Thermal instability of an internally heated fluid layer in a magnetic field

Yu, C.P.; Shih, Yang-Cheng

doi:10.1063/1.862988

Cited by 11 publications

(5 citation statements)

References 4 publications

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“…Therefore, the role of internal heat generation becomes very important in several applications including storage of radioactive materials, combustion and fire studies, geophysics, reactor safety analysis and metal waste form development for spent nuclear fuel. However, there are only few studies available in which the effect of internal heating on convective flow in a fluid layer has been investigated [34][35][36][37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source

Bhadauria

Kiran

2014

Ain Shams Engineering Journal

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In this paper, a theoretical investigation has been carried out to study the combined effect of rotation speed modulation and internal heating on thermal instability in a temperature dependent viscous horizontal fluid layer. Rayleigh-Be´nard momentum equation with Coriolis term has been considered to describe the convective flow. The system is rotating about it is own axis with non-uniform rotational speed. In particular, a time-periodic and sinusoidally varying rotational speed has been considered. A weak nonlinear stability analysis is performed to find the effect of modulation on heat transport. Nusselt number is obtained in terms of amplitude of convection and internal Rayleigh number, and depicted graphically for showing the effects of various parameters of the system. The effect of modulated rotation speed is found to have a stabilizing effect for different values of modulation frequency. Further, internal heating and thermo-rheological parameters are found to destabilize the system. Ó 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.

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Section: Introductionmentioning

confidence: 99%

Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source

Bhadauria

Kiran

2014

Ain Shams Engineering Journal

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“…Thus rescale the time t by using the time scale τ ¼ ϵ 2 t. Now, to study the stationary convection of the system, we write the non-linear equations (17) and (18) …”

Section: Mathematical Formulation Of the Problemmentioning

confidence: 99%

“…However, there are relatively very few studies available in which the effect of internal heating on convective flow has been investigated. Some of these studies are Roberts [14], Tveitereid and Palm [15], Tveitereid [16], Yu and Shih [17], Bhattacharya and Jena [18], Takashima [19], Tasaka and Takeda [20], and Joshi et al [21].…”

Section: Introductionmentioning

confidence: 99%

Effect of internal-heating on weakly non-linear stability analysis of Rayleigh–Bénard convection under g-jitter

Bhadauria¹,

Hashim²,

Siddheshwar³

2013

International Journal of Non-Linear Mechanics

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a b s t r a c tIn this paper, we study the combined effect of internal-heating and time-periodic gravity modulation on thermal instability in a viscous fluid layer, heated from below. The time-periodic gravity modulation, considered in this problem can be realized by vertically oscillating the fluid layer. A weak non-linear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number has been obtained in terms of the amplitude of convection which is governed by the non-autonomous Ginzburg-Landau equation derived for the stationary mode of convection. Effects of various parameters such as internal Rayleigh number, Prandtl number, and amplitude and frequency of gravity modulation have been analysed on heat transport. It is found that the response of the convective system to the internal Rayleigh number is destabilizing. Further, it is found that the heat transport can be controlled by suitably adjusting the external parameters of the system.

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“…Our study shows that the thermal stability of Newtonian nanofluids depends on six parameters: , , , , and .To validate our method, we compared our results with those obtained by Yu and Shih [30] concerning the onset of convective instability which is induced by a purely internal heating in a non-rotating layer of a regular fluid confined between two isothermal rigid boundaries without taking into account the radiation heat transfer mode ( Table 1) .To make this careful comparison , we must take into consideration the following restrictions : …”

Section: Validation Of the Methodsmentioning

confidence: 99%

“…The used method gives results with an absolute error of the order of 10 −3 to the critical values characterizing the onset of the convection. To show the accuracy of our method in this study, we will check some results treated by Yu and Shih [30] concerning the onset of convective instability which is induced by a purely internal heating in a non-rotating layer of a regular fluid confined between two isothermal rigid-rigid boundaries without taking into account the radiation heat transfer mode.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of a Thermal Convection Induced by a Purely Internal Heating in a Rotating Medium Saturated by a Radiating Nanofluid

Wakif¹,

Boulahia²,

Sehaqui³

2016

IJCA

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In this paper, we use the Buongiorno's mathematical model for studying numerically the convective instability which is induced by a purely internal heating in a rotating medium confined between two isothermal surfaces and filled of a Newtonian nanofluid layer (water + alumina) in the case where the radiation heat transfer mode is taken into consideration, such that the nanoparticle flux is zero on the boundaries. The linear study which was achieved in this investigation shows that the thermal stability of nanofluids depends of the Coriolis forces generated by the rotation of the system, the thermal radiation parameter, the Brownian motion, the thermophoresis of nanoparticles and other thermophysical properties of nanoparticles. The studied problem will be solved by converting our boundary value problem to an initial value problem, after this step we will approach numerically the searched solutions using the power series method (PSM).

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Thermal instability of an internally heated fluid layer in a magnetic field

Abstract: The onset of thermal instability of an electrically conducting fluid layer subjected to volumetric heating and bounded between two rigid surfaces in the presence of a magnetic field is considered. The stability conditions are found for different thermal boundary conditions.

Cited by 11 publications

References 4 publications

Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source

Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source

Effect of internal-heating on weakly non-linear stability analysis of Rayleigh–Bénard convection under g-jitter

Numerical Study of a Thermal Convection Induced by a Purely Internal Heating in a Rotating Medium Saturated by a Radiating Nanofluid

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