpretations of obtained results are also described for temperature and mass concentration distributions through various graphs. Rate of heat transportation has been explained through tabular data for acceptable ranges of involved engineering parameters. It is detected that escalating amount of Brownian constraint provides a constant temperature distribution. It is also inspected through present investigation that escalating amounts of activation energy factor, thermophoresis parameter, radiation parameter, Biot number and temperature ratio parameter improve the concentration field. Moreover, the amount of heat transport has considerably improved by increasing the amounts of temperature controlling indices and Biot number. Convergence analysis and error estimations of the numerical solution are also presented through various mesh refinement levels of the computational domain. Finally, comparison benchmarks with the restricted cases have been presented for the validation of the results obtained through the present parametric investigation. [ABSTRACT FROM AUTHOR]

With impressive thermal outcomes, the nanofluids present multidisciplinary applications in the cooling processes, thermal systems, extrusion processes, heat storage devices and many more. The aim of current research is to inspect thermal impact of Jeffrey fluid with tiny particles under the assumptions of variable thermal conductivity. The problem is supported with applications of chemical reaction, activation energy and magnetic force. For heat and mass transfer phenomenon, Cattaneo-Christov diffusion theories have been implemented. The formulated model is solved by using the homotopy analysis method (HAM) with excellent accuracy. The graphical analysis is performed with specified range of parameters like 0. 2 ⩽ H ⩽ 0.8 , 0. 1 ⩽ ϖ ⩽ 1.7 , 0. 0 ⩽ N ⩽ 1.5 , 0. 0 ⩽ Π ⩽ 3.1 , 0. 3 ⩽ γ ⩽ 0.6 , 0. 6 ⩽ Ψ ⩽ 3.2 , 0. 5 ⩽ Ω ⩽ 2.0 , 0. 0 ⩽ Σ ⩽ 1.5 , 0. 2 ⩽ N t ⩽ 1.7 , 1. 0 ⩽ Pr ⩽ 1.9 , 0. 5 ⩽ Sc ⩽ 1.4 , 0. 3 ⩽ β ⩽ 1.5 , 0. 1 ⩽ ε ⩽ 1.0 , 0. 2 ⩽ N b ⩽ 1.7. The assessment of flow parameters is graphically evaluated. It is observed that both velocity profiles periodically enhance for Deborah number while temperature, microorganisms and concentration distributions decelerate. The greater estimates of variable thermal conductivity and heat generation improve the temperature distribution while conflicting scenario ensures for thermic relaxation constant. [ABSTRACT FROM AUTHOR]

The current study explores a new direction of research in which the magnetohydrodynamic (MHD) effects on two-dimensional nanofluid boundary layer flow under the influence of radiation are investigated in a porous medium using inverse multiquadric (IMQ) radial basis neural networks (RBNNs) i.e. IMQ-RBNNs. A quite new computational approach is used here in which artificial neural networks (ANNs) acquired IMQ radial basis function as an activation function in an amalgam of globally searching solver named genetic algorithms (GAs) together with an efficient local searching sequential quadratic programming (SQP) solver. The basic equations that represent the fluid flow are first obtained in the form of partial differential equations (PDEs) and then converted into dimensionless ordinary differential equations (ODEs) by applying similarity transformations. The dynamical properties of the nanofluid including velocity, temperature along mass concentration are analyzed by varying physical parameters including radiation parameter, magnetic parameter, constant moving parameter, heat source parameter, Brownian motion parameter and Eckert number. Moreover, the escalation in the value of the constant moving parameter diminishes the fluid velocity but this effect is reversed in the case of magnetic parameter. The increasing values of heat source parameter, Brownian motion parameter and Eckert number inflate the nanofluid temperature but a reversal effect is observed in the case of radiation parameter. It is also observed that larger values of heat Brownian motion parameter and radiation parameter amplify the nanofluid concentration but an opposite effect is obtained in the case of heat source parameter. The numerical results of the proposed model obtained through the IMQ-RBNNs based solver optimized with GASQP algorithm. The efficacy and tendency of rapid convergence of the proposed solver are endorsed through graphical illustrations and tables using well-known statistical operators with various fitness analyses on MATLAB are also part of this research. [ABSTRACT FROM AUTHOR]

• Dynamics of Williamson nanofluid in the view of non-linear bidirectional stretching surface is explored. • Features of quadratic thermal radiation, quadratic convection and chemical reaction are incorporated. • Prescribed heat/mass flux conditions are used at the surface. • Numerical investigation is performed using Keller-Box method. Present work addresses the heat/mass transfer mechanism for higher order mixed convective flow of Williamson nanofluid impinging over a nonlinear bidirectional elongating surface with power-law heat/mass fluxes. For scientific relevancy, we also investigated the combined influence of chemical reaction, nonlinear emission of radiation and hydro-magnetic environment on the flow pattern. Novel combination of scaling transformations has been instigated to metamorphose the principal equations into a set of highly nonlinear coupled ordinary-differential equations and then Keller-Box method (KBM) has been utilized to attain the solution of modeled problem. Convergence of the solution has been discussed via grid independence methodology. Controls of sundry dominant parameters on temperature and concentration variations have been discussed via various plots, whereas variations in heat/mass transfer rates are explained through tabular arrangements. Our analysis shows that the Nusslet number and the Sherwood number are developed up-to 38% with the positive estimations of power-law index 0.1 ≤ n ≤ 0.5 , whereas thermal gradient θ ' (0) is reduced up-to 5% with the appraisal of thermo-migration of nanoparticles 0.4 ≤ N t ≤ 0.8. Rate of heat transference is improved up-to 24% and the rate of mass transference is improved up-to 5% with the inclusion of nonlinear thermal radiation aspects 1.1 ≤ θ w ≤ 1.5. The validation of the solution has been made by comparing the results for restricted cases with the available literature. [ABSTRACT FROM AUTHOR]

This article addresses the unsteady three-dimensional flow of second grade nanofluid due to thermophoresis and Brownian motion effects. The flow is generated due to unsteady stretching in two lateral directions. The zero nanoparticles mass flux boundary conditions are imposed to find the desired solutions. By introducing the dimensionless variables the governing system of partial differential equations are transformed into the system of ordinary differential equations. Series solutions of the transformed ordinary differential equations are computed. Solutions are carried out for dimensionless temperature and nanoparticles concentration. The behavior of physical parameters on the temperature and nanoparticles concentrations is examined through graphs and tabular data. The temperature and concentration distribution at the surface are also computed and analyzed. It can be noted that both the temperature and nanomaterial are reduced for higher values of unsteadiness parameter. It is also observed that the friction factor of second grade fluid parameter is less compared with viscous nanofluid. • Time-dependent 3D flow of viscoelastic nanofluid is examined. • Brownian motion and thermophoresis effects are considered. • The condition requiring zero nanoparticles mass flux is implemented. • Series solutions are obtained through homotopy analysis method (HAM). [ABSTRACT FROM AUTHOR]