Effect of Thermal Conductivity and Thickness of the Walls on the Natural Convection in a Horizontal Viscoelastic Jeffreys Fluid Layer

It is a common practice to use ideal thermal boundary conditions to investigate natural convection. These correspond to very good conducting walls and to very bad conducting walls. In particular, this has been the case in natural convection of viscoelastic fluids. In this paper, these conditions are generalized by taking into account the finite thermal conductivities and thicknesses of the walls in the natural convection of a viscoelastic Jeffreys fluid heated from below. The goal is to present more realistic results related to experimental conditions. The critical Rayleigh number Rc, the frequency of oscillation ωc, and the wavenumber kc have been plotted varying the properties of the walls from the case of very good thermal conductivity to very poor thermal conductivity. In order to understand the convective phenomena, two parameters are fixed and the other one varied among the nondimensional relaxation time F, the relative retardation time E, and the Prandtl number Pr of the viscoelastic fluid. The role of the relative retardation time E on the thermal instability is discussed in detail.

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Natural convection in partially divided square enclosures: Effects of thermal boundary conditions and thermal conductivity of the partitions

International Journal of Heat and Mass Transfer ◽

10.1016/j.ijheatmasstransfer.2012.08.004 ◽

2012 ◽

Vol 55 (25-26) ◽

pp. 7812-7822 ◽

Cited By ~ 19

Author(s):

V.A.F. Costa

Keyword(s):

Thermal Conductivity ◽

Natural Convection ◽

Boundary Conditions ◽

Thermal Boundary Conditions

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The effect of a weak heterogeneity of a porous medium on natural convection

Journal of Fluid Mechanics ◽

10.1017/s0022112093002162 ◽

1993 ◽

Vol 254 ◽

pp. 345-362 ◽

Cited By ~ 33

Author(s):

Carol Braester ◽

Peter Vadasz

Keyword(s):

Thermal Conductivity ◽

Porous Medium ◽

Natural Convection ◽

Rayleigh Number ◽

Effective Thermal Conductivity ◽

Critical Rayleigh Number ◽

General Rule ◽

Heterogeneous Porous Media ◽

Smooth Transition ◽

Medium Heterogeneity

The results of an investigation on the effect of a weak heterogeneity of a porous medium on natural convection are presented. A medium heterogeneity is represented by spatial variations of the permeability and of the effective thermal conductivity. As a general rule the existence of horizontal thermal gradients in heterogeneous porous media provides a sufficient condition for the occurrence of natural convection. The implications of this condition are investigated for horizontal layers or rectangular domains subject to isothermal top and bottom boundary conditions. Results lead to a restriction on the classes of thermal conductivity functions which allow a motionless solution. Analytical solutions for rectangular weak heterogeneous porous domains heated from below, consistent with a basic motionless solution, are obtained by applying the weak nonlinear theory. The amplitude of the convection is obtained from an ordinary non-homogeneous differential equation, with a forcing term representative of the medium heterogeneity with respect to the effective thermal conductivity. A smooth transition through the critical Rayleigh number is obtained, thus removing a bifurcation which usually appears in homogeneous domains with perfect boundaries, at the critical value of the Rayleigh number. Within a certain range of slightly supercritical Rayleigh numbers, a symmetric thermal conductivity function is shown to reinforce a symmetrical flow while antisymmetric functions favour an antisymmetric flow. Except for the higher-order solutions, the weak heterogeneity with respect to permeability plays a relatively passive role and does not affect the solutions at the leading order. In contrast, the weak heterogeneity with respect to the effective thermal conductivity does have a significant effect on the resulting flow pattern.

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Thermal Analysis of Multifunctional Satellite Structure-Battery

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.450-451.228 ◽

2012 ◽

Vol 450-451 ◽

pp. 228-234

Author(s):

Yang Wang ◽

Chao Yi Peng

Keyword(s):

Thermal Conductivity ◽

Heat Dissipation ◽

Lithium Ion ◽

Thermal Control ◽

Maximum Temperature ◽

Satellite Structure ◽

Working Environments ◽

Two Parameters ◽

Longitudinal Thermal Conductivity

To make the rapidly developing micro-satellite further smaller and lighter, based on gel polymer lithium-ion battery and high thermal conductivity carbon fiber reinforced epoxy resin composites and polymethacrylimide (PMI) foam, a kind of multifunctional satellite structure-battery (SB) is designed in the paper, and an investigation of its thermal property in certain working environments is carried out by numerical simulation approach. The role of two parameters, longitudinal thermal conductivity of carbon fibers and the heat dissipation area, play in the temperature distribution while the SB is working, is analyzed. The result shows that, enlarging the heat disspation area is an effective way to decrease the maximum temperature of SB and it also implys that by selecting the two parameters carefully, the largest temperature rising of the SB could be considerably lowered, alleviating the burden of satellite thermal control subsystem.

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The Effect of Suction on the Stability of Fluid between Horizontal Plates at Differing Temperatures

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/pime_proc_1985_199_105_02 ◽

1985 ◽

Vol 199 (2) ◽

pp. 145-151 ◽

Cited By ~ 1

Author(s):

M M Sorour ◽

M A Hassab ◽

F A Elewa

Keyword(s):

Rayleigh Number ◽

Fluid Layer ◽

Critical Rayleigh Number ◽

Linear Stability Theory ◽

Stability Criteria ◽

Thermal Boundary Conditions ◽

Wide Range ◽

Fluid Layers ◽

The Stability ◽

Horizontal Fluid Layer

The linear stability theory is applied to study the effect of suction on the stability criteria of a horizontal fluid layer confined between two thin porous surfaces heated from below. This investigation covers a wide range of Reynolds number 0 ≥ Re ≥ 30, and Prandtl number 0.72 ≥ Pr ≥ 100. The results show that the critical Rayleigh number increases with Peclet number, and is independent of Pr as far as Re < 3. However, for Re > 3 the critical Rayleigh number is function of both Pr and Pe. In addition, the analysis is extended to study the effect of suction on the stability of two special superimposed fluid layers. The results in the latter case indicate a more stabilizing effect. Furthermore, the effect of thermal boundary conditions is also investigated.

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Instability of Nanofluids in Natural Convection

Journal of Heat Transfer ◽

10.1115/1.2908427 ◽

2008 ◽

Vol 130 (7) ◽

Cited By ~ 110

Author(s):

D. Y. Tzou

Keyword(s):

Heat Transfer ◽

Thermal Conductivity ◽

Natural Convection ◽

Rayleigh Number ◽

Volume Fraction ◽

Critical Rayleigh Number ◽

Remarkable Change ◽

Closed Form Solutions ◽

Weighted Residuals ◽

Method Of Weighted Residuals

Abstract Instability of natural convection in nanofluids is investigated in this work. As a result of Brownian motion and thermophoresis of nanoparticles, the critical Rayleigh number is shown to be much lower, by one to two orders of magnitude, as compared to that for regular fluids. The highly promoted turbulence, in the presence of nanoparticles for as little as 1% in volume fraction, significantly enhances heat transfer in nanofluids, which may be much more pronounced than the enhancement of the effective thermal conductivity alone. Seven dominating groups are extracted from the nondimensional analysis. By extending the method of eigenfunction expansions in conjunction with the method of weighted residuals, closed-form solutions are derived for the Rayleigh number to justify such remarkable change by the nanoparticles at the onset of instability.

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The Effects of Gravity and Surface Tension Gradients on Cellular Convection in Fluid Layers With Parabolic Temperature Profiles

Journal of Heat Transfer ◽

10.1115/1.3449670 ◽

1970 ◽

Vol 92 (3) ◽

pp. 351-358 ◽

Cited By ~ 13

Author(s):

Walter R. Debler ◽

Louis W. Wolf

Keyword(s):

Surface Tension ◽

Free Surface ◽

Critical Rayleigh Number ◽

Numerical Procedure ◽

Surface Boundary ◽

Thermal Boundary Conditions ◽

Free Surface Boundary Condition ◽

Fluid Layers ◽

Surface Boundary Condition

The effects of surface tension and buoyancy on the convection stability of fluid layers with a mean parabolic temperature distribution is examined. A variety of free-surface, thermal boundary conditions are used. Quantitative values for the effect on the critical Rayleigh number of the free-surface boundary condition, fluid depth, and physical properties are given. The role of the mean temperature profile is also discussed. The results should be of value in judging experiments where a free surface is used to enhance the flow visualization. The numerical procedure used to find the eigenvalues was effective and easily altered to obtain results for similar stability problems.

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Site of Lysosome Production During Hepatic Injury

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100063652 ◽

1969 ◽

Vol 27 ◽

pp. 348-349

Author(s):

Nalin J. Unakar

Keyword(s):

Electron Microscopy ◽

Golgi Apparatus ◽

Mouse Liver ◽

Hepatic Injury ◽

Close Approximation ◽

Experimental Conditions ◽

Toxic Injury

The increased number of lysosomes as well as the close approximation of lysosomes to the Golgi apparatus in tissue under variety of experimental conditions is commonly observed. These observations suggest Golgi involvement in lysosomal production. The role of the Golgi apparatus in the production of lysosomes in mouse liver was studied by electron microscopy of liver following toxic injury by CCI4.

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