Nonlinear Thermal Instability in a Rotating Viscous Fluid Layer Under Temperature/Gravity Modulation

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
B. S. Bhadauria ◽  
P. G. Siddheshwar ◽  
Om P. Suthar
Keyword(s):  
Viscous Fluid ◽  
Heat Transport ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Landau Equation ◽  
Effect Of Temperature ◽  
Stationary Mode ◽  
Gravity Modulation ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear

In the present paper, the effect of time-periodic temperature/gravity modulation on the thermal instability in a rotating viscous fluid layer has been investigated by performing a weakly nonlinear stability analysis. The disturbances are expanded in terms of power series of amplitude of modulation, which has been assumed to be small. The amplitude equation, viz., the Ginzburg–Landau equation, for the stationary mode of convection is obtained and using the same, the effect of temperature/gravity modulation on heat transport has been investigated. The stability of the system is studied and the stream lines are plotted at different slow times as a function of the amplitude of modulation, Rossby number, and Prandtl number. It is found that the temperature/gravity modulation can be used as an external means to augment/diminish heat transport in a rotating system. Further, it is shown that rotation can be effectively used in regulating heat transport.

Weakly Nonlinear Oscillatory Convection in a Rotating Fluid Layer Under Temperature Modulation

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Palle Kiran ◽  
B. S. Bhadauria
Keyword(s):  
Heat Transport ◽  
Fluid Layer ◽  
Landau Equation ◽  
Complex Form ◽  
Oscillatory Mode ◽  
Temperature Modulation ◽  
Rotating Fluid ◽  
Nonlinear Stability Analysis ◽  
Ginzburg Landau ◽  
Weakly Nonlinear

A study of thermal instability driven by buoyancy force is carried out in an initially quiescent infinitely extended horizontal rotating fluid layer. The temperature at the boundaries has been taken to be time-periodic, governed by the sinusoidal function. A weakly nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of the Nusselt number, which is governed by the complex form of Ginzburg–Landau equation (CGLE), is calculated. The influence of external controlling parameters such as amplitude and frequency of modulation on heat transfer has been investigated. The dual effect of rotation on the system for the oscillatory mode of convection is found either to stabilize or destabilize the system. The study establishes that heat transport can be controlled effectively by a mechanism that is external to the system. Further, the bifurcation analysis also presented and established that CGLE possesses the supercritical bifurcation.

scholarly journals The Complex Ginzburg Landau Model for an Oscillatory Convection in a Rotating Fluid Layer

2020 ◽  
Vol 25 (1) ◽  
pp. 75-91
Author(s):  
S.H. Manjula ◽  
P. Kiran ◽  
P. Raj Reddy ◽  
B.S. Bhadauria
Keyword(s):  
Heat Transfer ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Landau Equation ◽  
Finite Amplitude ◽  
Oscillatory Mode ◽  
Stationary Mode ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Speed Modulation

AbstractA weakly nonlinear thermal instability is investigated under rotation speed modulation. Using the perturbation analysis, a nonlinear physical model is simplified to determine the convective amplitude for oscillatory mode. A non-autonomous complex Ginzburg-Landau equation for the finite amplitude of convection is derived based on a small perturbed parameter. The effect of rotation is found either to stabilize or destabilize the system. The Nusselt number is obtained numerically to present the results of heat transfer. It is found that modulation has a significant effect on heat transport for lower values of ωf while no effect for higher values. It is also found that modulation can be used alternately to control the heat transfer in the system. Further, oscillatory mode enhances heat transfer rather than stationary mode.

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.

Throughflow and G-Jitter Effects on Oscillatory Convection in a Rotating Porous Medium

2020 ◽  
Vol 12 (6) ◽  
pp. 781-791
Author(s):  
S. H. Manjula ◽  
Palle Kiran ◽  
B. S. Bhadauria
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transport ◽  
Landau Equation ◽  
Nonlinear Stability Analysis ◽  
Periodic Mode ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Analysis ◽  
The Impact

The impact of vertical throughflow and g-jitter effect on rotating porous medium is investigated. A feeble nonlinear stability analysis associate to complex Ginzburg-Landau equation (CGLE) has been studied. This weakly nonlinear analysis performed for a periodic mode of convection and quantified heat transport in terms of the Nusselt number, which is governed by the non-autonomous advanced CGLE. Each idea, rotation and throughflow is used as an external mechanism to the system either to extend or decrease the heat transfer. The results of amplitude and frequency of modulation on heat transport are analyzed and portrayed graphically. Throughflow has dual impact on heat transfer either to increase or decrease heat transfer in the system. Particularly the outflow enhances and inflow diminishes the heat transfer. High centrifugal rates promote heat transfer and low centrifugal rates diminish heat transfer. The streamlines and isotherms area portrayed graphically, the results of rotation and throughflow on isotherms shows convective development.

Convection in an Anisotropic Porous Medium with Temperature Dependent Viscosity and Throughflow under G-jittera

2017 ◽  
Vol 3 (01) ◽  
Author(s):  
B. S. Bhadauria ◽  
Ajay Singh
Keyword(s):  
Nusselt Number ◽  
Heat Transport ◽  
Variable Viscosity ◽  
Landau Equation ◽  
Power Series Expansion ◽  
Stationary Mode ◽  
Rheological Parameter ◽  
Gravity Modulation ◽  
Temperature Dependent Viscosity ◽  
Anisotropic Porous Media

In the present article, we study the combined effect of variable viscosity and throughflow in an anisotropic porous media under gravity modulation by reducing the model equations into Ginzgburg-Landau equation. A weakly non-linear stability analysis has been performed by adopting power series expansion in terms of the amplitude (assumed to be small) of gravity modulation. The Nusselt number is obtained in terms of the amplitude for the stationary mode of convection. Heat transfer mechanism is done by Nusselt number by taking different parameters, and depicted it graphically. Further, it is found that on increasing the value of thermo-rheological parameter, heat transport is more in the system. An increment in the amplitude (frequency) of gravity modulation enhances (diminishes) the heat transport. The behavior of Vadasz number, anisotropic parameters, and Peclet number are also studied.

scholarly journals Concordancing in ESP Class Rooms

2014 ◽  
Vol 4 (3) ◽  
pp. 434-439
Author(s):  
Sameh Benna ◽  
Olfa Bayoudh
Keyword(s):  
Rayleigh Number ◽  
Heat Transport ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Linear Analysis ◽  
Wave Number ◽  
Gravity Modulation ◽  
Non Linear ◽  
The Stability ◽  
Time Periodic

The effect of time periodic body force (or g-jitter or gravity modulation) on the onset of Rayleigh-Bnard electro-convention in a micropolar fluid layer is investigated by making linear and non-linear stability analysis. The stability of the horizontal fluid layer heated from below is examined by assuming time periodic body acceleration. This normally occurs in satellites and in vehicles connected with micro gravity simulation studies. A linear and non-linear analysis is performed to show that gravity modulation can significantly affect the stability limits of the system. The linear theory is based on normal mode analysis and perturbation method. Small amplitude of modulation is used to compute the critical Rayleigh number and wave number. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation. The non-linear analysis is based on the truncated Fourier series representation. The resulting non-autonomous Lorenz model is solved numerically to quantify the heat transport. It is observed that the gravity modulation leads to delayed convection and reduced heat transport.

scholarly journals Weakly Nonlinear Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium with Throughflow and Temperature Modulation

2018 ◽  
Vol 23 (3) ◽  
pp. 635-653 ◽  
Author(s):  
P. Kiran ◽  
Y. Narasimhulu ◽  
S.H. Manjula
Keyword(s):  
Porous Medium ◽  
Heat Transport ◽  
Viscoelastic Fluid ◽  
Saturated Porous Medium ◽  
Landau Equation ◽  
Oscillatory Mode ◽  
Stationary Mode ◽  
Temperature Modulation ◽  
Through Flow ◽  
Fluid Saturated Porous Medium

Abstract The effect of vertical throughfow and temperature modulation on a viscoelastic fluid saturated porous medium has been investigated. The amplitudes of temperature modulation at the lower and upper surfaces are considered to be very small and the disturbances are expanded in terms of power series of amplitude of convection. A weak nonlinear stability analysis has been performed for the oscillatory mode of convection, and heat transport in terms of the Nusselt number, which is governed by the non autonomous complex Ginzburg- Landau equation, is calculated. The effect of vertical through flow is found to stabilize the system irrespective of the direction of through flow in the case of permeable boundary conditions. The time relaxation has a destabilizing effect, while the time retardation parameter has a stabilizing effect on the system. The effects of amplitude and frequency of modulation on heat transport have been analyzed and depicted graphically. The study shows that the heat transport can be controlled effectively by a mechanism that is external to the system. Further, it is also found that heat transfer is more in oscillatory mode of convection rather than in stationary mode of convection.

Weakly Nonlinear Stability Analysis of a Thin Liquid Film With Condensation Effects During Spin Coating

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
C. K. Chen ◽  
M. C. Lin
Keyword(s):  
Liquid Film ◽  
Spin Coating ◽  
Multiple Scales ◽  
Landau Equation ◽  
Thin Liquid Film ◽  
Kinematic Model ◽  
Circular Disk ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
The Stability

This paper investigates the stability of a thin liquid film with condensation effects during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. The weakly nonlinear dynamics of a film flow are studied by the multiple scales method. The Ginzburg–Landau equation is determined to discuss the necessary conditions of the various states of the critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that decreasing the rotation number and the radius of the rotating circular disk generally stabilizes the flow.

scholarly journals Effect of Soret and Temperature Dependent Viscosity on Thermohaline Convection in a Ferrofluid Saturating a Porous Medium

2014 ◽  
Vol 19 (2) ◽  
pp. 321-336
Author(s):  
R. Sekar ◽  
K. Raju
Keyword(s):  
Porous Medium ◽  
Fluid Layer ◽  
Effect Of Temperature ◽  
Stationary Mode ◽  
Free Boundaries ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Onset Of Convection ◽  
Wide Range ◽  
Dependent Viscosity

Abstract Soret driven ferrothermoconvective instability in multi-component fluids has a wide range of applications in heat and mass transfer. This paper deals with the theoretical investigation of the effect of temperature dependent viscosity on a Soret driven ferrothermohaline convection heated from below and salted from above subjected to a transverse uniform magnetic field in the presence of a porous medium. The Brinkman model is used in the study. It is found that the stationary mode of instability is preferred. For a horizontal fluid layer contained between two free boundaries an exact solution is examined using the normal mode technique for a linear stability analysis. The effect of salinity has been included in magnetization and density of the fluid. The critical thermal magnetic Rayleigh number for the onset of instability is obtained numerically for sufficiently large values of the buoyancy magnetization parameter M1 using the method of numerical Galerkin technique. It is found that magnetization and permeability of the porous medium destabilize the system. The effect of temperature dependent viscosity stabilizes the system on the onset of convection.

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