Energy equation and stress–dilatancy relationship for sand

2021 ◽  
Author(s):  
Ching S. Chang ◽  
Yibing Deng
Keyword(s):  
2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ituen B. Okon ◽  
E. Omugbe ◽  
Akaninyene D. Antia ◽  
C. A. Onate ◽  
Louis E. Akpabio ◽  
...  

AbstractIn this research article, the modified approximation to the centrifugal barrier term is applied to solve an approximate bound state solutions of Dirac equation for spin and pseudospin symmetries with hyperbolic Hulthen plus hyperbolic exponential inversely quadratic potential using parametric Nikiforov–Uvarov method. The energy eigen equation and the unnormalised wave function were presented in closed and compact form. The nonrelativistic energy equation was obtain by applying nonrelativistic limit to the relativistic spin energy eigen equation. Numerical bound state energies were obtained for both the spin symmetry, pseudospin symmetry and the non relativistic energy. The screen parameter in the potential affects the solutions of the spin symmetry and non-relativistic energy in the same manner but in a revised form for the pseudospin symmetry energy equation. In order to ascertain the accuracy of the work, the numerical results obtained was compared to research work of existing literature and the results were found to be in excellent agreement to the existing literature. The partition function and other thermodynamic properties were obtained using the compact form of the nonrelativistic energy equation. The proposed potential model reduces to Hulthen and exponential inversely quadratic potential as special cases. All numerical computations were carried out using Maple 10.0 version and Matlab 9.0 version softwares respectively.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nadeem Ahmad Sheikh ◽  
Dennis Ling Chuan Ching ◽  
Ilyas Khan ◽  
Hamzah Bin Sakidin ◽  
Muhammad Jamil ◽  
...  

AbstractThe present work used fractional model of Casson fluid by utilizing a generalized Fourier’s Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.


2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Adriano Sciacovelli ◽  
Vittorio Verda

The aim of the paper is to investigate possible design modifications in tubular solid oxide fuel cell geometry to increase its performance. The analysis of the cell performances is conducted on the basis of the entropy generation. The use of this technique makes it possible to identify the phenomena provoking the main irreversibilities, understand their causes and propose changes in the system design and operation. The different contributions to the entropy generation are analyzed in order to develop new geometries that increase the fuel cell efficiency. To achieve this purpose, a CFD model of the cell is used. The model includes energy equation, fluid dynamics in the channels and in porous media, current transfer, chemical reactions, and electrochemistry. The geometrical parameters of the fuel cell are modified to minimize the overall entropy generation.


1983 ◽  
Vol 126 ◽  
pp. 307-313 ◽  
Author(s):  
S. S. Chawla ◽  
A. R. Verma

An exact solution of the free convective flow of a viscous incompressible fluid from a heated disk, rotating in a vertical plane, is obtained. The non-axisymmetric fluid motion consists of two parts; the primary von Kármán axisymmetric flow and the secondary buoyancy-induced cross-flow. A highly accurate solution of the energy equation is also derived for its subsequent use in the analysis of the cross-flow.


1992 ◽  
Vol 114 (3) ◽  
pp. 540-551 ◽  
Author(s):  
Hsing-Sen S. Hsiao ◽  
Bernard J. Hamrock

A complete solution is obtained for elastohydrodynamically lubricated conjunctions in line contacts considering the effects of temperature and the non-Newtonian characteristics of lubricants with limiting shear strength. The complete fast approach is used to solve the thermal Reynolds equation by using the complete circular non-Newtonian fluid model and considering both velocity and stress boundary conditions. The reason and the occasion to incorporate stress boundary conditions for the circular model are discussed. A conservative form of the energy equation is developed by using the finite control volume approach. Analytical solutions for solid surface temperatures that consider two-dimensional heat flow within the solids are used. A straightforward finite difference method, successive over-relaxation by lines, is employed to solve the energy equation. Results of thermal effects on film shape, pressure profile, streamlines, and friction coefficient are presented.


2013 ◽  
Vol 141 (8) ◽  
pp. 2869-2896 ◽  
Author(s):  
Matthew C. Brewer ◽  
Clifford F. Mass ◽  
Brian E. Potter

Abstract Despite the significant impacts of the West Coast thermal trough (WCTT) on West Coast weather and climate, questions remain regarding its mesoscale structure, origin, and dynamics. Of particular interest is the relative importance of terrain forcing, advection, and surface heating on WCTT formation and evolution. To explore such questions, the 13–16 May 2007 WCTT event was examined using observations and simulations from the Weather Research and Forecasting (WRF) Model. An analysis of the thermodynamic energy equation for these simulations was completed, as well as sensitivity experiments in which terrain or surface fluxes were removed or modified. For the May 2007 event, vertical advection of potential temperature is the primary driver of local warming and WCTT formation west of the Cascades. The downslope flow that drives this warming is forced by easterly flow associated with high pressure over British Columbia, Canada. When the terrain is removed from the model, the WCTT does not form and high pressure builds over the northwest United States. When the WCTT forms on the east side of the Cascades, diabatic heating dominates over the other terms in the thermodynamic energy equation, with warm advection playing a small role. If surface heat fluxes are neglected, an area of low pressure remains east of the Cascades, though it is substantially attenuated.


Lubricants ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 44
Author(s):  
Christian Ziese ◽  
Cornelius Irmscher ◽  
Steffen Nitzschke ◽  
Christian Daniel ◽  
Elmar Woschke

The vibration behaviour of turbocharger rotors is influenced by the acting loads as well as by the type and arrangement of the hydrodynamic bearings and their operating condition. Due to the highly non-linear bearing behaviour, lubricant film-induced excitations can occur, which lead to sub-synchronous rotor vibrations. A significant impact on the oscillation behaviour is attributed to the pressure distribution in the hydrodynamic bearings, which is influenced by the thermo-hydrodynamic conditions and the occurrence of outgassing processes. This contribution investigates the vibration behaviour of a floating ring supported turbocharger rotor. For detailed modelling of the bearings, the Reynolds equation with mass-conserving cavitation, the three-dimensional energy equation and the heat conduction equation are solved. To examine the impact of outgassing processes and thrust bearing on the occurrence of sub-synchronous rotor vibrations separately, a variation of the bearing model is made. This includes run-up simulations considering or neglecting thrust bearings and two-phase flow in the lubrication gap. It is shown that, for a reliable prediction of sub-synchronous vibrations, both the modelling of outgassing processes in hydrodynamic bearings and the consideration of thrust bearing are necessary.


1997 ◽  
Vol 119 (3) ◽  
pp. 405-411 ◽  
Author(s):  
R. E. Mayle ◽  
A. Schulz

A theory is presented for calculating the fluctuations in a laminar boundary layer when the free stream is turbulent. The kinetic energy equation for these fluctuations is derived and a new mechanism is revealed for their production. A methodology is presented for solving the equation using standard boundary layer computer codes. Solutions of the equation show that the fluctuations grow at first almost linearly with distance and then more slowly as viscous dissipation becomes important. Comparisons of calculated growth rates and kinetic energy profiles with data show good agreement. In addition, a hypothesis is advanced for the effective forcing frequency and free-stream turbulence level that produce these fluctuations. Finally, a method to calculate the onset of transition is examined and the results compared to data.


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