The flow of ferromagnetic nanofluid over an extending surface under the effect of operative Prandtl model: A numerical study

The purpose of this research is to investigate the impact of magnetic dipole on the flow of nanofluids over the extending surface. This study is based on steady and non-porous medium with no-slip conditions. Two types of nanofluids are examined under the effect of operative Prandtl model and thermal convection. The experimental results comprising the spreading of [Formula: see text] and [Formula: see text] have been used from the existing literature with and without the magnetic dipole. The basic governing equations are transformed using the transformation into a set of nonlinear differential equations for both categories of nanofluids. The fourth-order Runge Kutta numerical scheme has been executed to solve the nonlinear ordinary differential equations. The impacts of the embedded parameters such as nanofluid volume fraction, Prandtl number, and dissipation term have been examined and discussed. The important features of the study such as Curie temperature, skin friction, and local Nusselt number are also analyzed physically and numerically. (1) It is perceived that ethylene glycol–based nanofluids are more effective due to their strong thermophysical properties compared to water-based nanofluids. By increasing the volume fraction [Formula: see text], the temperature of the nanofluids [Formula: see text] and [Formula: see text] is increased, and this is due to the fact that nanofluids exhibit high thermal conductivity compared to ordinary heat transfer fluids. (2) It is observed from the obtained results that the magnetic dipole is usually used to control the turbulence behavior of the fluid flow.

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The Impact of Nanoparticles Due to Applied Magnetic Dipole in Micropolar Fluid Flow Using the Finite Element Method

Symmetry ◽

10.3390/sym12040520 ◽

2020 ◽

Vol 12 (4) ◽

pp. 520 ◽

Cited By ~ 1

Author(s):

Liaqat Ali ◽

Xiaomin Liu ◽

Bagh Ali ◽

Saima Mujeed ◽

Sohaib Abdal ◽

...

Keyword(s):

Heat Transfer ◽

Finite Element Method ◽

Finite Element ◽

Differential Equations ◽

Magnetic Dipole ◽

Thermal Stratification ◽

Volume Fraction ◽

Numerical Technique ◽

The Impact ◽

Element Method

The present work examines the effect of different magnetic nanoparticles and the heat transfer phenomena over the stretching sheet with thermal stratification and slips effect. The mixture of water (H 2 O) and ethylene glycol (C 2 H 6 O 2 ) is used as base fluid whereas the paramagnetic, diamagnetic, and ferromagnetic ferrites are taken as nanoparticles. In the presence of ferrite nanoparticles, the magnetic dipole has a significant effect in controlling the rate of heat transfer and the thermal boundary layers. By using suitable similarity transformations, the system of partial differential equations is transformed into nonlinear ordinary differential equations. The numerical solution of resulting equations is found out by using the variational finite element method. The effect of numerous emerging parameters on velocity, temperature, and micro-rotation velocity are represented graphically and analyzed numerically. It has been noticed that comparatively the diamagnetic ferrites have gained maximum thermal conductivity relative to the other nanoparticles. It was also observed that the thermal conduction of nanoparticles increases with the variation of volume fraction. Moreover, with increasing values of thermal stratification the thermal boundary layer thickness decreases and the heat transfer rate increases at the surface. Furthermore, the validation of code and the accuracy of the numerical technique has been confirmed by the assessment of current results with earlier studies.

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Numerical study of heat transfer and Hall current impact on peristaltic propulsion of particle-fluid suspension with compliant wall properties

Modern Physics Letters B ◽

10.1142/s0217984919504396 ◽

2019 ◽

Vol 33 (35) ◽

pp. 1950439 ◽

Cited By ~ 93

Author(s):

M. M. Bhatti ◽

Rahmat Ellahi ◽

A. Zeeshan ◽

M. Marin ◽

N. Ijaz

Keyword(s):

Heat Transfer ◽

Volume Fraction ◽

Hall Current ◽

Numerical Study ◽

Nonlinear Differential Equations ◽

Particle Volume Fraction ◽

Mathematical Formulation ◽

Solid Particles ◽

Particle Volume ◽

The Impact

In this paper, the effects of heat transfer and Hall current on the sinusoidal motion of solid particles through a planar channel has been discussed. The walls of the channel are considered as compliant under the effects of magnetohydrodynamics. The mathematical formulation has been performed using energy equation, momentum equation, and Ohm’s law. The modeled equations are further modified by taking the assumption of a zero Reynolds number and long wavelength. Numerical shooting technique has been employed to solve the nonlinear differential equations. The impact of all the emerging parameters such as wall rigidity, wall tension, mass characterization, Hall parameter, Hartmann number, Weissenberg number, particle volume fraction, Prandtl number, and Eckert number, respectively. Particularly, we discussed their effects on velocity and temperature profile.

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Numerical Study of Hydrodynamic Impact on Bubbly Water

Volume 7: Ocean Engineering ◽

10.1115/omae2015-41889 ◽

2015 ◽

Cited By ~ 1

Author(s):

Mehdi Elhimer ◽

Aboulghit El Malki Alaoui ◽

Kilian Croci ◽

Céline Gabillet ◽

Nicolas Jacques

Keyword(s):

Volume Fraction ◽

Numerical Study ◽

Numerical Data ◽

Void Volume Fraction ◽

Bubbly Liquid ◽

Impact Loads ◽

Hydrodynamic Impact ◽

Physical Mechanisms ◽

The Impact ◽

The Relationship

The phenomenon of slamming on a bubbly liquid has many occurrences in marine and costal engineering. However, experimental or numerical data on the effect of the presence of gas bubbles within the liquid on the impact loads are scarce and the related physical mechanisms are poorly understood. The aim of the present paper is to study numerically the relationship between the void volume fraction and the impact loads. For that purpose, numerical simulations of the impact of a cone on bubbly water have been performed using the finite element code ABAQUS/Explicit. The present results show the diminution of the impact loads with the increase of the void fraction. This effect appears to be related to the high compressibility of the liquid-gas mixture.

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Cumulative Impact of Micropolar Fluid and Porosity on MHD Channel Flow: A Numerical Study

Coatings ◽

10.3390/coatings12010093 ◽

2022 ◽

Vol 12 (1) ◽

pp. 93

Author(s):

Kottakkaran Sooppy Nisar ◽

Aftab Ahmed Faridi ◽

Sohail Ahmad ◽

Nargis Khan ◽

Kashif Ali ◽

...

Keyword(s):

Heat Transfer ◽

Chemical Reaction ◽

Micropolar Fluid ◽

Numerical Study ◽

Nonlinear Differential Equations ◽

X Rays ◽

Cumulative Impact ◽

Transfer Rates ◽

Mass And Heat Transfer ◽

The Impact

The mass and heat transfer magnetohydrodynamic (MHD) flows have a substantial use in heat exchangers, electromagnetic casting, X-rays, the cooling of nuclear reactors, mass transportation, magnetic drug treatment, energy systems, fiber coating, etc. The present work numerically explores the mass and heat transportation flow of MHD micropolar fluid with the consideration of a chemical reaction. The flow is taken between the walls of a permeable channel. The quasi-linearization technique is utilized to solve the complex dynamical coupled and nonlinear differential equations. The consequences of the preeminent parameters are portrayed via graphs and tables. A tabular and graphical comparison evidently reveals a correlation of our results with the existing ones. A strong deceleration is found in the concentration due to the effect of a chemical reaction. Furthermore, the impact of the magnetic field force is to devaluate the mass and heat transfer rates not only at the lower but at the upper channel walls, likewise.

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Analysis of Magnetic Properties of Nano-Particles Due to a Magnetic Dipole in Micropolar Fluid Flow over a Stretching Sheet

Coatings ◽

10.3390/coatings10020170 ◽

2020 ◽

Vol 10 (2) ◽

pp. 170 ◽

Cited By ~ 7

Author(s):

Liaqat Ali ◽

Xiaomin Liu ◽

Bagh Ali ◽

Saima Mujeed ◽

Sohaib Abdal ◽

...

Keyword(s):

Heat Transfer ◽

Finite Element ◽

Nusselt Number ◽

Fluid Flow ◽

Differential Equations ◽

Magnetic Dipole ◽

Stretching Sheet ◽

Nano Particles ◽

Boundary Parameter ◽

The Impact

This article explores the impact of a magnetic dipole on the heat transfer phenomena of different nano-particles Fe (ferromagnetic) and Fe3O4 (Ferrimagnetic) dispersed in a base fluid ( 60 % water + 40 % ethylene glycol) on micro-polar fluid flow over a stretching sheet. A magnetic dipole in the presence of the ferrities of nano-particles plays an important role in controlling the thermal and momentum boundary layers. The use of magnetic nano-particles is to control the flow and heat transfer process through an external magnetic field. The governing system of partial differential equations is transformed into a system of coupled nonlinear ordinary differential equations by using appropriate similarity variables, and the transformed equations are then solved numerically by using a variational finite element method. The impact of different physical parameters on the velocity, the temperature, the Nusselt number, and the skin friction coefficient is shown. The velocity profile decreases in the order Fe (ferromagnetic fluid) and Fe3O4 (ferrimagnetic fluid). Furthermore, it was observed that the Nusselt number is decreasing with the increasing values of boundary parameter ( δ ) , while there is controversy with respect to the increasing values of radiation parameter ( N ) . Additionally, it was observed that the ferromagnetic case gained maximum thermal conductivity, as compared to ferrimagnetic case. In the end, the convergence of the finite element solution was observed; the calculations were found by reducing the mesh size.

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Numerical Study of High Velocity Impact onto MMC/Ceramic Layered Systems

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.715.210 ◽

2016 ◽

Vol 715 ◽

pp. 210-215

Author(s):

Seung Hwan Lee ◽

Minh Lee

Keyword(s):

Mild Steel ◽

Ceramic Tile ◽

Volume Fraction ◽

Numerical Study ◽

Tungsten Alloy ◽

Layered Systems ◽

Depth Of Penetration ◽

Ballistic Performance ◽

Long Rod ◽

The Impact

Metal Matrix Composites (MMCs) can be applied to military applications due to the light weight and the ballistic performance. In this study, a numerical simulation has been performed for the penetration of a long-rod penetrator into MMC/Ceramic layered systems. The impact velocity is 1.5km/s and the length to diameter (L/D) ratio is 10.6. First, the ballistic performances of each candidate materials are examined by doing the semi-infinite target simulation to estimate the depth of penetration (DOP) data. The materials included in this study are four (tungsten alloy, mild steel, SiC, MMC. The MMC materials are SiC/Al7075 (volume fraction around 45%). For a reference data, the impact simulation into mild-steel target only was also carried out. Finally, the main simulation is performed by varying the position of ceramic tile at three types of the thickness of ceramic tile. The residual velocity, residual mass and residual kinetic energy of the long-rod are obtained from the simulation. Based on these predicted values, the optimum system of the layered plate has been estimated.

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Investigating Jeffery-Hamel flow with high magnetic field and nanoparticle by HPM and AGM

Open Engineering ◽

10.2478/s13531-013-0175-9 ◽

2014 ◽

Vol 4 (4) ◽

Cited By ~ 5

Author(s):

A. Rostami ◽

M. Akbari ◽

D. Ganji ◽

S. Heydari

Keyword(s):

Magnetic Field ◽

Differential Equations ◽

Homotopy Perturbation Method ◽

Volume Fraction ◽

Nonlinear Differential Equations ◽

Reynolds Numbers ◽

Solution Procedure ◽

Algebraic Equations ◽

Divergent Channel ◽

Mathematical Operations

AbstractIn this study, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using two powerful analytical methods, Homotopy Perturbation Method (HPM) and a simple and innovative approach which we have named it Akbari-Ganji’s Method(AGM). Comparisons have been made between HPM, AGM and Numerical Method and the acquired results show that these methods have high accuracy for different values of α, Hartmann numbers, and Reynolds numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.It is necessary to represent some of the advantages of choosing the new method, AGM, for solving nonlinear differential equations as follows: AGM is a very suitable computational process and is applicable for solving various nonlinear differential equations. Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration, the solution of the problem can be obtained very simply and easily. It is notable that this solution procedure, AGM, can help students with intermediate mathematical knowledge to solve a broad range of complicated nonlinear differential equations.

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Numerical Study of Lorentz Force Interaction with Micro Structure in Channel Flow

Energies ◽

10.3390/en14144286 ◽

2021 ◽

Vol 14 (14) ◽

pp. 4286

Author(s):

Shabbir Ahmad ◽

Kashif Ali ◽

Sohail Ahmad ◽

Jianchao Cai

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Viscous Dissipation ◽

Numerical Study ◽

Nonlinear Differential Equations ◽

Thermal Control ◽

Shear Stresses ◽

Fluid Temperature ◽

X Rays ◽

Micro Particles

The heat transfer Magnetohydrodynamics flows have been potentially used to enhance the thermal characteristics of several systems such as heat exchangers, electromagnetic casting, adjusting blood flow, X-rays, magnetic drug treatment, cooling of nuclear reactors, and magnetic devices for cell separation. Our concern in this article is to numerically investigate the flow of an incompressible Magnetohydrodynamics micropolar fluid with heat transportation through a channel having porous walls. By employing the suitable dimensionless coordinates, the flow model equations are converted into a nonlinear system of dimensionless ordinary differential equations, which are then numerically treated for different preeminent parameters with the help of quasi-linearization. The system of complex nonlinear differential equations can efficiently be solved using this technique. Impact of the problem parameters for microrotation, temperature, and velocity are interpreted and discussed through tables and graphs. The present numerical results are compared with those presented in previous literature and examined to be in good contact with them. It has been noted that the imposed magnetic field acts as a frictional force which not only increases the shear stresses and heat transfer rates at the channel walls, but also tends to rotate the micro particles in the fluid more rapidly. Furthermore, viscous dissipation may raise fluid temperature to such a level that the possibility of thermal reversal exists, at the geometric boundaries of the domain. It is therefore recommended that external magnetic fields and viscous dissipation effects may be considered with caution in applications where thermal control is required.

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SCATTERING OF A THIN LAYER OVER A NONLINEAR RADIALLY EXTENDING SURFACE WITH MAGNETO HYDRODYNAMIC AND THERMAL DISSIPATION

Surface Review and Letters ◽

10.1142/s0218625x18501238 ◽

2019 ◽

Vol 26 (01) ◽

pp. 1850123 ◽

Cited By ~ 12

Author(s):

TAZA GUL

Keyword(s):

Temperature Field ◽

Thin Layer ◽

Nonlinear Differential Equations ◽

Thermal Dissipation ◽

Flow Equations ◽

Dissipation Term ◽

Homotopy Analysis ◽

Number Formula ◽

Optimal Approach ◽

The Impact

The recent research is allied with the analysis of a thin layer, spreading over the nonlinear surface of a radially extended sheet. The temperature field has been taken with the accumulation of dissipation term. The similarity variables have been used to transform the basic flow equations into a set of nonlinear differential equations. The thickness of the spreading phenomenon has been taken as a variable. The approximate outcomes of the problem have been achieved using the optimal approach of the homotopy analysis method (HAM). The convergence of the HAM has been computed with numerical method. The impact of the variable thickness parameter [Formula: see text], generalized magnetic parameter [Formula: see text], Eckert number [Formula: see text] and [Formula: see text] on the spreading pattern and temperature field has been calculated and discussed. The attention has been paid to the important physical quantities of interest like the skin friction and Nusselt number under the effect of various embedded parameters.

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A hybrid three-scale model of tumor growth

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202518500021 ◽

2017 ◽

Vol 28 (01) ◽

pp. 61-93 ◽

Cited By ~ 14

Author(s):

H. L. Rocha ◽

R. C. Almeida ◽

E. A. B. F. Lima ◽

A. C. M. Resende ◽

J. T. Oden ◽

...

Keyword(s):

Tumor Microenvironment ◽

Differential Equations ◽

Tumor Growth ◽

Nonlinear Differential Equations ◽

Reaction Diffusion Equations ◽

Scale Model ◽

Wide Range ◽

Induced Stresses ◽

The Impact

Cancer results from a complex interplay of different biological, chemical, and physical phenomena that span a wide range of time and length scales. Computational modeling may help to unfold the role of multiple evolving factors that exist and interact in the tumor microenvironment. Understanding these complex multiscale interactions is a crucial step toward predicting cancer growth and in developing effective therapies. We integrate different modeling approaches in a multiscale, avascular, hybrid tumor growth model encompassing tissue, cell, and sub-cell scales. At the tissue level, we consider the dispersion of nutrients and growth factors in the tumor microenvironment, which are modeled through reaction–diffusion equations. At the cell level, we use an agent-based model (ABM) to describe normal and tumor cell dynamics, with normal cells kept in homeostasis and cancer cells differentiated into quiescent, proliferative, migratory, apoptotic, hypoxic, and necrotic states. Cell movement is driven by the balance of a variety of forces according to Newton’s second law, including those related to growth-induced stresses. Phenotypic transitions are defined by specific rule of behaviors that depend on microenvironment stimuli. We integrate in each cell/agent a branch of the epidermal growth factor receptor (EGFR) pathway. This pathway is modeled by a system of coupled nonlinear differential equations involving the mass laws of 20 molecules. The rates of change in the concentration of some key molecules trigger proliferation or migration advantage response. The bridge between cell and tissue scales is built through the reaction and source terms of the partial differential equations. Our hybrid model is built in a modular way, enabling the investigation of the role of different mechanisms at multiple scales on tumor progression. This strategy allows representing both the collective behavior due to cell assembly as well as microscopic intracellular phenomena described by signal transduction pathways. Here, we investigate the impact of some mechanisms associated with sustained proliferation on cancer progression. Speci- fically, we focus on the intracellular proliferation/migration-advantage-response driven by the EGFR pathway and on proliferation inhibition due to accumulation of growth-induced stresses. Simulations demonstrate that the model can adequately describe some complex mechanisms of tumor dynamics, including growth arrest in avascular tumors. Both the sub-cell model and growth-induced stresses give rise to heterogeneity in the tumor expansion and a rich variety of tumor behaviors.

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