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] Mott P. H. , Dorgan J. R. , Roland C. M. ( 2008 ), The bulk modulus and Poisson’s ration of incompressible materials . Journal of Sound and Vibration , 312 , 572 . 572 . [11

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Formulation for Nonlinear Incompressible Elastic and Inelastic Analysis Computers & Structures 26 1–2 357 – 409 . [5]. J

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We consider a compositionally and entropically stratified, compressible, rotating fluid earth and study gravitational-viscoelastic perturbations of its hydrostatic initial state. Using the Lagrangian representation and assuming infinitesimal perturbations, we deduce the incremental field equations and interface conditions of {\em gravitational viscoelastodynamics} (GVED) governing the perturbations. In particular, we distinguish the {\em material}, {\em material-local} and {\em local} forms of the incremental equations. We also demonstrate that their short-time asymptotes correspond to generalizations of the incremental field equations and interface conditions of {\em gravitational elastodynamics} (GED), whereas the long-time asymptotes agree with the incremental field equations and interface conditions of {\em gravitational viscodynamics} (GVD). The incremental thermodynamic pressure appearing in the long-time asymptote to the incremental constitutive equation is shown to satisfy the appropriate incremental state equation. Finally, we derive approximate field theories applying to gravitational-viscoelastic perturbations of isocompositional, isentropic and compressible or incompressible fluid domains.

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Abstract

Heat transfer in gas-solid two-phase flow is investigated numerically and experimentally. The numerical computations are carried out using four-way coupling Eulerian-Lagrangian approach. The effects of particle rotation and lift forces are included in the model. The gas-phase turbulence is modeled via low Reynolds number k-ε turbulence models. The SIMPLE algorithm is extended to take the effect of compressibility into account. The experimental study is performed using crushed limestone to simulate the solid phase. The effects of Reynolds numbers, particles size and temperature on the pressure drop and the temperature of the phases are investigated. The model predictions are found to be in a good agreement with available experimental data for high speed gas-solid flow and present experimental data for low speed flow. The present results indicate that heat transfer in gas solid flow can be modeled using ideal gas incompressible flow model at low conveying speed, while for high speed flow, a full compressible model should be used.

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Abstract

The aim of the paper is to fulfill the parametric analysis on the heating performance of a compact automotive radiator using computational fluid dynamics. The analysis has been carried out at different air velocities with different fins modeling as real fins and as porous media. SC-Tetra computational fluid dynamics software was used for this study. The fluids are incompressible; the flow was three-dimensional and turbulent. The geometry of the fins has a high impact to the heat transfer coefficient and the heat performance, so the shape, the size and the thickness of the fins are compared to each other. The results show that the ratio of the fin pitch, the wall thickness of the fins, the number of the fins, the flow depth and the geometry of the tube are the main factors of the heat transfer. The main goal is to find a dependable Nu-number correlation for this type of heat exchanger. Furthermore with the usage of this function the goal is to find the optimal shape of the radiator, which can decrease the temperature of the cooling liquid to the necessary value and has the smallest weight.

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] Kuzmin D. , Mierka O. , Turek S. On the implementation of the k-ε turbulence model in incompressible flow solvers based on a finite element discretization , Int. J. Computing Science and Mathematics , Vol. 1

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Duality and Perturbation Methods in Critical Point Theory Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow , 2nd ed., Gordon and Breach (New York, 1969

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Applications with historic annotations and many citations from Avogadro to Zermelo (404 pages) ISBN: 978-3-540-74645-4, Springer 2009. Contents: Prologue on ideal gases and incompressible fluids. Objectives of thermodynamics and its equations of

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J.E. Welch 1965 Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface Physics of Fluids 8 2182

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Sanford Klein and Gregory Nellis: Thermodynamics

Cambridge University Press, 1st Edition Printed in the United States of America, 2012, 1102 pp, ISBN: 978-0-521-19570-6

Journal of Thermal Analysis and Calorimetry
Author: Abhishek Saxena

-conserving candidate in any real process. In addition, “entropy change during phase change,” “Entropy relations for ideal gases,” and “Relations for incompressible substances,” are explained well with good examples. To keep track of the “Entropy changes,” “Generation

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