scholarly journals Couple Stress Impacton S-Wavesin an Anisotropic Pre-Stressed Medium under Gravity and Magnetic Field

2019 ◽  
Vol 8 (4) ◽  
pp. 7526-7530
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Wave Number ◽  
Density Parameter ◽  
Stress Parameter ◽  
Anisotropic Factor ◽  
Gravity And Magnetic ◽  
Rigidity Parameter

The gravity fieldand magnetic field impact with the inclusion of couple stress s r onshear waves in a transversely isotropic elastic solid medium is studied. Thedispersion equations for the particular problem have been obtained. Severalparticular cases are also examined. The numerical calculations are carriedout for specific rigidity parameter A, density parameter C, anisotropic factor N , initial stress parameter P , gravity parameter G, magnetic fieldparameter H , couple stress parameter  as well as wave number κ and theoutcomes are visually represented by graph.

On Superposed Couple-stress Fluids in Porous Medium in Hydromagnetics The Use of Quantum-Chemical Semiempirical Methods to Calculate the Lattice Energies of Organic Molecular Crystals. Part II: The Lattice Energies of - and -Oxalic Acid (COOH)2

2002 ◽  
Vol 57 (12) ◽  
pp. 955-960 ◽  
Author(s):  
◽  
R. C. Sharmab ◽  
R. S. Chandel
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Couple Stress ◽  
Kinematic Viscosity ◽  
Wave Number ◽  
Semiempirical Methods ◽  
Number Range ◽  
Lattice Energies ◽  
The Magnetic Field ◽  
Couple Stress Fluids

The Rayleigh-Taylor instability of two supersposed couple-stress fluids of uniform densities in a porous medium in the presence of a uniform horizontal magnetic field is studied. For mathematical simplicity, the stability analysis is carried out for two highly viscous fluids of equal kinematic viscosity and equal couple-stress kinematic viscosity. A potentially stable configuration remains stable under certain conditions, and a potentially unstable configuration is stable under certain conditions. The magnetic field stabilizes a certain wave-number range k>k*, which is unstable in the absence of the magnetic field.

scholarly journals Free convective flow of a couple stress fluid through a vertical porous channel in the presence of a transverse magnetic field

2018 ◽  
Vol 12 (1) ◽  
pp. 49-62
Author(s):  
M. Prasad Siddalinga ◽  
B. S. Shashikala
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Couple Stress ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Porous Channel ◽  
Couple Stress Fluid ◽  
Physical Parameters ◽  
Stress Parameter ◽  
Buoyancy Parameter

Nonlinear oberbeck convection of a couple stress fluid in a vertical porous channel in the presence of transverse magnetic field is investigated in this paper. Analytical solution is obtained using the perturbation technique for vanishing values of the buoyancy parameter. Numerical solution of the nonlinear governing equations is obtained using the finite difference technique to validate the results obtained from the analytical solutions. The influence of the physical parameters on the flow, such as couple stress parameter, Hartmann number, temperature parameter, porous parameter and buoyancy parameter are evaluated and presented graphically. A new approach is used to analyse the flow for strong, weak and comparable porosity cases. It is found that increase in porous parameter, couple stress parameter, Hartmann number and temperature parameters decrease the velocity considerably.Kathmandu University Journal of Science, Engineering and Technology Vol. 12, No. I, June, 2016, Page: 49-62

scholarly journals The Effect of the Magnetic Field on the Rayleigh-Taylor Instability in a Couple-Stress Fluid

2018 ◽  
Vol 23 (3) ◽  
pp. 611-622
Author(s):  
K.B. Chavaraddi ◽  
V.B. Awati ◽  
M.M. Nandeppanavar ◽  
P.M. Gouder
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Dispersion Relation ◽  
Boundary Conditions ◽  
Couple Stress ◽  
Taylor Instability ◽  
Wave Number ◽  
Special Cases ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

Abstract In this study we examine the effect of the magnetic field parameter on the growth rate of the Rayleigh-Taylor instability (RTI) in a couple stress fluids. A simple theory based on fully developed flow approximations is used to derive the dispersion relation for the growth rate of the RTI. The general dispersion relation obtained using perturbation equations with appropriate boundary conditions will be reduced for the special cases of propagation and the condition of instability and stability will be obtained. In solving the problem of the R-T instability the appropriate boundary conditions will be applied. The couple-stress parameter is found to be stabilizing and the influence of the various parameters involved in the problem on the interface stability is thoroughly analyzed. The new results will be obtained by plotting the curves between the dimensionless growth rate and the dimensionless wave number for various physical parameters involved in the problem (viz. the magnetic field, couple-stress, porosity, etc.) in the problem. It is found that the magnetic field and couple-stress have a stabilization effect whereas the buoyancy force (surface tension) has a destabilization effect on the RT instability in the presence of porous media.

scholarly journals The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium

2014 ◽  
Vol 62 (2) ◽  
pp. 357-362
Author(s):  
Gian C. Rana
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Thermal Convection ◽  
Couple Stress ◽  
Normal Mode Analysis ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Couple Stress Fluid ◽  
Stress Parameter ◽  
Medium Permeability

Abstract In this paper, the effect of magnetic field on thermal convection in couple-stress fluid saturating a porous medium is considered. By applying linear stability theory and the normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter Pι the couple-stress parameter F and the Chandrasekher number Q, satisfy the inequality the result clearly establishes the stabilizing character of couple-stress parameter and magnetic field whereas destabilizing character of medium permeability.

scholarly journals Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 867 ◽  
Author(s):  
Muhammad Ahmad ◽  
Poom Kumam ◽  
Zahir Shah ◽  
Ali Farooq ◽  
Rashid Nawaz ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Mathematical Model ◽  
Velocity Field ◽  
Differential Equations ◽  
Couple Stress ◽  
Stretching Sheet ◽  
Exponentially Stretching Sheet ◽  
Stress Parameter ◽  
Exponentially Stretching ◽  
Parameter Coefficient

In the last decade, nanoparticles have provided numerous challenges in the field of science. The nanoparticles suspended in various base fluids can transform the flow of fluids and heat transfer characteristics. In this research work, the mathematical model is offered to present the 3D magnetohydrodynamics Darcy–Forchheimer couple stress nanofluid flow over an exponentially stretching sheet. Joule heating and viscous dissipation impacts are also discussed in this mathematical model. To examine the relaxation properties, the proposed model of Cattaneo–Christov is supposed. For the first time, the influence of temperature exponent is scrutinized via this research article. The designed system of partial differential equations (PDE’s) is transformed to set of ordinary differential equations (ODE’s) by using similarity transformations. The problem is solved analytically via homotopy analysis technique. Effects of dimensionless couple stress, magnetic field, ratio of rates, porosity, and coefficient of inertia parameters on the fluid flow in x- and y-directions have been examined in this work. The augmented ratio of rates parameter upsurges the velocity profile in the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, and couple stress parameter diminishes the velocity field along the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, ratio of rates parameter, and couple stress parameter reduces the velocity field along the y-axis. The influences of time relaxation, Prandtl number, and temperature exponent on temperature profile are also discussed. Additionally, the influences of thermophoresis parameter, Schmidt number, Brownian motion parameter, and temperature exponent on fluid concentration are explained in this work. For engineering interests, the impacts of parameters on skin friction and Nusselt number are accessible through tables.

EFFECT OF MAGNETIC FIELD ON PERISTALTIC TRANSPORT OF COUPLE STRESS FLUIDS THROUGH A POROUS MEDIUM

2011 ◽  
Vol 19 (02) ◽  
pp. 251-262 ◽  
Author(s):  
S. K. PANDEY ◽  
M. K. CHAUBE
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Axial Velocity ◽  
Couple Stress ◽  
Magnetic Parameter ◽  
Amplitude Ratio ◽  
Perturbation Technique ◽  
Mean Velocity ◽  
Stress Parameter ◽  
Permeability Parameter

This paper analyses peristaltic flow of a couple stress fluid in a channel through a porous medium in the presence of an external magnetic field. The flow is induced by sinusoidal traveling waves along the walls of the channel. The nonlinear convective acceleration terms are duly considered and a perturbation technique is used to solve the problem for the case of small amplitude ratio. The effects of couple-stress parameter, magnetic parameter and permeability parameter on mean velocity on the channel walls, mean axial velocity and critical reflux condition are discussed in detail. Computational results show that the mean velocity at the boundary decreases with increasing couple stress parameter and permeability parameter while it increases with magnetic parameter. It is also revealed that mean axial velocity decreases with increasing couple stress parameter and magnetic parameter while it increases with permeability parameter.

scholarly journals Predictions of the geomagnetic secular variation based on the ensemble sequential assimilation of geomagnetic field models by dynamo simulations

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Sabrina Sanchez ◽  
Johannes Wicht ◽  
Julien Bärenzung
Keyword(s):  
Magnetic Field ◽  
Secular Variation ◽  
Geomagnetic Field ◽  
Wave Number ◽  
Main Magnetic Field ◽  
Candidate Model ◽  
Uncertainty Estimates ◽  
Geomagnetic Field Models ◽  
Dipole Configuration

Abstract The IGRF offers an important incentive for testing algorithms predicting the Earth’s magnetic field changes, known as secular variation (SV), in a 5-year range. Here, we present a SV candidate model for the 13th IGRF that stems from a sequential ensemble data assimilation approach (EnKF). The ensemble consists of a number of parallel-running 3D-dynamo simulations. The assimilated data are geomagnetic field snapshots covering the years 1840 to 2000 from the COV-OBS.x1 model and for 2001 to 2020 from the Kalmag model. A spectral covariance localization method, considering the couplings between spherical harmonics of the same equatorial symmetry and same azimuthal wave number, allows decreasing the ensemble size to about a 100 while maintaining the stability of the assimilation. The quality of 5-year predictions is tested for the past two decades. These tests show that the assimilation scheme is able to reconstruct the overall SV evolution. They also suggest that a better 5-year forecast is obtained keeping the SV constant compared to the dynamically evolving SV. However, the quality of the dynamical forecast steadily improves over the full assimilation window (180 years). We therefore propose the instantaneous SV estimate for 2020 from our assimilation as a candidate model for the IGRF-13. The ensemble approach provides uncertainty estimates, which closely match the residual differences with respect to the IGRF-13. Longer term predictions for the evolution of the main magnetic field features over a 50-year range are also presented. We observe the further decrease of the axial dipole at a mean rate of 8 nT/year as well as a deepening and broadening of the South Atlantic Anomaly. The magnetic dip poles are seen to approach an eccentric dipole configuration.

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