Third-Order Constitutive Equations and Transport in Rarefied Gases
Abstract
A description of transport of either heat, momentum, or mass in the transition regime is based upon third-order constitutive equations for the fluxes. The one-dimensional steady-state equation which governs the dependent variable P* (either dimensionless temperature, velocity, or concentration) as a function of distance x* is the linearized fourth-order differential equationN2(d4P*/dx*4) + (d2P*/dx*2)=0,where N is proportional to the Knudsen number. A solution is proposed based on reasonable boundary conditions for parallel plate geometry. Expressions are derived for the profile of P*, the slip or jump of P* at a wall, the effective transport coefficient, and the flux. The expressions have the proper limits for the continuum and free molecule regimes, and compare well with other theories for the transition regime and with subsonic experimental data.
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Several other forms are provided in the literature to estimate the effective thermal conductivity of an insulation material, such as using accommodation coefficient and/or coupling terms between the gas and solid.
“Similarly, several other forms are provided in literature to estimate the effective thermal conductivity of an insulation material such as using accommodation coefficient and/or coupling terms between the gas and solid [19,23,48,84,94].”
From Effective thermal conductivity of insulation materials for cryogenic LH2 storage tanks: A review (2023) · cites this paper as [19]
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Effective thermal conductivity of insulation materials for cryogenic LH2 storage tanks: A review
Ratnakar, R. R., Sun, Z., & Balakotaiah, V. (2023) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2022.11.130 · Cited by 73 · see citing works
- Authors
- Cha, C. Y., & McCoy, B. J.
- Affiliations
- University of California, Davis (US)
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 1972-04-01
- Volume
- 56
- Issue
- 7
- Pages
- 3265-3273
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2030824562
- Cited by
- 12
- References
- 0
- Citations by year
- 2024: 1 · 2022: 1 · 2014: 1
- FWCI
- 2.40
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Journal of Chemical Physics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Gas Dynamics and Kinetic Theory
- Physical Sciences › Engineering › Computational Mechanics › Fluid dynamics and aerodynamics studies
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Vacuum and Plasma Arcs
- Keywords
- rarefied gas, transition regime, heat transport, momentum transfer, mass transfer, Knudsen number, parallel plate geometry, slip boundary conditions, jump boundary conditions, effective transport coefficients, subsonic flow
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