FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W1896804526> ?p ?o ?g. }

• W1896804526 abstract "Part I Grad's thirteen moment method is applied to the problem of the shear flow and heat conduction between two concentric, rotating cylinders of infinite length. In order to concentrate on the effects of curvature the problem is linearized by requiring that the Mach number is small compared with unity, and that the temperature difference between the two cylinders is small compared with the mean temperature. The solutions of the linearized Grad equations show a qualitatively correct transition of the cylinder drag from free-molecule flow to the classical Navier-Stokes regime. However the magnitude of the curvature effect on the drag in rarefied flow is not given correctly, because Grad's distribution function ignores the wedge-like domains of influence of the two cylinders. The solution obtained for the heat transfer rate is physically unrealistic in the free-molecule flow limit, and this result is produced by a cross-coupling between the normal stresses and the radial heat flux imposed by Grad's distribution function. In this simple problem the difficulty can be eliminated by taking the normal stresses to be identically zero and employing a truncated moment method. However, in general this device cannot be utilized in problems involving curved solid boundaries, or when dissipation is considered. One concludes that the choice of the distribution function to be employed in Maxwell's moment equations is dictated by the requirements imposed in the limiting case of highly rarefied gas flows, as well as in the Navier-Stokes regime. Part II In this paper, the unsteady one-dimensional flow of a compressible, viscous and heat conducting fluid is treated, based on linearized Grad's thirteen moment equations. The fluid, initially at rest, is set into motion by some small external disturbances. Our interest is to examine the nature of all the responses. The fluid field extends to infinity in both directions; thus no length is involved, and also there is no solid wall boundary existing in the problem. The nature of the external disturbances is restricted to having a unit impulse in the momentum equation and a unit heat addition in the energy equation. The disturbances are located on an infinite plane normal to the flow direction; and the responses induced correspond to fundamental solutions of the problem. The method of Laplace transforms is applied, and the inverse transforms of all quantities are obtained in integral form. Because of the complicated expressions of the integrands involved, we consider only certain limiting cases which correspond to small and large times from the start of the motion, compared to the average time between molecular collisions. In order to study these limiting cases, it is essential to understand the behavior of the integrand in the complex plane; hence all singularities and branch points are obtained. When t is small, the integrand is expanded in powers of t to obtain a wave front approximation. All discontinuities are propagated along the characteristics of the linearized system, and a damping term also appears. At large values of time, the integrand gets its main contribution around the branch points, and these solutions are identical to those obtained from the Navier-Stokes equation. The fundamental solution of the one-dimensional unsteady flow, idealized as it seems to be, offers itself as a tool to understand other related problems. The piston problem, as well as the normal quantities in Rayleigh's problem (e.g., normal velocity, normal stress, and thermodynamical quantities), are governed by the same set of equations. Hence, certain parts of the fundamental solutions can be applied directly to these problems. The limiting forms of the normal quantities in Rayleigh's problem are expected to be worked out in another paper in the near future." @default.
• W1896804526 created "2016-06-24" @default.
• W1896804526 creator A5035836295 @default.
• W1896804526 date "1961-01-01" @default.
• W1896804526 modified "2023-09-27" @default.
• W1896804526 title "Part I. Cylindrical Couette Flow in a Rarefied Gas According to Grad's Equation. Part II. Small Perturbations in the Unsteady Flow of a Rarefied Gas Based on Grad's Thirteen Moment Approximation" @default.
• W1896804526 doi "https://doi.org/10.7907/9p2n-hf23." @default.
• W1896804526 hasPublicationYear "1961" @default.
• W1896804526 type Work @default.
• W1896804526 sameAs 1896804526 @default.
• W1896804526 citedByCount "0" @default.
• W1896804526 crossrefType "dissertation" @default.
• W1896804526 hasAuthorship W1896804526A5035836295 @default.
• W1896804526 hasConcept C121332964 @default.
• W1896804526 hasConcept C134306372 @default.
• W1896804526 hasConcept C159188206 @default.
• W1896804526 hasConcept C165231844 @default.
• W1896804526 hasConcept C172100665 @default.
• W1896804526 hasConcept C179254644 @default.
• W1896804526 hasConcept C195065555 @default.
• W1896804526 hasConcept C2524010 @default.
• W1896804526 hasConcept C2779099160 @default.
• W1896804526 hasConcept C33923547 @default.
• W1896804526 hasConcept C38349280 @default.
• W1896804526 hasConcept C50517652 @default.
• W1896804526 hasConcept C57879066 @default.
• W1896804526 hasConcept C72921944 @default.
• W1896804526 hasConcept C74650414 @default.
• W1896804526 hasConcept C97355855 @default.
• W1896804526 hasConceptScore W1896804526C121332964 @default.
• W1896804526 hasConceptScore W1896804526C134306372 @default.
• W1896804526 hasConceptScore W1896804526C159188206 @default.
• W1896804526 hasConceptScore W1896804526C165231844 @default.
• W1896804526 hasConceptScore W1896804526C172100665 @default.
• W1896804526 hasConceptScore W1896804526C179254644 @default.
• W1896804526 hasConceptScore W1896804526C195065555 @default.
• W1896804526 hasConceptScore W1896804526C2524010 @default.
• W1896804526 hasConceptScore W1896804526C2779099160 @default.
• W1896804526 hasConceptScore W1896804526C33923547 @default.
• W1896804526 hasConceptScore W1896804526C38349280 @default.
• W1896804526 hasConceptScore W1896804526C50517652 @default.
• W1896804526 hasConceptScore W1896804526C57879066 @default.
• W1896804526 hasConceptScore W1896804526C72921944 @default.
• W1896804526 hasConceptScore W1896804526C74650414 @default.
• W1896804526 hasConceptScore W1896804526C97355855 @default.
• W1896804526 hasLocation W18968045261 @default.
• W1896804526 hasOpenAccess W1896804526 @default.
• W1896804526 hasPrimaryLocation W18968045261 @default.
• W1896804526 hasRelatedWork W1540709125 @default.
• W1896804526 hasRelatedWork W1638275404 @default.
• W1896804526 hasRelatedWork W1932869643 @default.
• W1896804526 hasRelatedWork W1978588322 @default.
• W1896804526 hasRelatedWork W1984183505 @default.
• W1896804526 hasRelatedWork W1987428703 @default.
• W1896804526 hasRelatedWork W2003164741 @default.
• W1896804526 hasRelatedWork W2017859233 @default.
• W1896804526 hasRelatedWork W2024776514 @default.
• W1896804526 hasRelatedWork W2031849705 @default.
• W1896804526 hasRelatedWork W2054758423 @default.
• W1896804526 hasRelatedWork W2066907111 @default.
• W1896804526 hasRelatedWork W2095966023 @default.
• W1896804526 hasRelatedWork W2187668095 @default.
• W1896804526 hasRelatedWork W2271814178 @default.
• W1896804526 hasRelatedWork W2321403863 @default.
• W1896804526 hasRelatedWork W2325516608 @default.
• W1896804526 hasRelatedWork W385657017 @default.
• W1896804526 hasRelatedWork W974436787 @default.
• W1896804526 hasRelatedWork W2130403379 @default.
• W1896804526 isParatext "false" @default.
• W1896804526 isRetracted "false" @default.
• W1896804526 magId "1896804526" @default.
• W1896804526 workType "dissertation" @default.