Exploring magnetic dipole contribution on ferromagnetic nanofluid flow over a stretching sheet: An application of Stefan blowing

A tripe diffusion bioconvective model for thixotropic nanofluid with applications of induced magnetic field

Owing to enhanced thermal characteristics of nanomaterials, multidisciplinary applications of such particles have been utilized in the industrial and engineering processes, chemical systems, solar energy, extrusion processes, nuclear systems etc. The aim of current work is to suggests the thermal performances of thixotropic nanofluid with interaction of magnetic force. The suspension of microorganisms in thixotropic nanofluid is assumed. The investigation is further supported with the triple diffusion flow. The motivations for considering the triple diffusion phenomenon are associated to attaining more thermal applications. The flow pattern is subject to novel stagnation point flow. The convective thermal constraints are incorporated. The modeled problem is numerically evaluated by using shooting technique. Different consequences of physical parameters involving the problem are graphically attributed. The insight analysis is presented for proposed problem with different engineering applications. It is claimed that induced magnetic field enhanced due to magnetic parameter while declining results are observed for thixotropic parameter. The heat transfer enhances due to variation of Dufour number. Furthermore, low profile of nanoparticles concentration has been observed for thixotropic parameter and nano-Lewis number.

Applications of Nano-biofuel cells for Reiner-Philippoff nanoparticles with higher order slip effects

Owing to advanced thermal features and stable properties, scientists have presented many novel applications of nanomaterials in the energy sectors, heat control devices, cooling phenomenon and many biomedical applications. The suspension between nanomaterials with microorganisms is important in biotechnology and food sciences. With such motivations, the aim of current research is to examine the bioconvective thermal phenomenon due to Reiner-Philippoff nanofluid under the consideration of multiple slip effects. The assessment of heat transfer is further predicted with temperature dependent thermal conductivity. The radiative phenomenon and chemical reaction is also incorporated. The stretched surface with permeability of porous space is assumed to be source of flow. With defined flow constraints, the mathematical model is developed. For solution methodology, the numerical simulations are worked out via shooting technique. The physical aspects of parameters are discussed. It is claimed that suggested results claim applications in the petroleum sciences, thermal systems, heat transfer devices etc. It has been claimed that the velocity profile increases due to Bingham parameter and Philippoff constant. Lower heat and mass transfer impact is observed due to Philippoff parameter.

Magnetic dipole effects on unsteady flow of Casson-Williamson nanofluid propelled by stretching slippery curved melting sheet with buoyancy force

In particular, the Cattaneo-Christov heat flux model and buoyancy effect have been taken into account in the numerical simulation of time-based unsteady flow of Casson-Williamson nanofluid carried over a magnetic dipole enabled curved stretching sheet with thermal radiation, Joule heating, an exponential heat source, homo-heterogenic reactions, slip, and melting heat peripheral conditions. The specified flow's partial differential equations are converted to straightforward ordinary differential equations using similarity transformations. The Runge-Kutta-Fehlberg 4-5th order tool has been used to generate solution graphs for the problem under consideration. Other parameters are simultaneously set to their default settings while displaying the solution graphs for all flow defining profiles with the specific parameters. Each produced graph has been the subject of an extensive debate. Here, the analysis shows that the thermal buoyancy component boosts the velocity regime. The investigation also revealed that the melting parameter and radiation parameter had counterintuitive effects on the thermal profile. The velocity distribution of nanofluid flow is also slowed down by the ferrohydrodynamic interaction parameter. The surface drag has decreased as the unsteadiness parameter has increased, while the rate of heat transfer has increased. To further demonstrate the flow and heat distribution, graphical representations of streamlines and isotherms have been offered.

Influence of active and passive control of nanoparticles for the magnetized nanofluid flow over a slippery stretching cylinder

This paper explores the active and passive control implementation on the nanofluid flow over a stretching cylinder. Realistic velocity slip and thermal jump properties are clutched. Appearance of external heat source and magnetic influence is also reckoned. Concentration and temperature profiles are modified due to integration of Brownian motion together with thermophoresis. Leading equations are transfigured into ODEs by well-qualified similarity transfiguration and hence solved by RK-4 shooting technique. Entire simulation is settled by MAPLE software with proper rate of accuracy and the outcomes are portrayed by graphs and tables. Results are compared considering both slip and without slip conditions, whereas the concentration profile is described under active and passive control conditions. Mass transfer decreases for Brownian motion but reverse effect is found for thermophoresis parameter under passive control of flow. Mass transfer is changed by 10.1% in case of passive control condition for the Reynolds number parameter. Nusselt number is diminished by 6.16% under passive control provision for magnetic parameter.

A computational fluid dynamics analysis on Fe3O4-H2O based nanofluid axisymmetric flow over a rotating disk with heat transfer enhancement

In present times modern electronic devices often come across thermal difficulties as an outcome of excessive heat production or reduction in surface area for heat exclusion. The current study is aimed to inspect the role of iron (III) oxide in heat transfer enhancement over the rotating disk in an axisymmetric flow. Water is utilized as base fluid conveying nano-particle over the revolving axisymmetric flow mechanism. Additionally, the computational fluid dynamics (CFD) approach is taken into consideration to design and compute the present problem. For our convenience, two-dimensional axisymmetric flow configurations are considered to illustrate the different flow profiles. For radial, axial, and tangential velocity profiles, the magnitude of the velocity, streamlines, and surface graphs are evaluated with the similarity solution in the computational fluid dynamics module. The solution of dimensionless equations and the outcomes of direct simulations in the CFD module show a comparable solution of the velocity profile. It is observed that with an increment in nanoparticle volumetric concentration the radial velocity decline where a tangential motion of flow enhances. Streamlines stretch around the circular surface with the passage of time. The high magnetization force [Formula: see text] resist the free motion of the nanofluid around the rotating disk. Such research has never been done, to the best of the researchers' knowledge. The outcomes of this numerical analysis could be used for the design, control, and optimization of numerous thermal engineering systems, as described above, due to the intricate physics of nanofluid under the influences of magnetic field and the inclusion of complex geometry. Ferrofluids are metallic nanoparticle colloidal solutions. These kinds of fluids do not exist in nature. Depending on their purpose, ferrofluids are produced using a variety of processes. One of the most essential characteristics of ferrofluids is that they operate in a zero-gravity environment. Ferrofluids have a wide range of uses in engineering and medicine. Ferrofluids have several uses, including heat control loudspeakers and frictionless sealing. In the sphere of medicine, however, ferrofluid is employed in the treatment of cancer via magneto hyperthermia.

Significance of thermal radiation and bioconvection for Williamson nanofluid transportation owing to cone rotation

Numerical investigation for enhancement in thermal distribution of unsteady dynamics of Williamson nanofluids and ordinary nanofluids flow across extending surface of a rotating cone is represented in this communication. Bio-convection of gyrotactic micro-organisms and thermal radiative fluxes with magnetic fields are significant physical aspects of the study. The velocity slip conditions are considered along x and y directions. The leading formulation is transmuted into ordinary differential form via similarity functions. Five coupled equations with non-linear terms are resolved numerically through the utilization of Matlab code for the Runge-Kutta procedure. The parameters of buoyancy ratio and bio-convection Rayleigh number decrease the x-direction velocity. The slip parameter being proportional to viscosity reduces the speed of flow and hence rise in temperature. Also, the temperature rises with the rising values of magnetic field strength, radiative heat transportation, Brownian motion and thermophorsis.

Analysis of second grade hybrid nanofluid flow over a stretching flat plate in the presence of activation energy

The research of fluid containing nanoparticles for the heat transport characteristics is very famous because of its variety of real-life applications in various thermal systems. Although the thermal efficiency of the nanofluid was effective but still the nano scientists were trying to introduce some new advance class of fluid. Therefore, an advance class of fluid is developed by the dispersion of two different nano sized particles in the conventional base fluid known as "Hybrid nanofluid" which is more effective compared to simple nanofluids in many engineering and industrial applications. Therefore, motivated from the hybrid type of nanofluids in the current research we have taken two-dimensional laminar and steady flow of second grade fluid passing through porous plate. The engine oil base fluid is widely used fluid in the engineering and industrial problems. Keeping these applications in mind the engine oil is considered and two different nanoparticles Copper and aluminum oxide are added in ordered to get the required thermal characteristics. In addition to this the thermal radiation, chemical reaction, activation energy, Brownian motion and thermophoresis are also addressed during the current research. The present proposed higher-order PDE's is transformed to the non-linear system of ODE's. For the solution of the proposed high non-linear model HAM method is employed. As the hybrid nanofluid are highlighted on the second-grade fluid flow over a horizontal porous flat plate. During the present analysis and experimental study, it has been proved that the performance of hybrid nanofluid is efficient in many situations compared to nanofluid and regular fluid. For physical interpretation all the flow parameters are discussed through graphs. The impact of volume fraction is also addressed through graphs. Moreover, the comparative analysis between hybrid and nanofluid is carried out and found that hybrid nanofluid performed well as compared to nanofluid and regular fluid. The engineering quantities obtained from the present research have been presented in tables.

Verification of Dual Solutions for Water and Kerosene-Based Carbon Nanotubes over a Moving Slender Needle

This article focuses on the boundary layer for an axisymmetric flow and heat transfer of a nanofluid past a moving slender needle with single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). In this study, the streamlines of the flow are symmetrically located along the needle’s surface. Water and kerosene are two types of base fluids that are considered in this study. This analysis is presented with needle thickness, the ratio of velocity, nanoparticle volume fraction, and Prandtl number. The partial differential equations (PDEs) are transformed into dimensionless ordinary differential equations (ODEs) by adopting relevant similarity transformations. The bvp4c package is implemented in MATLAB R2018a to solve the governing dimensionless problems numerically. The behaviors of various sundry variables on the flow and heat transfer are observed and elaborated further. The magnitude of the skin friction, heat transfer rate, as well as velocity and temperature distributions are demonstrated in graphical form and discussed. It is worth mentioning that kerosene-based CNTs have the largest skin friction coefficient and heat transfer rate compared to water-based CNTs. The thin wall of the needle and the single-walled carbon nanotubes also contributes to high drag force and heat transfer rate on the surface. It is revealed from the stability analysis that the first solution exhibits a stable flow. Obtained results are also matched with the present data in the restricting situation, and excellent agreement is noticed.

A sensitivity analysis of MHD nanofluid flow across an exponentially stretched surface with non-uniform heat flux by response surface methodology

The current study investigates the MHD flow of nanofluid across an elongating surface while taking into account non-uniform heat flux. For this, we have considered the flow of a boundary layer over a stretched sheet containing (water-based) Al₂O₃ nanoparticles. The convective boundary conditions for temperature have been invoked. The flow created by a surface that is exponentially expanding in the presence of a magnetic field and a non-uniform heat flux has been mathematically formulated by using laws of conservation. Transformed non-dimensional systems of governing equations have been analyzed numerically by using Adam’s Bashforth predictor corrector approach. The effects of emerging parameters on the fluid velocity and temperature profiles have been further described by plotting graphs. An experimental design and a sensitivity analysis based on Response Surface Methodology (RSM) are used to examine the effects of various physical factors and the dependence of the response factors of interest on the change of the input parameter. To establish the model dependencies of the output response variables, which include the skin friction coefficient and the local Nusselt number, on the independent input parameters, which include the magnetic field parameter, the nanoparticle volume fraction, and the heat transfer Biot number, RSM is used. On the basis of statistical measures such as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q - Q$$\end{document}Q-Q residual plots, adjusted and hypothesis testing using p values, it is observed that both of our models for Skin Friction Coefficient (SFC) and the Local Nusselt Number (LNN) are best fitted. Further, it is concluded that the sensitivity of the SFC, as well as the LNN through heat transfer Biot number, is greater than that of nanoparticle volume fraction and magnetic field parameter. The SFC is sensitive to all combinations of the input parameters. At high levels of heat transfer Biot number, the LNN displays negative sensitivity via magnetic field parameters.

Fractional analysis of unsteady squeezing flow of Casson fluid via homotopy perturbation method

The objective of this article is to model and analyze unsteady squeezing flow of fractional MHD Casson fluid through a porous channel. Casson fluid model is significant in understanding the properties of non-Newtonian fluids such as blood flows, printing inks, sauces and toothpaste etc. This study provides important results as unsteady flow of Casson fluid in fractional sense with aforementioned effects has not been captured in existing literature. After applying similarity transformations along with fractional calculus a highly non-linear fractional-order differential equation is obtained. Modeled equation is then solved along with no-slip boundary conditions through a hybrid of Laplace transform with homotopy perturbation algorithm. For validity purposes, solution and errors at various values in fractional domain are compared with existing results. LHPM results are better in terms of accuracy than other available results in literature. Effects of fractional parameter on the velocity profile, skin friction and behaviors of involved fluid parameters is the focal point of this study. Comprehensive, quantitative and graphical analysis is performed for investigating the effects of pertinent fluid parameters on the velocity profile and skin friction. Analysis revealed that fractional parameter depicts similar effect in case of positive and negative squeeze number. Also, skin friction decreases with an increasing fractional parameter. Moreover, in fractional environment Casson parameter has shown similar effect on the velocity profile in case of positive and negative squeeze number.

Electromagnetic Trihybrid Ellis Nanofluid Flow Influenced with a Magnetic Dipole and Chemical Reaction Across a Vertical Surface

The purpose of this study is to evaluate the augmentation of thermal energy transfer in trihybrid Ellis nanofluid flow in the occurrence of magnetic dipole passes over a vertical surface. The ternary hybrid nanofluid is prepared by the dispersion of ternary nanoparticles (Al₂O₃, SiO₂, and TiO₂) in the Carreau Yasuda fluid. The velocity and heat transportation has been examined in the existence of the Darcy Forchhemier influence and heat source/sink. The phenomena of fluid flow have been mathematically designed for energy and fluid velocity in the form of a nonlinear partial differential equation (PDE)-based system. The system of PDEs is further refined to the set of ordinary differential equations via suitable similarity substitutions. The acquired dimensionless equations are numerically solved with the help of the HAM. It has been noticed that the energy contour is enhanced versus the variation of viscous dissipation and heat generation. A significant contribution of a magnetic dipole is observed to elevate the production of the thermal energy field, and an opposite trend is noticed versus the flow profile. The accumulation of Al₂O₃, SiO₂, and TiO₂ nanomaterials in the base fluid "engine oil" improves the velocity and energy profiles.

Thin film flow and heat transfer of Cu-nanofluids with slip and convective boundary condition over a stretching sheet

The flow and heat transfer in thin film of Cu-nanofluid over a stretching sheet by considering different shape factors (platelets, blades, bricks, sphere and cylinder) along with slip and convective boundary conditions is investigated. The governing partial differential equations are converted to nonlinear ordinary differential equations by means of suitable similarity transformation and then solved by using BVP4C in MATLAB. The physical significance of various parameters on velocity and temperature profiles are investigated and provided in the form of table and also presented graphically. It is noted that the Platelet-shaped nanoparticles has the highest heat transfer rate as compare to other particle’s shapes.

Analytical Approach for a Heat Transfer Process through Nanofluid over an Irregular Porous Radially Moving Sheet by Employing KKL Correlation with Magnetic and Radiation Effects: Applications to Thermal System

The aluminum nanoparticle is adequate for power grid wiring, such as the distribution of local power and the transmission of aerial power lines, because of its higher conductivity. This nanoparticle is also one of the most commonly used materials in applications in the electrical field. Thus, in this study, a radiative axisymmetric flow of Casson fluid, induced by water-based Al₂O₃ nanofluid by using the Koo–Kleinstreuer–Li (KKL) correlation, is investigated. The impact of the magnetic field is also taken into account. KKL correlation is utilized to compute the thermal conductivity and effective viscosity. Analytical double solutions are presented for the considered axisymmetric flow model after implementing the similarity technique to transmute the leading equations into ordinary differential equations. The obtained analytic forms were used to examine and discuss the velocity profile, the temperature distribution, reduced heat transfer, and coefficient of reduced skin friction. The analytic solutions indicate that the velocity profile decreases in the branch of the first solution and uplifts in the branch of the second solution due to the presence of an aluminum particle, whereas the dimensionless temperature enhances in both solutions. In addition, the Casson parameter increases the friction factor, as well as the heat transport rate.

Melting aspects in flow of second grade nanomaterial with homogeneous–heterogeneous reactions and irreversibility phenomenon: A residual error analysis

Here, we scrutinize the entropy analysis in magnetohydrodynamic flow of second-grade nanomaterials with melting effect subject to stretchable bended surface. Heat attribution is modeled through first law of thermodynamics with radiation effect. Major physical effect of random and thermophoretic motion is also addressed. Feature of irreversibility (entropy rate) analysis is also discussed. Isothermal cubic autocatalyses chemical reaction at catalytic surface is discussed. Nonlinear dimensionless differential system is developed through adequate transformation. Optimal homeotypic analysis method (OHAM) is employed to construct convergent solution. Influence of physical variables on entropy rate, fluid flow, concentration, and thermal field is discussed. An augmentation in fluid flow is noticed through curvature variable, while reverse effect holds for magnetic variable. A reverse effect holds for fluid flow and thermal field through melting variable. Entropy analysis is augmented with variation in melting variable. Reduction occurs in concentration through thermophoretic variable, while an opposite effect holds for thermal field. An increment in melting variable leads to reduced concentration. Larger estimation of radiation variable improves entropy analysis.

Computational Analysis of Nanoparticle Shapes on Hybrid Nanofluid Flow Due to Flat Horizontal Plate via Solar Collector

The present work discusses the 2D unsteady flow of second grade hybrid nanofluid in terms of heat transfer and MHD effects over a stretchable moving flat horizontal porous plate. The entropy of system is taken into account. The magnetic field and the Joule heating effects are also considered. Tiny-sized nanoparticles of silicon carbide and titanium oxide dispersed in a base fluid, kerosene oil. Furthermore, the shape factors of tiny-sized particles (sphere, bricks, tetrahedron, and platelets) are explored and discussed in detail. The mathematical representation in expressions of PDEs is built by considering the heat transfer mechanism owing to the effects of Joule heating and viscous dissipation. The present set of PDEs (partial differential equations) are converted into ODEs (ordinary differential equations) by introducing suitable transformations, which are then resolved with the bvp4c (shooting) scheme in MATLAB. Graphical expressions and numerical data are obtained to scrutinize the variations of momentum and temperature fields versus different physical constraints.

Performance-based comparison of Yamada-Ota and Hamilton-Crosser hybrid nanofluid flow models with magnetic dipole impact past a stretched surface

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.

Flow and heat transport phenomenon for dynamics of Jeffrey nanofluid past stretchable sheet subject to Lorentz force and dissipation effects

Survey of literature unveils that nanofluids are more efficient for heat transport in comparison to the traditional fluids. However, the enlightenment of developed techniques for the augmentation of heat transport in nanomaterials has considerable gaps and, consequently, an extensive investigation for aforementioned models is vital. The ongoing investigation aims to study the 2-D, incompressible Jeffrey nanofluid heat transference flow due to a stretchable surface. Furthermore, the effect of dispersion of graphene nanoparticles in base liquid ethylene glycol (EG) on the performance of flow and heat transport using the Tawari-Das model in the existence of Ohmic heating (electroconductive heating) and viscous heat dissipation is contemplated. The boundary-layer PDEs are reconstituted as ODEs employing appropriate similarity transformation. Keller-Box Method (KBM) is utilized to determine the numerical findings of the problem. Graphene conducts heat greater in rate than all of the other materials and it is a good conductor of electrical energy. Graphene/EG nanofluid is employed to look out the parametric aspects of heat transport flow, drag coefficient, and heat transference rate phenomena with the aid of graphs and tables. The numerical outcomes indicate that concentration and magnetic field abate the shear stresses for the nanofluid. An increase of Graphene nanoparticle volume fraction parameter can boost the heat transport rate. The effect of Prandtl Number is to slow down the rate of heat transport as well as decelerate the temperature. Additionally, the rate of heat transportation augments on a surface under Deborah's number. Results indicate that the temperature of the graphene-EG nanofluid is greater than the convectional fluid hence graphene-EG nanofluid gets more important in the cooling process, biosensors and drug delivery than conventional fluids.

Numerical investigation of nanofluid flow using CFD and fuzzy-based particle swarm optimization

This paper is focused on the application and performance of artificial intelligence in the numerical modeling of nanofluid flows. Suspension of metallic nanoparticles in the fluids has shown potential in heat transfer enhancement of the based fluids. There are many numerical studies for the investigation of thermal and hydrodynamic characteristics of nanofluids. However, the optimization of the computational fluid dynamics (CFD) modeling by an artificial intelligence (AI) algorithm is not considered in any study. The CFD is a powerful technique from an accuracy point of view. However, it could be time and cost-consuming, especially in large-scale and complicated problems. It is expected that the machine learning technique of the AI algorithms could improve such CFD drawbacks by patterning the CFD data. Once the AI finds the CFD pattern intelligently, there is no need for CFD calculations. The particle swarm optimization-based fuzzy inference system (PSOFIS) is considered in this study to predict the velocity profile of Al₂O₃/water turbulent flow in a heated pipe. One of the challenging problems in CFD modeling is the lost data for a specific boundary condition. For example, the CFD data are available for wall heat fluxes of 75, 85, 105, and 125 w/m², but there is no data for the wall heat flux of 95 w/m². So, the PSOFIS learns the available CFD data, and it predicts the velocity profile for where the data is not available (i.e., wall heat flux of 95 w/m²). The intelligence of PSOFIS is checked by the coefficient of determination (R² pattern) for different values of accept ratio (AR) and inertia weight damping ratio (IWDR). The best intelligence is obtained for the AR and IWDR of 0.7 and 0.99, respectively. At this condition, the velocity profile predicted by both CFD and PSOFIS is compatible. As the performance of the PSOFIS, for learning time of 268 s, the prediction of the CFD data lost was negligible (~ 1 s). In contrast, the CFD calculation takes around 600 s for each simulation.

Analysis of newly developed fractal-fractional derivative with power law kernel for MHD couple stress fluid in channel embedded in a porous medium

Fractal-fractional derivative is a new class of fractional derivative with power Law kernel which has many applications in real world problems. This operator is used for the first time in such kind of fluid flow. The big advantage of this operator is that one can formulate models describing much better the systems with memory effects. Furthermore, in real world there are many problems where it is necessary to know that how much information the system carries. To explain the memory in a system fractal-fractional derivatives with power law kernel is analyzed in the present work. Keeping these motivation in mind in the present paper new concept of fractal-fractional derivative for the modeling of couple stress fluid (CSF) with the combined effect of heat and mass transfer have been used. The magnetohydrodynamics (MHD) flow of CSF is taken in channel with porous media in the presence of external pressure. The constant motion of the left plate generates the CSF motion while the right plate is kept stationary. The non-dimensional fractal-fractional model of couple stress fluid in Riemann-Liouville sense with power law is solved numerically by using the implicit finite difference method. The obtained solutions for the present problem have been shown through graphs. The effects of various parameters are shown through graphs on velocity, temperature and concentration fields. The velocity, temperature and concentration profiles of the MHD CSF in channel with porous media decreases for the greater values of both fractional parameter [Formula: see text] and fractal parameter [Formula: see text] respectively. From the graphical results it can be noticed that the fractal-fractional solutions are more general as compared to classical and fractional solutions of CSF motion in channel. Furthermore, the fractal-fractional model of CSF explains good memory effect on the dynamics of couple stress fluid in channel as compared to fractional model of CSF. Finally, the skin friction, Nusselt number and Sherwood number are evaluated and presented in tabular form.

Effect of Magnetohydrodynamics on Heat Transfer Behaviour of a Non-Newtonian Fluid Flow over a Stretching Sheet under Local Thermal Non-Equilibrium Condition

A mathematical model is proposed to describe the flow, heat, and mass transfer behaviour of a non-Newtonian (Jeffrey and Oldroyd-B) fluid over a stretching sheet. Moreover, a similarity solution is given for steady two-dimensional flow subjected to Buongiorno’s theory to investigate the nature of magnetohydrodynamics (MHD) in a porous medium, utilizing the local thermal non-equilibrium conditions (LTNE). The LTNE model is based on the energy equations and defines distinctive temperature profiles for both solid and fluid phases. Hence, distinctive temperature profiles for both the fluid and solid phases are employed in this study. Numerical solution for the nonlinear ordinary differential equations is obtained by employing fourth fifth order Runge–Kutta–Fehlberg numerical methodology with shooting technique. Results reveal that, the velocity of the Oldroyd-B fluid declines faster and high heat transfer is seen for lower values of magnetic parameter when compared to Jeffry fluid. However, for higher values of magnetic parameter velocity of the Jeffery fluid declines faster and shows high heat transfer when compared to Oldroyd-B fluid. The Jeffery liquid shows a higher fluid phase heat transfer than Oldroyd-B liquid for increasing values of Brownian motion and thermophoresis parameters. The increasing values of thermophoresis parameter decline the liquid and solid phase heat transfer rate of both liquids.

Finite Element Study of Bio-Convective Stefan Blowing Ag-MgO/Water Hybrid Nanofluid Induced by Stretching Cylinder Utilizing Non-Fourier and Non-Fick's Laws

In the present framework, an analysis on nanofluid magneto-transport phenomena over an extending cylinder influenced by gyrotactic behavior of algal suspension, is made using the Cattaneo–Christov heat flux (non-Fourier) and mass flux (non-Fick’s) concept in modified Buongiorno’s model. Two dimensional incompressible MHD hybrid nanofluid which comprises chemically reactive hybrid nanomaterials (Ag-MgO NPs) and Stefan blowing effect along with multiple slips is considered. The experimental correlations with their dependency on initial nanoparticle volume fraction are used for viscosity and thermal conductivity of nanofluids. Similarity transformation is used to convert the governing PDE’s into non-linear ODE’s along with boundary conditions, which are solved using the Galerkin Finite Element Method (GFEM). The mesh independent test with different boundary layer thickness (ξ∞) has been conducted by taking both linear and quadratic shape functions to achieve a optimal desired value. The results are calculated for a realistic range of physical parameters. The validation of FEM results shows an excellent correlation with MATLAB bvp5c subroutine. The warmth exhibitions are assessed through modified version of Buongiorno’s model which effectively reflects the significant highlights of Stefan blowing, slip, curvature, free stream, thermophoresis, Brownian motion and bio-convection parameters. The present study in cylindrical domain is relevant to novel microbial fuel cell technologies utilizing hybrid nanoparticles and concept of Stefan blowing with bioconvection phenomena.

Significance of Stefan Blowing and Convective Heat Transfer in Nanofluid Flow Over a Curved Stretching Sheet with Chemical Reaction

The applications of fluid flow with Newtonian heating effect include conjugate heat conveyance around fins, petroleum industry, and heat exchangers designing. Motivated from these applications, an attempt has been made to analyze the stream of viscous nanomaterial subjected to a curved stretching sheet. Also, heat and mass transport mechanism due to a chemical reaction, Brownian and thermophoresis motion are discussed. The equations of the mathematical model are formulated by considering the Newtonian heating and Stefan blowing conditions at the boundary. These modelled equations are then changed to a system of nonlinear equation involving ordinary derivatives of a function by means of suitable similarity transformations. Further, shooting technique with Runge-Kutta-Fehlberg-45 process is utilized to solve the reduced equations. Outcomes disclose that, the gain in Stefan blowing parameter escalates the liquid velocity. The intensification in chemical reaction rate parameter deteriorates the concentration gradient. The rise in Schmidt number and thermophoresis parameter drops the mass transfer rate. The increased values of Newtonian heating parameter with respect to thermophoresis parameter decays the heat transport rate.