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.

Analytical solution for unsteady flow behind ionizing shock wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Analytical Solution ◽  
Axial Magnetic Field ◽  
Order Approximation ◽  
Ideal Gas ◽  
Field Region ◽  
First Order ◽  
First Order Approximation ◽  
Flow Variables

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.

scholarly journals Experimental and numerical investigation of plasma parameters in the magnetosheath

2018 ◽  
Vol 145 ◽  
pp. 03003
Author(s):  
Polya Dobreva ◽  
Monio Kartalev ◽  
Olga Nitcheva ◽  
Natalia Borodkova ◽  
Georgy Zastenker
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Numerical Investigation ◽  
Euler Equations ◽  
Ideal Gas ◽  
Bow Shock ◽  
Plasma Parameters ◽  
Wind Spacecraft ◽  
The Magnetic Field ◽  
Good Agreement

We investigate the behaviour of the plasma parameters in the magnetosheath in a case when Interball-1 satellite stayed in the magnetosheath, crossing the tail magnetopause. In our analysis we apply the numerical magnetosheath-magnetosphere model as a theoretical tool. The bow shock and the magnetopause are self-consistently determined in the process of the solution. The flow in the magnetosheath is governed by the Euler equations of compressible ideal gas. The magnetic field in the magnetosphere is calculated by a variant of the Tsyganenko model, modified to account for an asymmetric magnetopause. Also, the magnetopause currents in Tsyganenko model are replaced by numericaly calulated ones. Measurements from WIND spacecraft are used as a solar wind monitor. The results demonstrate a good agreement between the model-calculated and measured values of the parameters under investigation.

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 Mathematical Theory of Cylindrical Isothermal Blast Waves in a Magnetic Field

1981 ◽  
Vol 34 (3) ◽  
pp. 279 ◽  
Author(s):  
I Lerche
Keyword(s):  
Magnetic Field ◽  
Supernova Remnants ◽  
Magnetic Pressure ◽  
Blast Waves ◽  
Physical Domain ◽  
Fluid Flow Velocity ◽  
Magnetic Tension ◽  
Self Similar ◽  
The Magnetic Field ◽  
Similar Flows

An investigation is made of the self-similar flow behind a cylindrical blast wave from a line explosion (situated on r = 0, using conventional cylindrical coordinates r, 4>, z) in a medium whose density and magnetic field both vary as r -w ahead of the blast front, with the assumption that the flow is isothermal. The magnetic field can have components in both the azimuthal B(jJ and longitudinal B, directions. It is found that: (i) For B(jJ =f:. 0 =f:. B, a continuous single-valued solution with a velocity field representing outflow of material away from the line of explosion does not exist for OJ OJ > 0 the governing equation possesses a set of movable critical points. In this case it is shown that the fluid flow velocity is bracketed between two curves and that the asymptotes of the velocity curve on the shock are intersected by, or are tangent to, the two curves. Thus a solution always exists in the physical domain r ~ o. The overall conclusion from the investigation is that the behaviour of isothermal blast waves in the presence of an ambient magnetic field differs substantially from the behaviour calculated for no magnetic field. These results have an impact upon previous applications of the theory of self-similar flows to evolving supernova remnants without allowance for the dynamical influence of magnetic pressure and magnetic tension.

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.

Plane Magnetofluiddynamic Flows with Constantly Inclined Magnetic and Velocity Fields

1974 ◽  
Vol 52 (9) ◽  
pp. 753-758 ◽  
Author(s):  
H. Toews ◽  
O. P. Chandna
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Incompressible Flows ◽  
Fluid Flows ◽  
Velocity Fields ◽  
Parallel Flows ◽  
Definite Manner ◽  
Flow Variables ◽  
Compressible Fluid Flows ◽  
The Magnetic Field

Plane steady state nondissipative compressible fluid flows, in which the conductivity is infinite and in which the magnetic field and the velocity field are constantly inclined to one another, are considered. Sonic flows, and flows for which the velocity is constant along each streamline, are studied and the related results are applied to flows in poly-tropic gases. It is shown that if two distinct incompressible flows have the same streamline pattern, then the flow variables are related in a definite manner. Finally, solutions are obtained for vortex flows and also for parallel flows.

Blast waves propagation in magnetogasdynamics: power series method

2020 ◽  
Vol 75 (12) ◽  
pp. 1039-1050
Author(s):  
Munesh Devi ◽  
Rajan Arora ◽  
Deepika Singh
Keyword(s):  
Magnetic Field ◽  
Shock Waves ◽  
Power Series ◽  
Shock Front ◽  
Closed Form ◽  
Analytic Solutions ◽  
Blast Waves ◽  
Series Method ◽  
Power Series Method ◽  
The Magnetic Field

AbstractBlast waves are produced when there is a sudden deposition of a substantial amount of energy into a confined region. It is an area of pressure moving supersonically outward from the source of the explosion. Immediately after the blast, the fore-end of the blast wave is headed by the shock waves, propagating in the outward direction. As the considered problem is highly nonlinear, to find out its solution is a tough task. However, few techniques are available in literature that may give us an approximate analytic solution. Here, the blast wave problem in magnetogasdynamics involving cylindrical shock waves of moderate strength is considered, and approximate analytic solutions with the help of the power series method (or Sakurai’s approach [1]) are found. The magnetic field is supposed to be directed orthogonally to the motion of the gas particles in an ideal medium with infinite electrical conductivity. The density is assumed to be uniform in the undisturbed medium. Using power series method, we obtain approximate analytic solutions in the form of a power series in ${\left({a}_{0}/U\right)}^{2}$, where a0 and U are the velocities of sound in an undisturbed medium and shock front, respectively. We construct solutions for the first-order approximation in closed form. Numerical computations have been performed to determine the flow-field in an ideal magnetogasdynamics. The numerical results obtained in the absence of magnetic field recover the existing results in the literature. Also, these results are found to be in good agreement with those obtained by the Runge–Kutta method of fourth-order. Further, the flow variables are illustrated through figures behind the shock front under the effect of the magnetic field. The interesting fact about the present work is that the solutions to the problem are obtained in the closed form.

scholarly journals Numerical Analysis of Unsteady Hybrid Nanofluid Flow Comprising CNTs-Ferrousoxide/Water with Variable Magnetic Field

Nanomaterials ◽  
2022 ◽  
Vol 12 (2) ◽  
pp. 180
Author(s):  
Muhammad Sohail Khan ◽  
Sun Mei ◽  
Shabnam ◽  
Unai Fernandez-Gamiz ◽  
Samad Noeiaghdam ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Carbon Nanotubes ◽  
Velocity Profile ◽  
Variable Magnetic Field ◽  
The Body ◽  
Hybrid Nanofluid ◽  
Nano Fluid ◽  
Highly Nonlinear ◽  
The Impact ◽  
The Magnetic Field

The introduction of hybrid nanofluids is an important concept in various engineering and industrial applications. It is used prominently in various engineering applications, such as wider absorption range, low-pressure drop, generator cooling, nuclear system cooling, good thermal conductivity, heat exchangers, etc. In this article, the impact of variable magnetic field on the flow field of hybrid nano-fluid for the improvement of heat and mass transmission is investigated. The main objective of this study is to see the impact of hybrid nano-fluid (ferrous oxide water and carbon nanotubes) CNTs-Fe3O4, H2O between two parallel plates with variable magnetic field. The governing momentum equation, energy equation, and the magnetic field equation have been reduced into a system of highly nonlinear ODEs by using similarity transformations. The parametric continuation method (PCM) has been utilized for the solution of the derived system of equations. For the validity of the model by PCM, the proposed model has also been solved via the shooting method. The numerical outcomes of the important flow properties such as velocity profile, temperature profile and variable magnetic field for the hybrid nanofluid are displayed quantitatively through various graphs and tables. It has been noticed that the increase in the volume friction of the nano-material significantly fluctuates the velocity profile near the channel wall due to an increase in the fluid density. In addition, single-wall nanotubes have a greater effect on temperature than multi-wall carbon nanotubes. Statistical analysis shows that the thermal flow rate of (Fe3O4-SWCNTs-water) and (Fe3O4-MWCNTs-water) rises from 1.6336 percent to 6.9519 percent, and 1.7614 percent to 7.4413 percent, respectively when the volume fraction of nanomaterial increases from 0.01 to 0.04. Furthermore, the body force accelerates near the wall of boundary layer because Lorentz force is small near the squeezing plate, as the current being almost parallel to the magnetic field.

Magneto gas dynamic singular surfaces in an isothermal flow of gas

1987 ◽  
Vol 65 (7) ◽  
pp. 793-795
Author(s):  
S. N. Ojha ◽  
Ashok Singh
Keyword(s):  
Magnetic Field ◽  
Shock Wave ◽  
Magnetic Field Intensity ◽  
Isothermal Flow ◽  
Wave Formation ◽  
Singular Surfaces ◽  
Shock Wave Formation ◽  
Flow Variables ◽  
Derivatives Of ◽  
The Magnetic Field

The discontinuity surfaces across which the only discontinuities in the derivatives of flow variables exist are known as singular surfaces. The influence of a magnetic field on the propagation of singular surfaces in an isothermal flow of gas is investigated. We find that the expansive waves ultimately disperse while compressive waves grow into a shockwave in a finite time. The derivation of the shock-wave formation time and its dependence on the magnetic-field intensity reveal interesting differences between outward- and inward-moving singular surfaces. In the particular cases of plane and cylindrical singular surfaces, the shock-wave formation distances and times have been derived.

Design and Fuzzy Control of a Moving Magnetic Levitation Device for 3D Manipulation of Small Objects

2010 ◽  
Author(s):  
Mehdi Molavian Jazi ◽  
Gholamreza Vossoughi ◽  
Farid Tajaddodianfar
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Magnetic Levitation ◽  
Design Procedure ◽  
Control Input ◽  
Element Analysis ◽  
3D Manipulation ◽  
Highly Nonlinear ◽  
The Magnetic Field ◽  
Moving Magnet

Magnetic levitation is an appropriate solution for noncontact 3D manipulation. Workspace of the previously proposed maglev systems are confined to a relatively small cube, and this severely limits application of this technology. In addition, most of the previously given mechanisms require design and application of a subsystem for unifying their magnetic field. In this paper, a moving magnet is implemented which results in horizontally extendable work space; moreover, the field unifying section is not needed since one electromagnet only is used. Further, details of the mechanism and finite element based design procedure of the magnet are presented. Dynamic equations of the system derived by finite element analysis of the magnetic field are highly nonlinear and non-affine with respect to the control input. Two decoupled Fuzzy logic based controllers are used to deal with the 3D manipulation of the ball. The designed controllers provide the system with the precise trajectory tracking capability and robust stability. Simulation results confirm the findings.

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