Hydromagnetic Stagnation Point Flow Research Articles

Impact of Arrhenius activation energy on magnetic nanofluid flow over a slendering stretchable sheet with nonlinear radiative heat transfer: A machine learning algorithm

Thermal systems in the contemporary world need effective cooling and heating methods. Heat transfer technology plays a vital role in various industries, including aerospace, electronic equipment, automobiles, and transportation. Considering the importance of effective cooling and heating processes, this framework explores the hydromagnetic stagnation point flow with binary chemical reactions, ohmic heating, Arrhenius activation energy, nonlinear thermal radiation, thermophoresis, and Brownian motion. At first, the flow equations are determined in a formal way as dimensional partial differential equations. Then, they are transformed into simpler, dimensionless ordinary differential equations using self-similar variables. The present study describes a novel approach to intelligent numerical computing, utilizing a Levenberg-Marquard algorithm-based MLP (Multi-Layer Perceptron) feed-forward back-propagation ANN (Artificial Neural Networks) implementation. The collection of data was conducted to facilitate the evaluation, validation, and instruction of the artificial neural network model. The utilization of appropriate self-similarity variables has facilitated the conversion of fluid transport equations into ordinary differential equations. The Runge–Kutta–Fehlberg (RKF) technique was used to solve these equations. The numerical results are presented visually for numerous constraints of the governing parameters. The increased values of the velocity ratio enhanced the fluid velocity. The nonlinear thermal radiation and temperature differential characteristics significantly raise the temperature of the fluid. Increasing the nonlinear radiation and magnetic field parameters improves the rate of heat transfer. The temperature of the fluid decreases as the size of stagnation increases. The skin friction coefficients decrease as the wall thickness and magnetic parameters increase.

Computational method for energy transport of MHD nanofluids flow near non-aligned stagnation point with non-linear thermal radiation and interface slip

Haemodialysis, nuclear reactors, cooling and heating systems, and heat exchangers are glimpses of applications where thermal problems are considered as a fundamental for flow over aligned stagnation points with heat and mass transfer components. The purpose of this study is to present steady dual solutions for non-aligned stagnation point flow of nanofluid over a linearly contracting/expanding surface under temperature and velocity slips. The mathematical model is established using boundary layer assumption. The authors acknowledge from prior investigations and studies that the non-aligned stagnation point flow across a contracting/expanding surface is highly rare in the field of engineering and fluid dynamics research. In the backdrop of non-linear thermal radiation, the problem of oblique hydromagnetic stagnation point flow of an electrically conducting optically dense viscous incompressible nanofluid across a convectively heated stretching sheet is formulated. The effects of Brownian motion and thermophoresis are incorporated into the nanofluid model. With the use of appropriate similarity transformations, the governing nonlinear partial differential equations for momentum, energy, and nanoparticle concentration are converted into a set of nonlinear ordinary differential equations. Using the BVP4c approach, the modified equations are numerically solved. It is discovered that when the strength of the magnetic field increases, the non-alignment of the re-attachment point on the sheet surface becomes less pronounced. The thickness of the thermal boundary layer grows as the magnetic and Biot parameters expand. The extent of the skin friction factor ascends with increasing magnetic field and suction variable inputs. The heat transfer rate detract with radiative parameter.

Wavelet-based numerical solution of a mathematical model on the Hydro-magnetic stagnation point flow

The steady two-dimensional flow of an incompressible electrically conducting fluid near the stagnation point on a stretching sheet is investigated. The governing highly nonlinear PDEs are altered into highly nonlinear ODE by utilizing non-similar and similar variables and then solved numerically using a Hermite wavelet collocation method (HWCM). It is interesting to note that the results of the previous authors are in good agreement with the results of this study tabulated which is evident from the tabular values. Further, the effects of the magnetic parameter, viscoelastic parameter, stagnation point flow, and stretching of the sheet parameters on the flow field characteristics are obtained and discussed. The Lorentz force opposes the flow. Further, the fluid flow velocity decreases as the viscoelastic parameter increases. This practically indicates that the characteristics of fluid flow in viscoelastic fluids may be influenced by modifying the change in the viscoelastic parameter.

Interaction of nanoparticles with micro organisms under Lorentz force in a polymer liquid with zero mass flux

BackgroundRheological fluids enduring bio convection are gaining great attention in modern day industrial, technological and several manufacturing industries. Such flows are evident in chemical and mining industry, biomedical flows, and many other fields of science and engineering. Among the many other rheolgical liquids, Sutterby fluid model is significant due to its characteristics of Pseudoplastic and dilatant fluids. It portrays dilute polymer solutions, which has numerous applications in industrial practice. MethodsIn this theoretical research two-dimensional hydromagnetic stagnation point flow of Sutterby bio convective fluid through an elastic surface has been discussed. The mathematical model of governed problem is transformed into a set of ordinary differential equations using similarity transformation. These nonlinear coupled ordinary differential equations are handled by using shooting scheme (numerical technique). Significant findingsInfluence of all physical constraints for temperature, concentration of gyrotactic microorganism and velocity profiles are presented graphically. Local heat & mass flux and density of microorganisms (Physical quantities of interest) are presented numerically through bar charts.

Analysis of entropy generation in the nonlinear thermal radiative micropolar nanofluid flow towards a stagnation point with catalytic effects

The major goal of this work is to analyze the entropy generation in a micropolar nanofluid’s hydromagnetic stagnation point flow with the involvement of the catalytic and nonlinear thermal radiation effects. The magnetite nanoparticle is added to the water to form the -water nanofluid. A vertical stretchable sheet is assumed to initiate the two-dimensional time-independent flow. The impacts of Joule heating and viscous dissipation are considered in the development of the governing equations of the concerned problem. An appropriate procedure of similarity transformations is implemented in the system of partial differential equations (PDE) to establish the nonlinear setup of ordinary differential equations (ODE). The behavior of various aspects of fluid such as micro-rotation, entropy generation, temperature, velocity, Bejan number, and concentration relative to the pertinent parameters is graphically revealed. The graphical nature of local Nusselt number and skin friction relative to the physical parameters is also exhibited in this analysis. This study concludes that the amplification in the magnetic field develops a minimization in the velocity field. The Bejan number shows the declining behavior corresponding to the larger quantities of the Brinkman number and Reynolds number, but the entropy of the system escalates for these parameters.

Aspects of second‐order velocity slip and radiation absorption on hydromagnetic stagnation point flow of Jeffrey fluid with chemical reaction

AbstractThe present article describes the magnetohydrodynamic flow of a moving Jeffrey fluid along a convectively heated porous stretching surface with second‐order velocity slip and radiation absorption effects. Furthermore, chemical reactions and viscous dissipation impacts are also taken into account. The governing equations are converted into dimensionless ordinary differential equations (ODEs) using appropriate similarity transformations. The highly nonlinear ODEs are solved numerically by employing a shooting technique based on the Runge–Kutta Cash–Karp formula. The figures are used to study the variations in temperature, velocity, and concentration profiles for several physical factors. The numerical values of the local skin friction, Sherwood number, and Nusselt number are explained and shown in tables. The analysis reveals that the velocity profile is enhanced for amplifying values of velocity ratio parameter and first‐order velocity slip parameter. However, the temperature profile of Jeffrey nanofluid is highlighted w.r.t. Eckert number and radiation absorption parameter. This study may find significant applications in polymer production, food processing, instrumentation, combustion modeling, catalytic chemical reactors, and so on.

Hydromagnetic stagnation point flow of a magnetite ferrofluid past a convectively heated permeable stretching/shrinking sheet in a Darcy–Forchheimer porous medium

Hydromagnetic stagnation point flow of a magnetite ferrofluid past a convectively heated permeable stretching/shrinking sheet in a Darcy–Forchheimer porous medium

Time‐dependent hydromagnetic stagnation point flow of a Maxwell nanofluid with melting heat effect and amended Fourier and Fick's laws

AbstractAn unsteady stagnation point flow of a Maxwell fluid over a unidirectional linearly stretching sheet is studied under the influence of a magnetic field. The parabolic energy equation, which is based on parabolic Fourier law is replaced with a hyperbolic energy equation incorporating the heat flux model of Cattaneo–Christov. The Buongiorno model is used to characterize the properties of nanofluids using thermophoresis and Brownian diffusion coefficients. The phenomenon of melting heat transfer and slip mechanism is also embodied in the present study. Coupled nonlinear differential equations have appeared when the specified similarity transformations are applied. The mathematical problem is tackled via the homotopy analysis method. The impact of important physical parameters on the velocity, concentration, and temperature are highlighted via graphs. To verify our present results, a comparison is given with a limiting case with an already published article. It is witnessed through the graphs that the higher unsteadiness parameter and melting heat coefficient both are responsible for the reduction in the velocity and temperature of the nanofluid. Also, the velocity slip parameter detracts the velocity profile and affiliated boundary layer thickness of the Maxwell nanofluid.

A Lie group integrator to solve the hydromagnetic stagnation point flow of a second grade fluid over a stretching sheet

<abstract><p>In the present paper, a Lie-group integrator, based on $ GL(4, \mathbb{R}) $ has been newly constructed to consider the flow characteristics in an electrically conducting second grade fluid over a stretching sheet. Present method which have a very fast convergence, permits us to explore some missing initial values at the left-end. Accurate initial values can be achieved when the determined target equation is valid, and then we can apply the group preserving scheme (GPS) as a geometric approach to obtain a rather accurate numerical solution. Finally, effects of magnetic parameter, viscoelastic parameter, stagnation point flow and stretching of the sheet parameters are illustrated.</p></abstract>

Transportation of heat and mass transport in hydromagnetic stagnation point flow of Carreau nanomaterial: Dual simulations through Runge-Kutta Fehlberg technique

In this research communication, MHD time dependent stagnation point flow of non-Newtonian fluid (Carreau fluid) is addressed subject to stretchable and shrinking surface of sheet. Stagnation point flow is considered. The novel features of slip mechanisms like Brownian and thermophoresis diffusions are accounted for the modeling of energy expression. The nonlinear partial differential expressions are converted to ordinary ones in the presence of similarity transformations and then dual solutions are obtained through implementation of Runge-Kutta Fehlberg Technique (RKFT) along with Shooting method (SM). The dual solutions are also computed which elaborate the Skin fraction, Nusselt number and Sherwood number and stress model number and its they're first and second solutions. A numerical compression is also prepared to justify our solutions with the available results as a limiting case.

ENTROPY GENERATION OF HYDRO-MAGNETIC STAGNATION POINT FLOW OF MICROPOLAR FLUID WITH ENERGY TRANSFER UNDER THE EFFECT OF UNIFORM SUCTION/ INJECTION

Abstract-- The entropy generation of hydro-magnetic stagnation point flow of micro-polar fluid with energy transfer has been analyzed numerically. An uniform magnetic field is applied normal to the plate. The partial differential equations are transformed into ordinary differential equations using similarity transformations. The effects of magnetic parameter, material parameter, Prandtl number, Grashof number on the flow and entropy generation are discussed and plotted graphically using the MATLAB built in bvp4c solver.

Mixed Convective Hydromagnetic Stagnation Point Flow of Nanofluid over an Inclined Stretching Plate with Prescribed Surface Heat Flux

Mixed Convective Hydromagnetic Stagnation Point Flow of Nanofluid over an Inclined Stretching Plate with Prescribed Surface Heat Flux

Entropy generation and regression analysis on stagnation point flow of Casson nanofluid with Arrhenius activation energy

This article presents the study of two-dimensional hydromagnetic stagnation point flow of Casson nanofluid over a stretching sheet in a non-Darcy porous medium with binary chemical reaction stimulated by Arrhenius activation energy. The energy equation is obtained by considering the production of heat due to Joule and viscous dissipations, heat generation/absorption and thermal radiation of the liquid. The flow model is developed and presented in the form of a system of nonlinear partial differential equations together with appropriate boundary conditions. The particle flux at the sheet is taken to be zero. The leading PDEs are transformed into dimensionless coupled ordinary differential equations (ODEs) by the usual procedure of transformation. The obtained ODEs are solved using optimal homotopy analysis method, and the effects of underlying parameters on the fluid velocity, temperature, concentration, entropy generation and Bejan number are demonstrated with the help of graphs. Also, the numerical values of skin friction coefficient, Nusselt number and Sherwood number are presented in tabular form. Linear as well as quadratic regression analysis for quantities of physical interest has also been carried out. Entropy generation is perceived to rise on increasing diffusive variable and Brinkman number, whereas Brownian diffusion has an adverse effect on it. Skin friction coefficient is reduced on increasing Casson fluid parameter and activation energy.

Non-Aligned Stagnation Point Flow of a Casson Fluid Past a Stretching Sheet in a Doubly Stratified Medium

This paper investigates the problem of oblique hydro magnetic stagnation point flow of an electrically conducting Casson fluid over stretching sheet embedded in a doubly stratified medium in the presence of thermal radiation and heat source/absorption with first order chemical reaction. It is assumed that the fluid impinges on the wall obliquely. Similarity variables were used to convert the partial differential equations to ordinary differential equations. The transformed ordinary differential equations are solved numerically using Runge-Kutta-Fehlberg method with shooting technique. It is observed that a boundary layer is formed when the stretching velocity of the surface is less than the in viscid free stream velocity at a point decreases with increase in the nonNewtonian rheology parameter. The augmentation of the temperature is observed with the magnetic parameter, heat source parameter and thermal radiation parameter while a reverse effect with thermal stratification number, Prandtl number and the velocity ratio parameter. Influence of Skin friction coefficient, Nusselt number and Sherwood number on the flow configurations for different values of pertinent parameters are portrayed graphically and discussed. Numerical results are compared with the published results and are found to be in good agreement with previously published results as special cases of present problem. The mass concentration is seen to be decrease with Schmidt number, chemical reaction parameter and solutal stratification number.

Stagnation Point Flow with Heat Transfer and Temporal Stability of Ferrofluid Past a Permeable Stretching/Shrinking Sheet

In this paper, the hydromagnetic stagnation point flow and temporal stability of Fe3O4-water ferrofluid over a convectively heated permeable stretching/shrinking sheet is theoretically investigated. The model equations of momentum and energy balance are obtained and transformed into ordinary differential equations using appropriate similarity variable. Using shooting method together with Runge-Kutta-Fehlberg numerical scheme the model nonlinear boundary value problem is tackled numerically. Pertinent results with respect to the basic steady flow velocity, temperature, skin friction and Nusselt number are obtained graphically and in tabular form. It is found that a critical value of shrinking parameter (λc) exists below which no real solution can be found. In addition, dual solutions (upper and lower branch) are observed for a range of shrinking/stretching parameter (λc<λ< 1), while for the stretching case (λ 1), the solution is unique. The obtained steady state solutions are examined for temporal development of small disturbances. The smallest eigenvalues reveal that the upper solution branch is stable and physically reliable while the lower solution branch is unstable and unrealistic. Both suction and magnetic field widen the range of the shrinking parameter for which the solution exists and boost the flow stability while nanoparticles volume fraction lessens it.

Hydromagnetic Stagnation Point Flow and Heat Transfer of Particle Suspended Fluid Towards a Radially Stretching Sheet with Heat Generation

In this article, we examine the hydromagnetic stagnation point flow of a dusty fluid towards a radially stretching surface in the presence of internal heat generation. By suitable similarity transformation, the governing coupled nonlinear partial differential equations with their corresponding boundary conditions are converted into a set of nonlinear coupled ordinary differential equations. The resulting equations are then solved numerically and the numerical solutions are then compared with existing literature. The effects of the parameters involving in the problem on flow and heat transfer characteristics are presented and discussed with the aid of graphs and tables.

Effects of Suction and Freestream Velocity on a Hydromagnetic Stagnation-Point Flow and Heat Transport in a Newtonian Fluid Toward a Stretching Sheet

Forced flow of an electrically conducting Newtonian fluid due to an exponentially stretching sheet is studied numerically. Free stream velocity is present and so is suction at the sheet. The governing coupled, nonlinear, partial differential equations of flow and heat transfer are converted into coupled, nonlinear, ordinary differential equations by similarity transformation and are solved numerically using shooting method, and curve fitting on the data is done by differential transform method together with Padé approximation. Prescribed exponential order surface temperature (PEST) and prescribed exponential order surface heat flux are considered for investigation of heat transfer related quantities. The influence of Chandrasekhar number, suction/injection parameter, and freestream parameter on heat transport is presented and discussed. Coefficient of friction and heat transport is also evaluated in the study. The results are of interest in extrusions and such other processes.

Non-aligned MHD stagnation point flow of variable viscosity nanofluids past a stretching sheet with radiative heat

This paper investigates the problem of oblique hydromagnetic stagnation point flow of a variable viscosity electrically conducting optically dense viscous incompressible nanofluid over a convectively heated stretching sheet in the presence of thermal radiation. The nanofluid model employed in this study incorporates the effects of Brownian motion and thermophoresis. The governing nonlinear partial differential equations for momentum, energy and nanoparticles concentration are reduced into a set of non-linear ordinary differential equations with the aid of suitable similarity transformations. The transformed equations are numerically integrated using fourth–fifth order Runge–Kutta–Fehlberg method. The effects of various controlling parameters on the dimensionless velocity, temperature, nanoparticles concentration, skin friction, Nusselt and Sherwood numbers are analysed and presented graphically. Obtained numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. It is found that non-alignment of the re-attachment point on the sheet surface decreases with an increase in magnetic field intensity.

Stagnation point flow of MHD chemically reacting nanofluid over a stretching convective surface with slip and radiative heat

This paper investigates the combined effects of buoyancy forces, homogeneous chemical reaction, thermal radiation, partial slip, heat source, Thermophoresis and Brownian motion on hydromagnetic stagnation point flow of nanofluid with heat and mass transfer over a stretching convective surface. The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point. Using similarity transformation, the governing nonlinear partial differential equations are reduced to a set of nonlinear ordinary differential equations which are solved numerically by employing by shooting method coupled with Runge–Kutta Fehlberg integration technique. Graphical results showing the effects of various thermophysical parameters on the velocity, temperature, nanoparticle concentration, local skin friction, local Nusselt number and local Sherwood number are presented and discussed quantitatively.

A model of solar radiation and Joule heating in magnetohydrodynamic (MHD) convective flow of thixotropic nanofluid

This paper reports the hydromagnetic stagnation point flow of thixotropic nanofluid towards an impermeable stretching surface. Effects of Brownian motion and thermophoresis are present. Heat and mass transfer analysis is performed in the presence of viscous dissipation, Joule heating and convective boundary conditions. Meaningful transformations are utilized to obtain nonlinear ordinary differential systems. Convergent solutions of the resulting differential systems are presented in series forms. Moreover the numerical values of skin friction coefficient, local Nusselt and Sherwood numbers are computed and analyzed.