scholarly journals Weak Nonlinear Double-Diffusive Magnetoconvection in a Newtonian Liquid under Temperature Modulation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
B. S. Bhadauria ◽  
Palle Kiran
Keyword(s):  
Magnetic Field ◽  
Mass Transport ◽  
Landau Equation ◽  
Newtonian Liquid ◽  
Temperature Modulation ◽  
System Effect ◽  
Heat And Mass Transport ◽  
Electrically Conducting ◽  
Time Periodic ◽  
Double Diffusive

The present paper deals with a weak nonlinear theory of double-diffusive magnetoconvection in an electrically conducting Newtonian liquid, confined between two horizontal surfaces, under a constant vertical magnetic field, and subjected to imposed time-periodic thermal boundaries. The temperature of both walls is varied time periodic in this case. The disturbances are expanded in terms of power series of amplitude of convection, which is assumed to be small. Using nonautonomous Ginzburg-Landau equation, the Nusselt and Sherwood numbers obtained analytically and studied heat and mass transport in the system. Effect of various parameters on the heat and mass transport is discussed extensively. It is found that the effect of magnetic field is to stabilize the system. Further, it is also notified that the heat and mass transport can be controlled by suitably adjusting the external parameters of the system.

scholarly journals Weakly Nonlinear Magnetic Convection in a Nonuniformly Rotating Electrically Conductive Medium Under the Action of Modulation of External Fields

2020 ◽  
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Landau Equation ◽  
Temperature Modulation ◽  
External Fields ◽  
Ginzburg Landau ◽  
Electrically Conductive ◽  
Weakly Nonlinear ◽  
Conductive Fluid ◽  
Ginzburg Landau Equations

In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear non-autonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.

Double Diffusive Marangoni Convection Flow of Electrically Conducting Fluid in a Square Cavity With Chemical Reaction

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
M. Saleem ◽  
M. A. Hossain ◽  
Suvash C. Saha
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Sherwood Number ◽  
Average Nusselt Number ◽  
Marangoni Convection ◽  
Convection Flow ◽  
Square Cavity ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Double Diffusive

Double diffusive Marangoni convection flow of viscous incompressible electrically conducting fluid in a square cavity is studied in this paper by taking into consideration of the effect of applied magnetic field in arbitrary direction and the chemical reaction. The governing equations are solved numerically by using alternate direct implicit (ADI) method together with the successive over relaxation (SOR) technique. The flow pattern with the effect of governing parameters, namely the buoyancy ratio W, diffusocapillary ratio w, and the Hartmann number Ha, is investigated. It is revealed from the numerical simulations that the average Nusselt number decreases; whereas the average Sherwood number increases as the orientation of magnetic field is shifted from horizontal to vertical. Moreover, the effect of buoyancy due to species concentration on the flow is stronger than the one due to thermal buoyancy. The increase in diffusocapillary parameter, w causes the average Nusselt number to decrease, and average Sherwood number to increase.

Combined Effect of Temperature Modulation and Magnetic Field on the Onset of Convection in an Electrically Conducting-Fluid-Saturated Porous Medium

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
B. S. Bhadauria
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Saturated Porous Medium ◽  
Effect Of Temperature ◽  
Temperature Modulation ◽  
Vertical Magnetic Field ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Fluid Saturated Porous Medium

The effect of temperature modulation on the onset of thermal convection in an electrically conducting fluid-saturated-porous medium, heated from below, has been studied using linear stability analysis. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small. The porous medium is confined between two horizontal walls and subjected to a vertical magnetic field; flow in porous medium is characterized by Brinkman–Darcy model. Considering only infinitesimal disturbances, and using perturbation procedure, the combined effect of temperature modulation and vertical magnetic field on thermal instability has been studied. The correction in the critical Rayleigh number is calculated as a function of frequency of modulation, Darcy number, Darcy Chandrasekhar number, magnetic Prandtl number, and the nondimensional group number χ. The influence of the magnetic field is found to be stabilizing. Furthermore, it is also found that the onset of convection can be advanced or delayed by proper tuning of the frequency of modulation. The results of the present model have been compared with that of Darcy model.

scholarly journals Singular diffusionless limits of double-diffusive instabilities in magnetohydrodynamics

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170344 ◽  
Author(s):  
Oleg N. Kirillov
Keyword(s):  
Magnetic Field ◽  
Hopf Bifurcation ◽  
Smooth Transition ◽  
Neutral Stability ◽  
Ohmic Dissipation ◽  
Azimuthal Magnetic Field ◽  
Electrically Conducting ◽  
Whitney Umbrella ◽  
Finite Distance ◽  
Double Diffusive

We study local instabilities of a differentially rotating viscous flow of electrically conducting incompressible fluid subject to an external azimuthal magnetic field. In the presence of the magnetic field, the hydrodynamically stable flow can demonstrate non-axisymmetric azimuthal magnetorotational instability (AMRI) both in the diffusionless case and in the double-diffusive case with viscous and ohmic dissipation. Performing stability analysis of amplitude transport equations of short-wavelength approximation, we find that the threshold of the diffusionless AMRI via the Hamilton–Hopf bifurcation is a singular limit of the thresholds of the viscous and resistive AMRI corresponding to the dissipative Hopf bifurcation and manifests itself as the Whitney umbrella singular point. A smooth transition between the two types of instabilities is possible only if the magnetic Prandtl number is equal to unity, Pm =1. At a fixed Pm ≠1, the threshold of the double-diffusive AMRI is displaced by finite distance in the parameter space with respect to the diffusionless case even in the zero dissipation limit. The complete neutral stability surface contains three Whitney umbrella singular points and two mutually orthogonal intervals of self-intersection. At these singularities, the double-diffusive system reduces to a marginally stable system which is either Hamiltonian or parity–time-symmetric.

Flow and thermal management of MHD Cross nanofluids over a thin needle with auto catalysis chemical reactions

2020 ◽  
Vol 34 (30) ◽  
pp. 2050287
Author(s):  
Yu-Ming Chu ◽  
M. Ijaz Khan ◽  
M. Israr Ur Rehman ◽  
Seifedine Kadry ◽  
M. K. Nayak
Keyword(s):  
Heat Flux ◽  
Mass Transport ◽  
Radiative Heat ◽  
Research Work ◽  
Skin Friction Coefficient ◽  
Heterogeneous Reactions ◽  
Radiative Heat Flux ◽  
Heat And Mass Transport ◽  
Electrically Conducting ◽  
Flow Heat

This research work concerns the investigation of electrically conducting stagnation point flow, heat and mass transport of magneto-Cross nanofluids towards a moving and stretched surface of thin needle. The Buongiorno nanofluid model is incorporated to model the governing expressions. The flow is conducted electrically and generated through stretching impact. Internal diffusion of particle, homogenous–heterogeneous reactions and radiative heat flux effects are utilized to examine the behavior of heat and mass transport on the surface of thin needle. Suitable similarity variables and boundary layer approximations are used to turn into dimensionless one. After that, numerical outcomes are computed by a Shooting method (bvp4c) package in MATLAB. The incentives of sundry relevant parameters on the flow field, skin friction coefficient, heat transfer rate, temperature field and concentration distribution are portrayed via graphical tactic and have been elucidated in detail. The outcomes indicate that the temperature distribution is more versus rising values of radiative heat flux, magnetic parameter and Eckert number.

scholarly journals Study of Weakly nonlinear Mass transport in Newtonian Fluid with Applied Magnetic Field under Concentration/Gravity modulation

2019 ◽  
Vol 8 (1) ◽  
pp. 513-522 ◽  
Author(s):  
Om Prakash Keshri ◽  
Vinod K. Gupta ◽  
Anand Kumar
Keyword(s):  
Mass Transport ◽  
Fluid Layer ◽  
Landau Equation ◽  
Periodic Part ◽  
Gravity Modulation ◽  
Nonlinear Stability Analysis ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Mass Transfer Effect ◽  
Time Periodic

Abstract In the present paper, a weakly nonlinear stability analysis is used to analyze the effect of time-periodic concentration/gravity modulation on mass transport. We have considered an infinite horizontal fluid layer with constant appliedmagnetic flux salted from above, subjected to an imposed time-periodic boundary concentration (ITBC) or gravity modulation (ITGM). In the case of ITBC, the concentration gradient between the plates of the fluid layer consists of a steady part and a time-dependent oscillatory part. The concentration of both walls is modulated. In the case of ITGM, the gravity fleld consists of two parts: a constant part and an externally imposed time periodic part, which can be realized by oscillating the fluid layer. We have expanded the infinitesimal disturbances in terms of power series of an amplitude of modulation, which is assumed to be small. Ginzburg-Landau equation is derived for dinding the rate of mass transfer. Effect of various parameters on the mass transport is also discussed. It is found that the mass transport can be controlled by suitably adjusting the frequency and amplitude of modulation.

Time-periodic Heating of a Rotating Horizontal Fluid Layer in a Vertical Magnetic Field

2005 ◽  
Vol 60 (8-9) ◽  
pp. 583-592 ◽  
Author(s):  
Beer Singh Bhadauria
Keyword(s):  
Magnetic Field ◽  
Fluid Layer ◽  
Vertical Axis ◽  
Horizontal Layer ◽  
Vertical Magnetic Field ◽  
Onset Of Convection ◽  
Electrically Conducting ◽  
Dependent Part ◽  
Horizontal Fluid Layer ◽  
Time Periodic

Thermal instability in a horizontal layer of an electrically conducting fluid heated from below has been investigated under the effects of uniform rotation about a vertical axis and an applied uniform vertical magnetic field. The temperature field between the walls of the fluid layer consists of two parts; a steady part and a time-dependent part, which varies periodically. The effect of modulation of the walls temperature on the onset of convection has been studied using Floquets theory. Stabilizing and destabilizing effects on the onset of convective instability have been found. Some comparisons have been made. - 2000 Mathematics Subject Classification: 76E06, 76R10.

Sign in / Sign up

Export Citation Format

Share Document