XXV. <i>On the conduction of heat in a spherical mass of air confined by walls at a constant temperature</i>

Rayleigh, Lord

doi:10.1080/14786449908621264

Cited by 22 publications

(7 citation statements)

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“…The gas where Pr is the Prandtl number of the initial state. The dimensionless equations for a compressible, viscous, conducting, inert, perfect gas can be written [11] as p,+(pu)x=0 , (1) p=pT,…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Here dQ/dt=O (1) and Q(0)=0. The solutions are found in terms of asymptotic expansions based on the limit ~ --+ 0.…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The temperature rise associated with heat addition causes a localized gas-expansion process which in turn can generate acoustic effects. Lord Rayleigh [1] provided an early account of acoustic wave generation in a confined gas due to a small impulsive increase in boundary temperature. A linearized energy equation was derived by assuming that disturbances were small and that the transient pressure response was spatially homogeneous.…”

Section: Introductionmentioning

confidence: 99%

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The response of a confined gas to a thermal disturbance: rapid boundary heating

Radhwan

Kassoy

1984

J Eng Math

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Summa~An inert compressible gas confined between infinite parallel planar walls is subjected to significant heat addition at the boundaries. The wall temperature is increased during an interval which is scaled by the acoustic time of the container, defined as the passage time of an acoustic wave across the slab. On this time scale heat transfer to the gas occurs in thin conductive boundary layers adjacent to the walls. Temperature increases in these layers cause the gas to expand such that a finite velocity exists at the boundary-layer edge. This mechanical effect, which is like a time-varying piston motion, induces a planar linear acoustic field in the basically adiabatic core of the slab. A spatially homogeneous pressure rise and a bulk velocity field evolve in the core as the result of repeated passage of weak compression waves through the gas. Eventually the thickness of the conduction boundary layers is a significant fraction of the slab width. This occurs on the condition time scale of the slab which is typically a factor of 106 larger than the acoustic time. The further evolution of the thermomechanical response of the gas is dominated by a conductive-convective balance throughout the slab. The evolving spatially-dependent temperature distribution is affected by the homogeneous pressure rise (compressive heating) and by the deformation process occurring in the confined gas. Superimposed on this relatively slowly-varying conduction-dominated field is an acoustic field which is the descendent of that generated on the shorter time scale. The short-time-scale acoustic waves are distorted as !hey propagate through a slowly-varying inhomogeneous gas in a finite space. Solutions are developed in terms of asymptotic expansions valid when the ratio of the acoustic to conduction time scales is small. The results provide an explicit expression for the piston analogy of boundary heat addition.

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Section: Mathematical Modelmentioning

confidence: 99%

“…Here dQ/dt=O (1) and Q(0)=0. The solutions are found in terms of asymptotic expansions based on the limit ~ --+ 0.…”

Section: Mathematical Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The response of a confined gas to a thermal disturbance: rapid boundary heating

Radhwan

Kassoy

1984

J Eng Math

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“…Rayleigh [1] first approached the idea that a slight variation in temperature can create a mechanical reaction in the form of an acoustic wave in the rest of the fluid. The resulted fluid motion from rapid heating, termed as thermoacoustic convection [2], was numerically investigated by Ozoe et al Through use of matched asymptotic expansions and multiple-time-scale technique, Kassoy [3] and Radhwan and Kassoy [4] conducted pioneering studies on the thermoacoustic interaction in a confined perfect gas under slow and rapid boundary heating.…”

Section: Introductionmentioning

confidence: 99%

On the transition from thermoacoustic convection to diffusion in a near-critical fluid

Shen¹,

Zhang²

2010

International Journal of Heat and Mass Transfer

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“…If eq 5 is solved simultaneously with the equation of conservation for momentum, the continuity equation, and an equation of state that provides for a change of density with temperature, a compressive, slightly supersonic pressure wave is predicted with an accompanying rise in temperature. Rayleigh 8 in 1899 derived an approximate solution for the compressive wave motion in a gas heated instantaneously at a plane but did not associate his results with the anomalous prediction of eq 5. This behavior, which has now been completely resolved both theoretically and experimentally by Brown and Churchill 9 and which occurs with liquids and solids as well as with gases, needs to be accounted for in a practical sense only for the very rapid imposition of a large temperature difference, such as with lightning, for which the pressure wave is evident as thunder.…”

Section: Thermal Conductionmentioning

confidence: 99%

Critical Choice of Variables in the Modeling and Correlation of Mechanisms for Transport and Reaction

Churchill

2002

Ind. Eng. Chem. Res.

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Although the choice of variables is known to be a major factor in the modeling of mechanisms of transport and reaction, as well as in the derivation of analytical solutions, the efficient execution of numerical solutions, and the development of correlating equations thereof, the analysis presented here may be the broadest and most detailed one yet attempted in this context. Although some general principles and methodologies are identified and described herein, the most effective techniques and choices are found to be somewhat specific to the particular technical topic. The illustrative examples of both effective and ineffective choices of variables are taken from fluid flow, chemical conversions, thermal conduction, thermal radiation, and thermal convection because of their general familiarity, but the results are presumed to be applicable to all aspects of chemical engineering and allied topics, both new and old. The techniques identified as most effective are dimensional analysis, the elimination of unimportant variables, the derivation of asymptotes, the introduction of virtual variables, the recognition of analogies, and the critical testing of results with experimental data or computed values. The most underutilized technique is that of speculation: asking the question "What if?". This particular technique is applicable and often effective in conjunction with each of the others.

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XXV. On the conduction of heat in a spherical mass of air confined by walls at a constant temperature

Cited by 22 publications

References 0 publications

The response of a confined gas to a thermal disturbance: rapid boundary heating

The response of a confined gas to a thermal disturbance: rapid boundary heating

On the transition from thermoacoustic convection to diffusion in a near-critical fluid

Critical Choice of Variables in the Modeling and Correlation of Mechanisms for Transport and Reaction

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