Presence Of Lorentz Force Research Articles

Entropy generation of thermophysical properties on heat and mass transfer pulsatile flow of non-Newtonian nanofluid

Purpose The purpose of this study is to investigate the effects of entropy generation of some embedded thermophysical properties on heat and mass transfer of pulsatile flow of non-Newtonian nanofluid flows between two porous parallel plates in the presence of Lorentz force are taken into account in this research. Design/methodology/approach The governing partial differential equations (PDEs) were nondimensionalized using suitable nondimensional quantities to transform the PDEs into a system of coupled nonlinear PDEs. The resulting equations are solved using the spectral relaxation method due to the effectiveness and accuracy of the method. The obtained velocity and temperature profiles are used to compute the entropy generation rate and Bejan number. The influence of various flow parameters on the velocity, temperature, entropy generation rate and Bejan number are discussed graphically. Findings The results indicate that the energy losses can be minimized in the system by choosing appropriate values for pertinent parameters; when thermal conductivity is increasing, this leads to the depreciation of entropy generation, and while this increment in thermal conductivity appreciates the Bejan number, the Eckert number on entropy generation and Bejan number, the graph shows that each time of increase in Eckert will lead to rising of entropy generation while this increase shows a reduction in Bejan number. To shed more light, these results were further demonstrated graphically. The current research was very well supported by prior literature works. Originality/value All results are presented graphically, and the results in this article are anticipated to be helpful in the area of engineering.

Effects of some embedded thermophysical properties on heat and mass transfer using erying powell model non-Newtonian nanofluid, between two poropus parallel plates

The effects of couple stress on the heat and mass transfer of pulsatile using Erying powel model non-Newtonian nanofluid flows between two porous parallel plates in the presence of Lorentz force are elucidated. The governing partial differential equations (PDEs) were non-dimensionalized using suitable non-dimensional quantities to transform the PDEs into a system of coupled non-linear partial differential equations (PDEs). The resulting equations are solved using the spectral relaxation method (SRM). The obtained results were plotted for concentration, temperature, and velocity and analyzed using some pertinent embedded parameters and physical quantities of scientific and engineering interest. In order to shed more light, these results were further demonstrated graphically. and in tabular forms.

Nanomaterial heat transfer within thermal porous system in presence of Lorentz force

A curved enclosure in attendance of MHD was evaluated in this article. Both outer cold and inner hot surfaces have curved shapes which boosts the convective rate. The impact of MHD in equations has been applied and there is one negative term is x direction if horizontal magnetic fields have been applied. Presence of such a field leads to generation of Lorentz force which prevents the nanofluid from moving faster. Such reduction in velocity with growth of Ha makes Nu decrease. Adding nanoparticles with greater “m” and φ can increase the convective flow. When Ra = 700, dispersing nano-powders can enhance the Nu in existence of MHD about 41.9%. When Ra = 150, Nu can improve about 12.01% if “m” is enhanced. Nu decreases around 40.1% with growth of Ha while it increases about 43.36% in existence of greater Ra.

Investigation of nanofluid physical behavior inside porous container utilizing mathematical numerical method

The numerical method for modeling the behavior of nanofluid within the closed container in the presence of Lorentz force was dissected in this paper. The working fluid contains water and two shapes of nanoparticles. The porous geometry has one sinusoidal inner surface which faces constant heat flux. Influences of gravity and vertical Lorentz was complicated in modeling and momentum equations have been edited with adding related source terms. The precision of code was tested and respectable agreement has been obtained. The influences of loading nanomaterial and strength of two important forces (gravity and buoyancy) have been analyzed in the result section. Loading nanoparticles leads to a growth of Nu around 26.99% and 41.04% when [Formula: see text] and 15. Increasing buoyancy leads to augment of Nu about 44.34% and 1.46% in the absence and existence of Ha. Applying Lorentz force makes Nu to decrease about 40.39% when [Formula: see text].

Thermal and solute aspects among two viscosity models in synovial fluid inserting suspension of tri and hybrid nanomaterial using finite element procedure

Inclusion of nanoparticles boosts thermal performance and is essential for thermal transport. The current investigation has been made to conduct research on heat mass transport in synovial material with the mixing of hybrid and tri-hybrid comprising variable viscosity past over a heated surface having constant density and a steady environment. The conservation laws have been considered in the presence of Lorentz force, heat generation/absorption, modified heat and mass fluxes together with chemical reaction. The mathematical model is developed in Cartesian coordinate in the form of coupled partial differential equation (PDEs). The derived PDEs are simplified by a boundary layer approach (BLA) and reduced PDEs have been converted into ordinary differential equation (ODEs) using scaling group Similarity transformation. The converted ODEs are highly nonlinear and have been solved numerically by finite elements scheme (FES). The used scheme is effective for nonlinear problem and can be frequently utilized to tackle nonlinear problems arising in mathematical physics.

Application of the successive over relaxation method for analyzing the dusty flow over a surface subject to convective boundary condition

Heat transport features of a dusty fluid flow within a resistive porous medium are numerically interpreted under the magnetohydrodynamic environment. Fluid and dust phase characteristics are overlooked against the preeminent parameters. The main concern, in this work, is to analyze how much the resistive porous media affects the dusty flow in the presence of Lorentz force. The use of convection boundary conditions will aid attain the desired heat transfer rate in engineering applications. The nonlinear partial differential equations governing the fluid and dust phase are transmuted into a system of coupled and highly nonlinear ordinary differential equations which are first discretized using central differences, and then tackled numerically using the successive over-relaxation (SOR) method. This technique creates an effective way to solve complex dynamical problems comprising highly nonlinear-coupled differential equations. The flow features of the concerned problem are explored for different parameters such as the magnetic field, the porosity of the medium, the relative density of the two phases, ratio of free stream velocity, specific heat capacity ratio of the fluid to the dust phase as well as Prandtl number. Our results may be helpful to understand the dusty airflow during storms, mud particles in canals, ponds, and rivers.

Significance of Ramped Temperature in the Dynamics of Unsteady Viscoelastic Fluid Subjected to Lorentz Force

Viscoelastic fluids, such as polymers, paints, and DNA suspensions, are almost everywhere and very useful in the industry. This article aims to study the significance of ramped temperature in the dynamics of viscoelastic fluid. Magnetohydrodynamic (MHD) effect is considered in the presence of Lorentz force. The flow is considered in a porous medium using generalized Darcy’s law. Heat transfers through convection, and the fluid near the plate takes heat in a ramped nature. Instead of the classical fluid model which has certain limitations, a generalized model is considered with fractional derivatives of the Atangana–Baleanu type. The well-known technique of Laplace transform was adopted to obtain the solutions which are displayed in various plots with detailed discussion analysis. From the graphical analysis, it is worth noting that the Atangana–Baleanu fractional model shows a good memory effect on the dynamics of the viscoelastic fluid as compared to its classical form.

Numerically simulated behavior of radiative Fe3O4 and multi-walled carbon nanotube hybrid nanoparticle flow in presence of Lorentz force

Numerically simulated behavior of radiative Fe3O4 and multi-walled carbon nanotube hybrid nanoparticle flow in presence of Lorentz force

A coarse-grid projection method for accelerating incompressible MHD flow simulations

Coarse grid projection (CGP) is a multiresolution technique for accelerating numerical calculations associated with a set of nonlinear evolutionary equations along with stiff Poisson’s equations. In this article, we use CGP for the first time to speed up incompressible magnetohydrodynamics (MHD) flow simulations. Accordingly, we solve the nonlinear advection–diffusion equation on a fine mesh, while we execute the electric potential Poisson equation on the corresponding coarsened mesh. Mapping operators connect two grids together. A pressure correction scheme is used to enforce the incompressibility constrain. The study of incompressible flow past a circular cylinder in the presence of Lorentz force is selected as a benchmark problem with a fixed Reynolds number but various Stuart numbers. We consider two different situations. First, we only apply CGP to the electric potential Poisson equation. Second, we apply CGP to the pressure Poisson equation as well. The maximum speed-up factors achieved here are approximately 3 and 23, respectively, for the first and second situations. For the both situations, we examine the accuracy of velocity and vorticity fields as well as the lift and drag coefficients. In general, the results obtained by CGP are in an excellent to reasonable range of accuracy. The CGP results are significantly more accurate compared to the numerical simulations of the advection–diffusion and electric potential Poisson equations on pure coarse scale grids.

Second Law Analysis of Magneto Radiative GO-MoS2/H2O–(CH2OH)2 Hybrid Nanofluid

Entropy Generation Optimization (EGO) attained huge interest of scientists and researchers due to its numerous applications comprised in mechanical engineering, air conditioners, heat engines, thermal machines, heat exchange, refrigerators, heat pumps and substance mixing etc. Therefore, the study of radiative hybrid nanofluid (GO-MoS2/C2H6O2–H2O) and the conventional nanofluid (MoS2/C2H6O2–H2O) is conducted in the presence of Lorentz forces. The flow configuration is modeled between the parallel rotating plates in which the lower plate is permeable. The models which govern the flow in rotating system are solved numerically over the domain of interest and furnished the results for the temperature, entropy generation and thermophysical characteristics of the hybrid as well as conventional nanofluids, respectively. It is examined that the thermal profile intensifies against stronger thermal radiations and magnetic field. The surface of the plate is heated due to the imposed thermal radiations and magnetic field which cause the increment in the temperature. It is also observed that the temperature declines against more rotating plates. Further, the entropy production increases for more dissipative effects and declines against more magnetized fluid. Thermal conductivities of the hybrid nanofluid enhances promptly in comparison with regular liquid therefore, under consideration hybrid nanofluid is reliable for the heat transfer. Moreover, dominating thermal transport is perceived for the hybrid nanofluid which showed that hybrid suspension GO-MoS2/C2H6O2–H2O is better for industrial, engineering and technological uses.

Significance of temperature-dependent viscosity and thermal conductivity of Walter's B nanoliquid when sinusodal wall and motile microorganisms density are significant

The progressed thermal features of nanoparticles in presence of Lorentz force, chemical reaction and activation energy utilizes novel applications various engineering and industrial processes, thermal engineering and medical sciences. On this end, current continuation aims to address the temperature dependent viscosity and variable thermal consequences in order to inspect the bioconvection aspects in non-Newtonian nanofluid over periodically moving surface. The rheological consequences for non-Newtonian fluid are addressed by using Walter's B liquid. The activation energy effects are also tested to improve the concentration of nano-materials more effectively. The Brownian motion and thermophoretic diffusion significances are incorporated explicitly with alliance of Buongiorno's mathematical model. Although some studies are already reported for nanofluid with constant viscosity but consideration of temperature dependent viscosity for bioconvection of non-Newtonian nanoparticles still need to be attention. Unlike typical contributions, here the flow is originated by periodically accelerated configuration. The appropriate variables enable to develop the non-dimensional for which the employed analytical simulations are carried out via homotopic procedure. The flow parameters are physically inspected with applications of various curves. The numerical iterative values are compiled for local Nusselt number, local motile density number and local Sherwood expressions. The results reveal that a reduced velocity profile is augmented to be the viscosity parameter. The assumption of variable thermal conductivity and temperature dependent viscosity are more effective for enrichment of nanoparticles temperature. It is also concluded that the microorganism for nanofluid increases for buoyancy ratio constant and bioconvection Rayleigh number.

Influence of Heat Generation/Absorption on Mixed Convection Flow Behaviour in the Presence of Lorentz Forces in a Vertical Micro Circular Duct Having Time Periodic Boundary Conditions: Steady Periodic Regime

The problem of mixed convection flow of a heat generating/absorbing fluid in the presence existence of Lorentz forces in a vertical micro circular subjected to a periodic sinusoidal temperature change at the surface has been studied taking the first-order slip and jump effects into consideration. The research analysis is carried out by considering a fully developed parallel flow and steady periodic regime. The governing equations, together with the constraint equations which arise from the definition of mean velocity and temperature, are written in a dimensionless form and mapped into equations in the complex domain. One obtains two independent boundary value problems, which provide the mean value and the oscillating term of the velocity and temperature distributions. These boundary value problems are solved analytically. A parametric study of some of the physical parameters involved in the problem is conducted. The results of this research revealed that the magnetic field has a damping impact on the flow and results in decreases in fluid velocity for both air and water. Furthermore, the presence of the heat generation parameter is seen to enhance the temperature distribution and this is reflected as an increase in the magnitude of the oscillation dimensionless velocity, whereas in the presence of heat absorption a reversed trend occurs.

Numerical simulation of a nonlinear coupled differential system describing a convective flow of Casson gold–blood nanofluid through a stretched rotating rigid disk in the presence of Lorentz forces and nonlinear thermal radiation

Extensive analysis has recently been presented on the applications of nanofluids in heat transfer developments. The primary concern of this work is to excogitate the flow features of blood flow with the inclusion of gold plated nanoparticles. In this regard, the Casson fluid model was adopted to simulate the transportation of blood flow. The momentum features of flowing fluid are divulged by incorporating magnetization and porosity aspects whereas thermal attributes of concerned flow are anticipated under nonlinearized radiating thermal flux. Formulated governing expressions are transmuted into the system of the nonlinearized ordinary differential structure by implementing appropriate conversion. The solution is headed by implementing an efficient build in routine renowned as bvp4c based on the finite differencing. The impacts of the involved parameters on the resulting dimensionless profiles are discussed thoroughly. The results indicating that the velocity in radial direction declines with augmenting the nanoparticle volume fraction, while the velocity in the azimuthal direction and the temperature upsurge. Besides, the velocities in the radial and azimuthal directions augment due to rotation parameter and the temperature shrinks.

Study of EDL phenomenon in Peristaltic pumping of a Phan-Thien-Tanner Fluid through asymmetric channel

This paper is mainly attained to examine the electric double layer (EDL) phenomena and rheological effects on peristaltic pumping through asymmetric microchannel in presence of Lorentz force. To examine the electroosmosis mechanism, Poisson-Boltzmann equation is considered. To describe the rheological behavior of the fluids, a Phan-Thien-Tanner model is taken into account. The governing equations are simplified by using scaling analysis with low Reynolds number and large wavelength approximations. The set of non-linear partial differential equations are solved by regular perturbation technique to find out the series solutions for stream function, axial velocity and pressure gradient. Furthermore, the shear stress at the channel wall is derived. The graphical results for velocity, pressure gradient, stream lines and shear stress are illustrated using the in-house code written in Mathematica software. It is revealed that velocity field, shear stress and trapping phenomenon are strongly altered with EDL thickness, electric and magnetic fields. It is further concluded that rheological parameter i.e. Weissenberg number significantly affects the physical mechanisms. This model can be applicable in various complex systems where the rheological fluids can be transported by novel microfluidics peristaltic pumps.

Visco-elastic behavior of articular cartilage under applied magnetic field and strain-dependent permeability

In the present article, we investigate the biomechanical response of a fiber reinforced solid matrix (soft tissue) saturated with an electrically conducting fluid. A constant magnetic field was exposed to the binary mixture of fluid and deformable porous solid. The governing mechanism of multiphasic deformation was based on the loading imposed at the rigid bony interface. The fluid flow through the cartilage network depends upon the rate of applied compression and strain-dependent permeability of the solid matrix. The components of the mixture were intrinsically incompressible; however, in the derivation of governing dynamics, the visco-elastic behavior of the solid and an interstitial fluid was developed. The continuum mixture theory was employed in modeling solid deformation and local fluid pressure. We incorporated strain-dependent permeability in the governing equations of binary mixture that was found in an early experimental study. The governing non-linear coupled system of partial differential equations was developed for the solid deformation and fluid pressure in the presence of Lorentz forces. In the case of strain-dependent permeability, a numerical solution is computed using the method of lines (MOL), whereas, the exact solution is provided when permeability is kept constant. Graphical results highlight the influence of various physical parameters on both solid displacement and fluid pressure.

Generalized differential quadrature analysis of unsteady three‐dimensional MHD radiating dissipative Casson fluid conveying tiny particles

AbstractIt is worth remarking that little is known about generalized differential quadrature analysis of three‐dimensional flow of non‐Newtonian Casson fluid in the presence of Lorentz force, thermal radiation, haphazard motion of tiny particles, thermomigration of these tiny particles due to temperature gradient, heat source, significant conversion of kinetic energy into internal energy, first‐order chemical reaction, convectively heated horizontal wall, and zero nanoparticles mass flux at the stretching surface. The revised form of Buongiorno's nanofluid model accounted for significant influences of Brownian motion and thermophoresis. The similarity solution was complemented with a powerful collocation procedure based on the generalized differential quadrature method and Newton–Raphson iterative scheme to achieve accuracy and convergent outcomes. The numerical effects disclose that the Casson nanofluid parameter slows down the axial velocities in both directions. Also, the unsteadiness parameter tends to decline generally the temperature throughout the medium and decrease particularly the concentration profile away from the stretching surface. These examinations are applicable in the field of biomechanics, polymer processing, and for characterizing the cement slurries.

Numerical Study of a Liquid Metal Oscillating inside a Pore in the Presence of Lorentz and Capillary Forces

In order to ensure stable power exhaust and to protect the walls of fusion reactors, liquid metals that are fed to the wall surface through a capillary porous system (CPS) are considered as alternative plasma-facing components (PFCs). However, operational issues like drop ejection and plasma contamination may arise. In this study, the unsteady flow of a liquid metal inside a single pore of the CPS in the presence of Lorentz forces is investigated. A numerical solution is performed via the finite element methodology coupled with elliptic mesh generation. A critical magnetic number is found (Bondm = 4.5) below which the flow after a few oscillations reaches a steady state with mild rotational patterns. Above this threshold, the interface exhibits saturated oscillations. As the Lorentz force is further increased, Bondm > 5.8, a Rayleigh–Taylor instability develops as the interface is accelerated under the influence of the increased magnetic pressure and a finite time singularity is captured. It is conjectured that eventually, drop ejection will take place that will disrupt cohesion of the interface and contaminate the surrounding medium. Finally, the dynamic response of different operating fluids is investigated, e.g., gallium, and the stabilizing effect of increased electrical conductivity and surface tension is demonstrated.

Comparative Analysis Between Three-Dimensional Flow of Water Conveying Alumina Nanoparticles and Water Conveying Alumina–Iron(III) Oxide Nanoparticles in the Presence of Lorentz Force

In the manufacturing companies of the hybrid-powered engine, little is known on the significance of adding iron(III) oxide nanoparticles to an existing alumina–water nanofluid in the presence of Lorentz force. This study presents the three-dimensional flow of water conveying alumina nanoparticles and water conveying alumina/iron(III) oxide nanoparticles within the thin boundary layer formed on a bidirectional linearly stretchable surface. The governing equation that models the transport phenomena was non-dimensionalized and parameterized using the suitable similarity variables. The boundary value problem of the corresponding ordinary differential equation was solved numerically. The technique of slope of the linear regression through the data point was adopted to quantify the observed results. The results of this study show that the addition of Fe3O4 nanoparticles to Al2O3–water nanofluid slightly reduces the motion of the flow at all points from the wall to the free stream. However, the temperature distribution across the flow may be improved. The two components of velocity for the motion of both fluids along x-direction and y-direction increase and decreases across the fluid domain, respectively, when Lorentz force is minimum and maximum due to the significance of stretching rate that is predominant along y-direction. When the stretching rate is small, the maximum velocity along x-direction is ascertained in the flow of nanofluid. Skin friction coefficients in the flow along both directions decrease with both Lorentz force and stretching rate.

Simultaneous solutions for first order and second order slips on micropolar fluid flow across a convective surface in the presence of Lorentz force and variable heat source/sink

This report presents the flow and heat transfer characteristics of MHD micropolar fluid due to the stretching of a surface with second order velocity slip. The influence of nonlinear radiation and irregular heat source/sink are anticipated. Simultaneous solutions are presented for first and second-order velocity slips. The PDEs which govern the flow have been transformed as ODEs by the choice of suitable similarity transformations. The transformed nonlinear ODEs are converted into linear by shooting method then solved numerically by fourth-order Runge-Kutta method. Graphs are drowned to discern the effect of varied nondimensional parameters on the flow fields (velocity, microrotation, and temperature). Along with them the coefficients of Skin friction, couple stress, and local Nussel number are also anticipated and portrayed with the support of the table. The results unveil that the non-uniform heat source/sink and non-linear radiation parameters plays a key role in the heat transfer performance. Also, second-order slip velocity causes strengthen in the distribution of velocity but a reduction in the distribution of temperature is perceived.

Stability analysis for multiple solutions of boundary layer flow towards a shrinking sheet: Analytical solution by using least square method

The Purpose:In some cases, most of the boundary value problems contain multiple solutions in which one of the solution is stable or physical reliable and other solutions are unstable. In this study, the problem of hydromagnetic flow due to shrinking sheet is considered and calculated dual solutions against velocity ratio parameter in case of shrinking sheet. A stability analysis is performed for the checking, which solution is stable. The main materials and methods used:Initially, due to more than one independent variable, the flow is governed by partial differential equations (PDEs). For simplicity the conversion of these PDEs were made in form of ODEs (ordinary differential equations) and solved analytically by using weighted residual method named as least square method. The resulting nonlinear system of equations is linearized by using Newton method (Burden and Faires, 1991). For the accuracy of this method, a comparison is made with the previous published work (Wang, 2008). The algorithm of least square method is constructed in Mathematica software and is very easy to apply as compare to analytical method namely: homotopy analysis method. In case of shrinking sheet there exists more than one solution. To check which solution is physical reliable or stable and unstable, a present problem is converted into time dependent problem and then stability analysis is performed and BVP4c method is used for calculating the eigenvalues. The main results obtained:In case of shrinking sheet there exists dual solutions and dual solutions are calculated for some values of velocity ratio parameter λand magnetic parameterM by using least square method. The range of dual solutions is shown by plotting the graphs of skin friction coefficient and local Nusselt number. After performing the stability analysis, the smallest eigenvalues are calculated for various values of λ and M. The main conclusions of the work:It is observed that positive eigenvalue corresponds to stable solution or physical reliable i.e. the disturbance in the solution decay initially and negative eigenvalue corresponds to unstable solution i.e. it produces initial growth of disturbance. It is also observed that eigenvalues become higher in the presence of Lorentz force.