Numerical and Statistical Analysis of Dissipative and Heat Absorbing Graphene Maxwell Nanofluid Flow Over a Stretching Sheet

2021 ◽  
Vol 10 (4) ◽  
pp. 600-607
Author(s):  
A. Bhattacharyya ◽  
R. Sharma ◽  
M. K. Mishra ◽  
Ali J. Chamkha ◽  
E. Mamatha
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Numerical Solution ◽  
Physical Parameters ◽  
Nonlinear Mathematical Model ◽  
Nanofluid Flow ◽  
Maxwell Nanofluid ◽  
Highly Nonlinear ◽  
Numeric Data ◽  
The Magnetic Field

This paper is basically devoted to carry out an investigation regarding the unsteady flow of dissipative and heat absorbing hydromagnetic graphene Maxwell nanofluid over a linearly stretched sheet taking momentum and thermal slip conditions into account. Ethylene glycol is selected as a base fluid while graphene particles are considered as nanoparticles. The highly nonlinear mathematical model of the problem is converted into a set of nonlinear coupled differential equations by means of fitting similarity variables. Further, Runge-Kutta Fehlberg algorithms along with the shooting scheme are instigated to analyse the numerical solution. The variations in graphene Maxwell nanofluid velocity and temperature owing to different physical parameters have been demonstrated via numerous graphs whereas Nusselt number and skin friction coefficients are illustrated in numeric data form and are reported in different tables. In addition, a statistical method is implemented for multiple quadratic regression estimation analysis on the numerical figures of wall velocity gradient and local Nusselt number to establish the connection among heat transfer rate and physical parameters. Our numerical findings reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. The regression analysis confers that Nusselt number is more prone to heat absorption parameter as compared to Eckert number. Finally, the numerical findings are compared with those of earlier published articles under restricted conditions to validate the numerical solution. The comparison of numerical findings shows an excellent conformity among the results.

scholarly journals Hydromagnetic Dissipative and Radiative Graphene Maxwell Nanofluid Flow Past a Stretched Sheet-Numerical and Statistical Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1929 ◽  
Author(s):  
Syed M. Hussain ◽  
Rohit Sharma ◽  
Manas R. Mishra ◽  
Sattam S. Alrashidy
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Physical Parameters ◽  
Maxwell Nanofluid ◽  
Nusselt Numbers ◽  
Highly Nonlinear ◽  
Numeric Data ◽  
The Relationship ◽  
The Magnetic Field

The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations (PDE) of mathematical model in the form of nonlinear ordinary differential equations (ODE). Further, these transformed equations are numerically solved by making use of Runge-Kutta-Fehlberg algorithm along with the shooting scheme. The significance of pertinent physical parameters on the flow of graphene Maxwell nanofluid velocity and temperature are enumerated via different graphs whereas skin friction coefficients and Nusselt numbers are illustrated in numeric data form and are reported in different tables. In addition, a statistical approach is used for multiple quadratic regression analysis on the numerical figures of wall velocity gradient and local Nusselt number to demonstrate the relationship amongst heat transfer rate and physical parameters. Our results reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. Finally, we have compared our numerical results with those of earlier published articles under the restricted conditions to validate our solution. The comparison of results shows an excellent conformity among the results.

scholarly journals Crossbreed impact of double-diffusivity convection on peristaltic pumping of magneto Sisko nanofluids in non-uniform inclined channel: A bio-nanoengineering model

2021 ◽  
Vol 104 (3) ◽  
pp. 003685042110336
Author(s):  
Safia Akram ◽  
Maria Athar ◽  
Khalid Saeed ◽  
Alia Razia
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Physical Parameters ◽  
Induced Magnetic Field ◽  
Long Wavelength ◽  
Inclined Channel ◽  
Graphical Data ◽  
Peristaltic Pumping ◽  
Highly Nonlinear ◽  
Linear Pdes

The consequences of double-diffusivity convection on the peristaltic transport of Sisko nanofluids in the non-uniform inclined channel and induced magnetic field are discussed in this article. The mathematical modeling of Sisko nanofluids with induced magnetic field and double-diffusivity convection is given. To simplify PDEs that are highly nonlinear in nature, the low but finite Reynolds number, and long wavelength estimation are used. The Numerical solution is calculated for the non-linear PDEs. The exact solution of concentration, temperature and nanoparticle are obtained. The effect of various physical parameters of flow quantities is shown in numerical and graphical data. The outcomes show that as the thermophoresis and Dufour parameters are raised, the profiles of temperature, concentration, and nanoparticle fraction all significantly increase.

HEXAGON-STRIPE TRANSITION AT THE MAGNETIC FIELD INDUCED PHASE TRANSFORMATIONS OF THE MAGNETORHEOLOGICAL SUSPENSIONS

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2345-2351 ◽  
Author(s):  
A. CEBERS
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Physical Parameters ◽  
Phase Boundaries ◽  
Modulated Phases ◽  
Magnetorheological Suspensions ◽  
Perturbed State ◽  
Magnetorheological Suspension ◽  
The Magnetic Field ◽  
Hele Shaw Cell

The phase diagram of the magnetorheological suspension allowing for the modulated phases in the Hele-Shaw cell under the action of the normal field is calculated. The phase boundaries between the stripe, the hexagonal and the unmodulated phases in dependence on the layer thickness and the magnetic field strength are found. The existence of the transitions between the stripe and the hexagonal phases at the corresponding variation of the physical parameters is illustrated by the numerical simulation of the concentration dynamics in the Hele-Shaw cell. It is remarked that those transitions in the case of the magnetorheological suspensions can be caused by the compression or the expansion of the layer. Among the features noticed at the numerical simulation of the concentration dynamics in the Hele-Shaw cell are: the stripe patterns formed from the preexisting hexagonal structures are more ordered than arising from the initial randomly perturbed state; at the slightly perturbed boundary between the concentrated and diluted phases the hexagonal and the inverted hexagonal phases are formed and others.

scholarly journals Propagation of Blast waves in a Non-Ideal Magnetogasdynamics

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 458 ◽  
Author(s):  
Astha Chauhan ◽  
Rajan Arora ◽  
Mohd Siddiqui
Keyword(s):  
Magnetic Field ◽  
Gas Dynamics ◽  
Approximate Analytical Solution ◽  
Ideal Gas ◽  
Specific Conductance ◽  
Blast Waves ◽  
Highly Nonlinear ◽  
Vast Literature ◽  
Flow Variables ◽  
The Magnetic Field

Blast waves are generated when an area grows abruptly with a supersonic speed, as in explosions. This problem is quite interesting, as a large amount of energy is released in the process. In contrast to the situation of imploding shocks in ideal gas, where a vast literature is available on the effect of magnetic fields, very little is known about blast waves propagating in a magnetic field. As this problem is highly nonlinear, there are very few techniques that may provide even an approximate analytical solution. We have considered a problem on planar and radially symmetric blast waves to find an approximate solution analytically using Sakurai’s technique. A magnetic field has been taken in the transverse direction. Gas particles are supposed to be propagating orthogonally to the magnetic field in a non-deal medium. We have further assumed that specific conductance of the medium is infinite. Using Sakurai’s approach, we have constructed the solution in a power series of ( C / U ) 2 , where C is the velocity of sound in an ideal gas and U is the velocity of shock front. A comparison of obtained results in the absence of a magnetic field within the published work of Sakurai has been made to generate the confidence in our results. Our results match well with the results reported by Sakurai for gas dynamics. The flow variables are computed behind the leading shock and are shown graphically. It is very interesting that the solution of the problem is obtained in closed form.

Entropy generation of nanofluid flow and heat transfer driven through a paralleled microchannel

2019 ◽  
Vol 97 (6) ◽  
pp. 678-691 ◽  
Author(s):  
Hang Xu ◽  
Ammarah Raees ◽  
Xiao-Hang Xu
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Entropy Generation ◽  
Current Model ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Buongiorno’S Model ◽  
Flow Models ◽  
Flow And Heat Transfer

In this paper, a fully-developed, immiscible nanofluid flow in a paralleled microchannel in the presence of a magnetic field is investigated. Buongiorno’s model is applied to describe the behaviors of the nanofluid flow. Different from most previous studies on microchannel flow, here the pressure term is considered as unknown, which makes the current model compatible with the commonly accepted channel flow models. The influences of various physical parameters on important physical quantities are given. The entropy generation analysis is performed. Variations of local and global entropy generations with the magnetic field parameter, the electric field, and the viscous dissipation parameter under various ratios of the thermophoresis parameter to the Brownian motion parameter are illustrated. The results indicate that the entropy generation rate strongly depends on the thermophoresis and the Brownian motion parameters. Their increase enhances the total irreversibility of entropy generation.

Boiling heat transfer characteristics of binary magnetic fluid flow in a vertical circular pipe with a partly heated region

2004 ◽  
Vol 218 (2) ◽  
pp. 223-232 ◽  
Author(s):  
S Shuchi ◽  
K Sakatani ◽  
H Yamaguchi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Boiling Heat Transfer ◽  
Transfer Rate ◽  
Heated Region ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
The Magnetic Field

An investigation was conducted for heat transfer characteristics of binary magnetic fluid flow in a partly heated circular pipe experimentally. The boiling heat transfer characteristics on the effects of the relative position of the magnetic field to the heated region were particularly considered in the present study. From the experimental verification, the Nusselt number, representing boiling heat transfer characteristics, was obtained for various flow and magnetic conditions which were represented by the non-dimensional parameters of the Reynolds number and the magnetic pressure number. Additionally, the rate of change of the Nusselt number found by applying the magnetic field was also estimated and the optimal position of the field to the partly heated region was discussed. The results indicated that the effect of the magnetic field to the heat transfer rate from the heated wall was mainly subjected to the effect of the vortices induced in the magnetic field region and the possibility of controlling the heat transfer rate by applying an outer magnetic field to utilize the effect.

In Search of the Jerk Element

2021 ◽  
Author(s):  
Zachary P. Belyaev ◽  
Samuel N. Downes ◽  
Philip A. Voglewede
Keyword(s):  
Magnetic Field ◽  
Motion Planning ◽  
System Performance ◽  
Theoretical Background ◽  
Physical Parameters ◽  
Common Elements ◽  
Planning And Control ◽  
Magneto Rheological ◽  
And Control ◽  
The Magnetic Field

Abstract Mechanical components, such as springs, dampers and mass, alter and influence an engineered system’s motion based upon a system’s position, velocity and acceleration, respectively. This paper aims to discover and develop another element (dubbed the damper) which provides a force proportional to a system’s jerk (i.e., the derivative of acceleration) to better engineer a system’s response. By utilizing the known applications of jerk in motion planning and control theory, existing possible physical implementations and uses of jerk and the jerk element are discussed in relation to its influence on the system’s response, specifically vibration. Using a Buckingham Pi approach, the theoretical background of the jerk element is presented and possible physical parameters are combined to show how the jerk element could be created from common elements and parameters. The most promising approach of varying the magnetic field of existing magneto-rheological dampers is developed to give an example of the jerk element along with the difficulties and concerns in developing the jerk element. This paper serves less of a purpose towards answering all questions of the jerk element, but rather focuses more on posing the appropriate questions which sets the stage for an easily realizable future jerk element which can improve system performance.

scholarly journals The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1014 ◽  
Author(s):  
Essam R. EL-Zahar ◽  
Ahmed M. Rashad ◽  
Laila F. Seddek
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Surface Temperature ◽  
Drag Coefficient ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Grid Points ◽  
The Impact ◽  
Sinusoidal Surface ◽  
The Magnetic Field

The spotlight of this investigation is primarily the effectiveness of the magnetic field on the natural convective for a Fe3O4 ferrofluid flow over a vertical radiate plate using streamwise sinusoidal variation in surface temperature. The energy equation is reduplicated by interpolating the non-linear radiation effectiveness. The original equations describing the ferrofluid motion and energy are converted into non-dimensional equations and solved numerically using a new hybrid linearization-differential quadrature method (HLDQM). HLDQM is a high order semi-analytical numerical method that results in analytical solutions in η -direction, and so the solutions are valid overall in the η domain, not only at grid points. The dimensionless velocity and temperature curves are elaborated. Furthermore, the engineering curiosity of the drag coefficient and local Nusselt number are debated and sketched in view of various emerging parameters. The analyzed numerical results display that applying the magnetic field to the ferroliquid generates a dragging force that diminishes the ferrofluid velocity, whereas it is found to boost the temperature curves. Furthermore, the drag coefficient sufficiently minifies, while an evolution in the heat transfer rate occurs as nanoparticle volume fraction builds. Additionally, the augmentation in temperature ratio parameter signifies a considerable growth in the drag coefficient and Nusselt number. The current theoretical investigation may be beneficial in manufacturing processes, development of transport of energy, and heat resources.

scholarly journals A Non-Newtonian Magnetohydrodynamics (MHD) Nanofluid Flow and Heat Transfer with Nonlinear Slip and Temperature Jump

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1199 ◽  
Author(s):  
Jing Zhu ◽  
Yaxin Xu ◽  
Xiang Han
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Jump ◽  
Thin Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Slip Condition ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Flow And Heat Transfer

The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. Similarity transformation and Lie point symmetry are adopted to convert the derived governed equations to ordinary differential equations. An approximate analytical solution is gained through the homotopy analysis method. The impacts of velocity slip, temperature jump, and other physical parameters on flow and heat transfer are illustrated. Results indicate that the first-order slip and nonlinear slip parameters reduce the velocity boundary layer thickness and Nusselt number, whereas the effect on shear stress is converse. The temperature jump parameter causes a rise in the temperature, but a decline in the Nusselt number. With the increase of the order, we can get that the error reaches 10 − 6 from residual error curve. In addition, the velocity contours and the change of skin friction coefficient are computed through Ansys Fluent.

scholarly journals Analytical model for cluster radio relics

2020 ◽  
Vol 493 (2) ◽  
pp. 2306-2317 ◽  
Author(s):  
M Brüggen ◽  
F Vazza
Keyword(s):  
Magnetic Field ◽  
Flux Distribution ◽  
Cosmic Ray ◽  
Analytical Models ◽  
Physical Parameters ◽  
Mass Relation ◽  
Intracluster Medium ◽  
Large Area ◽  
Shock Dynamics ◽  
The Magnetic Field

ABSTRACT Radio relics are vast synchrotron sources that sit on the outskirts of merging galaxy clusters. In this work we model their formation using a Press–Schechter formalism to simulate merger rates, analytical models for the intracluster medium and the shock dynamics, as well as a simple model for the cosmic ray electrons at the merger shocks. We show that the statistical properties of the population of radio relics are strongly dependent on key physical parameters, such as the acceleration efficiency, the magnetic field strength at the relic, the geometry of the relic and the duration of the electron acceleration at merger shocks. It turns out that the flux distribution as well as the power–mass relation can constrain key parameters of the intracluster medium. With the advent of new large-area radio surveys, statistical analyses of radio relics will complement what we have learned from observations of individual objects.

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