Aligned Angle Research Articles

Numerical treatment of cross-diffusion impact on heat and mass transfer with magnetic radiation of micropolar fluid flow over a porous stretching surface

Cross-diffusion effects are essential in industry because they can improve process efficiency, optimize product development, improve environmental sustainability, and drive technological advancements. The effects of cross-diffusion, aligned magnetization, and radiation are considered and adequately reported on the micropolar fluid boundary layer. The momentum, energy, and species reaction models are utilized to quantitatively represent the flow equations containing the thermophysical parameters at an aligned angle. The described fluid models are transformed into ordinary systems of derivatives. The solution to the resulting equations is determined via Fehlberg Runge–Kutta. The impacts of related terms are presented on various plots. The investigation revealed that the aligned angle strengthens magnetic field parameters, which can also lower the flow. For injection cases, microrotation has a parabolic distribution. An inclined value of radiation term contributed to improving the temperature profile. Temperature and concentration profiles rise and decrease with the Soret number, affecting heat, and species transport rates. The porosity and the thermal buoyancy parameter exhibit conflicting behaviors for both the coefficient of plate drag and the couple stress.

The Effects of an Aligned Magnetic Field on Nanofluid Flow with Newtonian Heating

Magnetic field involvement can influence heat absorption in electrically conducting fluid flow, which is useful in the control of features of final products in industries such as radiation therapy, aeronautics, and MHD generators. Consequently, this study investigates the effect of an aligned magnetic field on nanofluid flow over a stretching sheet with the boundary condition of Newtonian heating. Steady nanofluid flow with copper as chosen nanoparticles and water as conventional base fluid is considered. The problem is governed by a system of nonlinear boundary layer equations with appropriate boundary conditions which are then transformed into non-dimensionless equations using an appropriate similarity transformation. A numerical approach known as Keller-Box method is used to solve the transformed governing equations. The numerical solutions obtained are presented graphically in the form of velocity and temperature profiles for different values of aligned angle of magnetic field, Newtonian heating parameter, Prandtl number and nanoparticles volume fraction. A significant increase in aligned angle results in a decrease in fluid velocity, but an increase in temperature profile of nanofluid flow. The increment in the Newtonian heating parameter as well as the nanoparticle volume fraction also causes the temperature to increase.

Impact of Nanoparticles Shapes on Magnetohydrodynamic Flow and Heat Transfer of Casson Hybrid Nanofluids over a Moving Inclined Plate

This study investigated the impact of different nanoparticles shape on magnetohydrodynamic of Casson hybrid nanofluids flow and heat transfer over a moving inclined plate with convective boundary conditions. The study infused water with silver (Ag) and Titanium Oxide (TiO2) to analysed the velocity and temperature profiles as well as skin friction and Nusselt number. The numerically method solved by by applying the implicit finite difference, Keller Box method based on similarity transformation techniques that used to convert the partial differential equations of Casson hybrid nanofluids to an ordinary differential equation. The results showed that platelet shaped nanoparticles had the highest velocity and temperature profiles, while a parameter of aligned angle of magnetic field, , interaction of magnetic field, , mixed convection parameters, , inclined angle parameters, , Casson parameters, , and Biot numbers, is increased, the velocity is increased and temperature is decreased. Conversely, as the volume fraction of nanoparticles, is increased, the velocity is decreased and temperature is increased. For moving inclined plate, the highest skin friction is moving against the flow while moving along the flow plate has the highest Nusselt number. The findings of the study can be useful in designing and optimizing various industrial applications that involve the transport of Casson hybrid nanofluids.

Entropy Generation of Unsteady Magnetohydrodynamics Nanofluid Flow Over a Porous Inclined Stretching Surface with Velocity Slip and Viscous Dissipation

The numerical investigation of the effects of inclined variable magnetic field, velocity slip, thermal radiation and viscous dissipation on the entropy generation of an unsteady MHD nanofluid flow over an inclined stretching sheet in a porous medium has been carried out here. The non-dimensional non-linear governing ordinary differential equations obtained after suitable similarity transformations are solved by SQLM. Effects of important factors of the model on the flow characteristics were numerically analysed and discussed in details with tables and graphs. Important physical quantities of skin friction, Nusselt number and the local Sherwood number were calculated and illustrated on tables. The aligned angle of the variable magnetic field between 0° and 90° was found to significantly influence the fluid flow rate, temperature, mass flux and entropy generation through the Bejan number. The velocity slip slip was found to have no signicant effects on the mass flux, however it influenced significantly the fluid flow rate and temperature. The inclination of the stretching sheet and the porosity of the medium were also found to influence the fluid flow rate, temperature and mass flux.

Aligned MHD Jeffrey Fluid Flow Containing Carbon Nanoparticles over Exponential Stretching Sheet with Viscous Dissipation and Newtonian Heating Effects

This study investigates the influence of viscous dissipation on aligned Magnetohydrodynamic (MHD) flow of Jeffry fluid containing Carbon Nanoparticles (CNTs) over an exponential stretching sheet with boundary condition of Newtonian Heating (NH). The model proposed by Tiwari and Das is adopted. The numerical computation using Runge-Kutta Fehlberg (RKF45) method is used to generate the results. The numerical solutions of the several parameters on the velocity and temperature profiles are analysed and presented graphically. It is revealed that an increase in aligned angle, magnetic field, and ratio of relaxation to retardation times leads to the decreasing in velocity and increasing in temperature profiles. Meanwhile, both velocity and temperature profiles increase with a rise in volume fraction parameter.

Aligned magnetohydrodynamic effect on magnetic nanoparticle with different base fluids past a moving inclined plate

This paper deals with the numerical solutions for the aligned MHD free convection laminar boundary layer flow over a moving inclined plate for two magnetic nanofluids, namely Fe3O4-water and Fe3O4-kerosene. It is assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid is on the right surface. The mathematical model has been constructed and based on the Tiwari-Das model, appropriate similarity transformations are used to convert the governing partial differential equations into nonlinear ordinary differential equations and solved numerically using the Keller-Box method. Numerical results for the skin friction coefficient and local Nusselt number were presented whilst the velocity and temperature profiles were illustrated graphically and analyzed. It is found that the velocity increases and temperature decrease with an increase of aligned magnetic field angle parameter, magnetic strength parameter, and Grashof number while the velocity decreases and temperature increase when inclined plate angle parameter and volume fractions of nanoparticles increase. For the convective parameter, both velocity and temperature profile increase when the Biot number increase. Comparisons with previously published studies are performed and excellent agreement is obtained.

Entropy Generation in MHD Second-Grade Nanofluid Thin Film Flow Containing CNTs with Cattaneo-Christov Heat Flux Model Past an Unsteady Stretching Sheet

Entropy generation plays a significant role in several complex processes, extending from cosmology to biology. The entropy generation minimization procedure can be applied for the optimization of mechanical systems including heat exchangers, elements of nuclear and thermal power plants, ventilation and air-conditioning systems. In order to present our analysis, entropy generation in a thin film flow of second grade nanofluid holding single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with a Cattaneo–Christov heat flux model is studied in this article. The flow is considered passing a linearly extending surface. A variable magnetic field with aligned angle ε is functioned along the extending sheet. With the aid of the homotopy analysis method (HAM), the fluid flow model is elucidated. The impressions of embedded factors on the flow are obtainable through figures and discussed in detail. It is observed that the velocity profile escalated with the increasing values of volume fraction of nanoparticles and second grade fluid parameter. The higher values of volume fraction of nanoparticles, second grade fluid parameter, non-linear heat source/sink, and thermal radiation parameter intensified the temperature profile. Surface drag force escalated with heightening values of nanoparticles volume fraction, unsteadiness, film thickness, magnetic, and second grade fluid parameters. Entropy generation increased with enhancing values of magnetic parameter, Brinkman number, and Reynolds number.

Numerical Investigation of Aligned Magnetic Flow Comprising Nanoliquid over a Radial Stretchable Surface with Cattaneo–Christov Heat Flux with Entropy Generation

The influence of entropy generation on aligned magnetic flow-including nanoparticles through a convectively heated radial stretched surface in the existence of Cattaneo–Christov heat flux is inspected. The highly nonlinear leading PDE’s via the similar scaling transformation are developed. The resulting system via the bvp4c technique from Matlab is computed. The impacts of rising constraints on the liquid velocity, nanoparticles concentration and temperature profile are argued and showed via portraits and table. In addition, the performance of liquid flow is inspected through the friction factor, the mass and heat transfer rate. With the rise in the thermal relaxation constraint, the thermal boundary layer is appreciably altered. Due to an aligned angle, the velocity of nanoliquid declines, while the concentration and temperature of nanofluid augment. It is also observed that the values of friction factor increase, whereas the values of heat and mass transfer decline due to an aligned angle. Entropy generation profiles developed due to magnetic parameters and the aligned angle. Lastly, a comparative scrutiny is composed via the previous studies which lead to support for our presently developed model.

Influence of inclined Lorentz forces through a porous media on squeezing Cu-H2o nanofluid in the presence of heat source/sink

PurposeThe purpose of this paper is to find the approximate solutions of unsteady squeezing nanofluid flow and heat transfer between two parallel plates in the presence of variable heat source, viscous dissipation and inclined magnetic field using collocation method (CM).Design/methodology/approachThe partial governing equations are reduced to nonlinear ordinary differential equations by using appropriate transformations and then are solved analytically by using the CM.FindingsIt is observed that the enhancing values of aligned angle of the magnetic causes a reduction in temperature distribution. It is also seen that the effect of nanoparticle volume fraction is significant on the temperature but negligible on the velocity profile.Originality/valueTo the best of the authors’ knowledge, no research has been carried out considering the combined effects of inclined Lorentz forces and variable heat source on squeezing flow and heat transfer of nanofluid between the infinite parallel plates.

Heat Transfer and Flow Analysis of Magnetohydrodynamic Dissipative Carreau Nanofluid over a Stretching Sheet with Internal Heat Generation

The unsteady two-dimensional flow and heat transfer analysis of Carreau nanofluid over a stretching sheet subjected to magnetic field, temperature dependent heat source/sink and viscous dissipation is presented in this paper. Similarity transformations are used to reduce the systems of the developed governing partial differential equations to nonlinear third and second orders ordinary differential equation which are solved using differential transform method. Using kerosene as the base fluid embedded with the silver (Ag) and copper (Cu) nanoparticles, the effects of pertinent parameters on reduced Nusselt number, flow and heat transfer characteristics of the nanofluid are investigated and discussed. From the results, it is established temperature field and the thermal boundary layers of Ag-Kerosene nanofluid are highly effective when compared with the Cu-Kerosene nanofluid. Heat transfer rate is enhanced by increasing in power-law index and unsteadiness parameter. Skin friction coefficient and local Nusselt number can be reduced by magnetic field parameter and they can be enhanced by increasing the aligned angle. Friction factor is depreciated and the rate of heat transfer increases by increasing the Weissenberg number. Also, for the purpose of verification, the results of the analytical of the approximate analytical solutions are compared with the results of numerical solution using Runge-Kutta coupled with Newton method. A very good agreement is established between the results. This analysis can help in expanding the understanding of the thermo-fluidic behaviour of the Carreau nanofluid over a stretching sheet.

Numerical and analytical comparisons of slanted Lorentz forces on thermal radiation flow of a micropolar fluid

The transient flow of a viscous incompressible electrically conducting micro-stretch fluid over an infinite vertical porous plate in the presence of slanted hydromagnetic flow with an aligned angle of 0° to 90° and thermal radiation effects has been analyzed. The governing equations are solved analytically by using the technique of the state-space approach and the inversion of the Laplace trans-forms is carried out using a numerical approach for varies physical parameters on the velocity, microrotation, micro-stretch and temperature profiles are shown graphically. In order to verify the accuracy of the present results, we have compared these results with the numerical solution by using the Crank-Nicolson implicit finite difference method. It is found that the thickness of thermal boundary-layer increases with an increase in the value of thermal radiation whereas antithesis trend is seen with increasing the Prandtl number.

Effects of Inclined Magnetic Field on Entropy Generation in Nanofluid Over a Stretching Sheet with Partial Slip and Nonlinear Thermal Radiation

The effects of inclined magnetic field on entropy generation in nanofluid over a stretching sheet were investigated in the presence of partial slip and nonlinear thermal radiation. Applying a similarity variable, the governing equations are reduced to a set of nonlinear ODEs. These equations are solved both analytically and numerically by hypergeometric function and Runge–Kutta Gill method with shooting technique, respectively. For Ag–water, magnetic, aligned angle, nanosolid volume fraction and slip parameters on velocity, temperature, skin friction coefficient and reduced Nusselt number were analyzed. The entropy generation for the influence of the same parameters, radiation parameter and the Reynolds number is discussed for Ag nanoparticles. It is observed that the nanosolid volume fraction and slip parameter reduce the entropy generation. But aligned magnetic field enhances the entropy generation.

Inclined Lorentz force effects on 3D micropolar fluid flow due to a stretchable rotating disks with higher order chemical reaction

The present work deals with an inclined magnetohydrodynamic flow of a micropolar fluid occurring between two stretchable disks rotating co-axially at a constant distance apart by taking into account higher order chemical reaction effects. Using similarity variables the Navier–Stokes equations, which represent the momentum, microrotation, energy, and concentration, are transformed into ordinary differential equations. The transformed conservation equations are solved numerically by using the Nachtsheim–Swigert shooting iteration technique along with sixth-order Runge–Kutta integration scheme. The influence of governing parameters are shown graphically and discussed. It was observed that an increase in the aligned angle strengthens the applied magnetic field and decreases the momentum boundary layer profiles of the micropolar fluid flow. Heat transfer rate reduces for larger values of chemical reaction Cr for both n = 1 and n = 2.

Flow and heat transfer of aligned magnetic field with Newtonian heating boundary condition

Influence of aligned magnetic field on the steady boundary layer flow and heat transfer over a stretching sheet with Newtonian heating boundary condition is considered. The transformed governing nonlinear boundary layer equations in the form of ordinary differential equations are solved numerically by Keller box method. The details on computation have been presented and elaborated. The obtained numerical solutions have been captured graphically in the form of velocity and temperature distributions for different values of aligned angle, magnetic field parameter, Prandtl number and conjugate parameter. It is found that, increases in aligned angle associated with magnetic field delayed the velocity profile of the flow and enhances the temperature profile.

Aligned magnetic field on dusty Casson fluid over a stretching sheet with Newtonian heating

Boundary layer flow and heat transfer on Casson fluid with dust particle over a stretching sheet is numerically investigated. The influences of aligned magnetic field together with Newtonian heating are considered in this problem. The governing equations are first transformed into ordinary differential equations using the appropriate similarity transformation variables. The numerical computation using Runge-Kutta Fehlberg (RKF45) method is employed to generate the results. Several physical parameters for both phases (fluid and particle) such as aligned angle, magnetic field parameter, Casson parameter, fluid particle interaction parameter, Prandtl number and conjugate parameter are investigated and analysed. The results in term of distribution velocity and temperature are presented graphically. The finding revealed that a rise in aligned angle and magnetic field parameter led to decrease the velocity profile and increase the temperature profile for both phases.

Aligned Magnetic Field Effect on Radiative Bioconvection Flow Past a Vertical Plate with Thermophoresis and Brownian Motion

This study covers a numerical investigation of gyrotactic microorganisms contained MHD flow over a vertical plate bearing thermal radiation, thermophoresis, Brownian motion, chemical reaction and inclined magnetic field effects. With the assistance of similarity transforms, the derived governed equations are transformed as set of ODEs and solved numerically by R-K and Newton’s methods. Graphs are exhibited and explained for various parameters of interest. For engineering interest, we mainly talked about the Skin friction coefficient, reduced Sherwood, Nusselt numbers and density of motile microorganisms. We noticed a rise in the heat transfer rate of motile microorganisms for rising values of the thermophoresis and Brownian motion parameters. Increasing values of the aligned angle hikes the drag force.

Effects of aligned magnetic field and CNTs in two different base fluids over a moving slip surface

In this article, combine effects of the inclined magnetic field and velocity slip conditions are analyzed for nanofluid flow over a moving over a flat surface. Two different kind of Carbon nanotubes are also incorporated within the base fluid, namely: Single wall carbon nanotubes (SWCNTs) and multiple wall carbon nanotubes (MWCNTs). Rheological characteristics of CNTs-Water and CNTs-Kerosene are studied under the influence of inclined applied magnetic field between 0≤γ≤π/2. Close form solutions are obtained for both momentum and energy equation in the form of hypergeometric function. The core objective of aligned angle magnetic field is to use the governing magnetic intensity on the nanofluid and to extend the appraisals of aligned angle of the magnetic field produce to upgrade the local skin friction and decline the local Nusselt number. Significant consequences of inclined magnetic field with rest of the physical parameters including Hartmann number, velocity slip and solid volume fraction nanoparticles are presented and analyzed via numerical and graphical illustrations. It is found that SWCNTs-kerosene depicts the high friction and heat transfer rate at the surface as compare to the rest of the mixtures.

Effects of inclined Lorentz forces on boundary layer flow of Sisko fluid over a radially stretching sheet with radiative heat transfer

The inclined magnetic field effect on the boundary layer flow of Sisko fluid model over a radially stretching sheet is investigated. The effects of viscous dissipation and thermal radiations are also taken into account. It is assumed that the magnetic field is applied with an inclined angle γ which varies from \(0^{\circ}\) to \(90^{\circ }\). The suitable transformations are used to convert the governing partial differential equations into a set of non-linear coupled ordinary differential equations. The numerical solution of the governing problem is obtained by using fourth-order Runge–Kutta method with shooting technique. The obtained results for velocity and temperature are expressed through graphs against various emerging physical parameters such as magnetic parameter, angle of inclination, Prandtl number, radiation number, Eckert number and material parameter of the Sisko fluid for different values of power law index. It is found that increasing value of aligned angle strengthens the magnetic field and decreases the velocity profile and enhances the heat transfer rate. Further, the numerical values are given in tabular form for the local skin friction coefficient and the local Nusselt number.

Aligned magnetic field effects on water based metallic nanoparticles over a stretching sheet with PST and thermal radiation effects

This study deals the simultaneous effects of inclined magnetic field and prescribed surface temperature (PST) on boundary layer flow of nanofluid over a stretching sheet. In order to make this mechanism more feasible, we have further considered the velocity slip and thermal radiation effects. Moreover, this perusal is made to consider the two kinds of nanofluid namely: Cu-water and Al2O3-water. Inclined magnetic field is utilized to accompanying an aligned angle that varies from 0 to π/2. The exact solutions are acquired from the transformed non-dimensional momentum and energy equations in the form of confluent hypergeometric function. Lorentz forces and aligned magnetic field depicts the significant effects on nanofluid. We found that, due to the increase in the aligned angle provides the enhancement in local skin friction coefficient and a reduction in the local Nusselt number. The combined impacts of inclined magnetic field with other emerging parameters such as velocity slip, thermal radiation and nanoparticles volume fraction on velocity, temperature, local Nusselt number and skin friction coefficient are examined. Flow behavior of nanofluid is also determined via stream lines pattern.

Effect of frictional heating on radiative ferrofluid flow over a slendering stretching sheet with aligned magnetic field

The pivotal objective of this paper is to look into the flow of ferrofluids past a variable thickness surface with velocity slip. Magnetite (Fe3O4 nanoparticles are embedded to the regular fluid. The occurrence of frictional heating in the flow is also taken into account. So the flow equations will be coupled and nonlinear. These are remodelled into dimensionless form with the support of suitable transmutations. The solution of the transformed equations is determined with the support of an effective Runge-Kutta (RK)-based shooting technique. Ultimately, the effects of a few flow modulating quantities on fluid motion and heat transport were explored through plots which are procured using the MATLAB tool box. Owing to the engineering applications, we also calculated the friction factor and the heat transfer coefficient for the influencing parameters. The results are presented comparatively for both regular fluid (water) and water-based ferrofluid. This study enables us to deduce that inflation in the aligned angle or surface thickness reduces the fluid velocity. The radiation and dissipation parameters are capable of providing heat energy to the flow.