scholarly journals Application of an Innovate Energy Balance to Investigate Viscoelastic Problems

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Saeed Shahsavari ◽  
Mehran Moradi
Keyword(s):  
Energy Balance ◽  
Energy Distribution ◽  
Total Energy ◽  
Nonlinear Problems ◽  
Residual Energy ◽  
Conservation Equation ◽  
Energy Conservation Equation ◽  
Linear Viscoelastic ◽  
Inertial Energy ◽  
Energy Components

Modeling and investigating of energy distribution especially the wasted one is very important in viscoelastic problems. In this article, an applied energy model based on separation of energy components of the system is extracted and expanded to apply in linear viscoelastic problems, although this method is applicable in nonlinear problems as well. It is assumed that the whole energy of the system can be divided into two parts: Residual and non-inertial energies. The non-inertial energy is the sum of the energies that do not depend on the inertia of the system, while residual energy is the remaining of total energy. When an amount of energy is applied to the system, by determining the non-inertial energy from a novel energy conservation equation, the residual energy can be calculated. Some basic viscoelastic examples are investigated and obtained results will be compared with the expected ones.  

scholarly journals An Energy Conservation Algorithm for Nonlinear Dynamic Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Jian Pang ◽  
Yu Du ◽  
Ping Hu ◽  
Weidong Li ◽  
Z. D. Ma
Keyword(s):  
Energy Conservation ◽  
Nonlinear Problems ◽  
Current Method ◽  
Conservation Equation ◽  
Iteration Formula ◽  
Energy Conservation Equation ◽  
Numerical Result ◽  
Nonlinear Dynamic Equation ◽  
Runge Kutta Method ◽  
Runge Kutta

An energy conservation algorithm for numerically solving nonlinear multidegree-of-freedom (MDOF) dynamic equations is proposed. Firstly, by Taylor expansion and Duhamel integration, an integral iteration formula for numerically solving the nonlinear problems can be achieved. However, this formula still includes a parameter that is to be determined. Secondly, through some mathematical manipulations, the original dynamical equation can be further converted into an energy conservation equation which can then be used to determine the unknown parameter. Finally, an accurate numerical result for the nonlinear problem is achieved by substituting this parameter into the integral iteration formula. Several examples are used to compare the current method with the well-known Runge-Kutta method. They all show that the energy conservation algorithm introduced in this study can eliminate algorithm damping inherent in the Runge-Kutta algorithm and also has better stability for large integral steps.

Nonlinear Thermal Vibration Analysis of a Thin Laminated Microstructure

2005 ◽  
Author(s):  
Xiaoling He
Keyword(s):  
Steady State ◽  
Total Energy ◽  
Transient State ◽  
Mechanical Analysis ◽  
Conservation Equation ◽  
Thermal Buckling ◽  
Thermal Fields ◽  
Energy Conservation Equation ◽  
Transient Thermal ◽  
Laminated Structures

Nonlinear deformation can occur in thin laminated structures due to thermal fields present in the laminates. Thermally induced laminate response in buckling and vibration has been previously studied in nonlinear dynamics by approximations that compromise the total energy of the system. In this paper, this problem is studied based on the nonlinear thermal mechanical analysis of a thin laminated structure using a Galerkin type approach, with total energy conservation. Equation of motion for laminates in orthotropic and isotropic structures in thermal buckling response in a simply supported boundary condition is obtained in a decoupled modal form of the Duffing equation, with consideration of both non-uniform in-plane and transverse temperature variations, in steady state and transient state. Analysis is made for the thermal buckling behavior of an isotropic laminate with respect to the steady-state and transient thermal fields. In particular, chaos and instability due to the transient thermal field are investigated.

Heat Transfer Analysis of a Novel Pressurized Air Receiver for Concentrated Solar Power via Combined Cycles

2009 ◽  
Vol 1 (4) ◽  
Author(s):  
I. Hischier ◽  
D. Hess ◽  
W. Lipiński ◽  
M. Modest ◽  
A. Steinfeld
Keyword(s):  
Heat Transfer ◽  
Thermal Efficiency ◽  
Porous Ceramic ◽  
Conservation Equation ◽  
Heat Transfer Analysis ◽  
Operational Parameters ◽  
Small Aperture ◽  
Solar Absorber ◽  
Energy Conservation Equation ◽  
Combined Cycles

A novel design of a high-temperature pressurized solar air receiver for power generation via combined Brayton–Rankine cycles is proposed. It consists of an annular reticulate porous ceramic (RPC) bounded by two concentric cylinders. The inner cylinder, which serves as the solar absorber, has a cavity-type configuration and a small aperture for the access of concentrated solar radiation. Absorbed heat is transferred by conduction, radiation, and convection to the pressurized air flowing across the RPC. A 2D steady-state energy conservation equation coupling the three modes of heat transfer is formulated and solved by the finite volume technique and by applying the Rosseland diffusion, P1, and Monte Carlo radiation methods. Key results include the temperature distribution and thermal efficiency as a function of the geometrical and operational parameters. For a solar concentration ratio of 3000 suns, the outlet air temperature reaches 1000°C at 10 bars, yielding a thermal efficiency of 78%.

Energy conservation, time-reversal invariance and reciprocity in ducts with flow

2001 ◽  
Vol 431 ◽  
pp. 223-237 ◽  
Author(s):  
WILLI MÖHRING
Keyword(s):  
Energy Conservation ◽  
Sound Wave ◽  
Conservation Equation ◽  
Smooth Transition ◽  
Rotational Flow ◽  
Flow Energy ◽  
Energy Conservation Equation ◽  
Reversal Invariance ◽  
Edge Conditions ◽  
Piecewise Continuous

A sound wave propagating in an inhomogeneous duct consisting of two semi-infinite uniform ducts with a smooth transition region in between and which carries a steady flow is considered. The duct walls may be rigid or compliant. For an irrotational sound wave it is shown that the three properties of the title are closely related, such that the validity of any two implies the validity of the third. Furthermore it is shown that the three properties are fulfilled for lossless locally reacting duct walls provided the impedance varies at most continuously. For piecewise-continuous wall properties edge conditions are essential. By an analytic continuation argument it is shown that reciprocity remains true for walls with loss. For rotational flow, energy conservation theorems have been derived only with the help of additional potential-like variables. The inter-relation between the three properties remains valid if one considers these additional variables to be known. If only the basic gasdynamic variables in both half-ducts are known, one cannot formulate an energy conservation equation; however, reciprocity is fulfilled.

scholarly journals Total energy expenditure assessed by salivary doubly labelled water analysis and its relevance for short-term energy balance in humans

2015 ◽  
Vol 30 (1) ◽  
pp. 143-150 ◽  
Author(s):  
Stefano Guidotti ◽  
Berthe M. A. A. A. Verstappen-Dumoulin ◽  
Henk G. Jansen ◽  
Anita T. Aerts-Bijma ◽  
André A. van Vliet ◽  
...  
Keyword(s):  
Energy Balance ◽  
Energy Expenditure ◽  
Total Energy ◽  
Water Analysis ◽  
Total Energy Expenditure ◽  
Short Term ◽  
Doubly Labelled Water ◽  
Term Energy

scholarly journals INDOOR AIR TEMPERATURE DISTRIBUTION – AN ALTERNATIVE APPROACH TO BUILDING SIMULATION

2003 ◽  
Vol 2 (1) ◽  
Author(s):  
A. T. Franco ◽  
C. O. R. Negrão
Keyword(s):  
Temperature Distribution ◽  
Air Temperature ◽  
Indoor Air ◽  
Linear Equations ◽  
Three Dimensional ◽  
Momentum Conservation ◽  
Conservation Equation ◽  
Algebraic Equations ◽  
Conservation Of Energy ◽  
Energy Conservation Equation

The current paper presents a model to predict indoor air temperature distribution. The approach is based on the energy conservation equation which is written for a certain number of finite volumes within the flow domain. The magnitude of the flow is estimated from a scale analysis of the momentum conservation equation. Discretized two or three-dimensional domains provide a set of algebraic equations. The resulting set of non-linear equations is iteratively solved using the line-by-line Thomas Algorithm. As long as the only equation to be solved is the conservation of energy and its coefficients are not strongly dependent on the temperature field, the solution is considerably fast. Therefore, the application of such model to a whole building system is quite reasonable. Two case studies involving buoyancy driven flows were carried out and comparisons with CFD solutions were performed. The results are quite promising for cases involving relatively strong couplings between heat and airflow.

scholarly journals A Two-Layer Model for Steady-Amplitude Gravity Waves and Convection Generated by a Thermal Forcing

2018 ◽  
Vol 75 (7) ◽  
pp. 2199-2216 ◽  
Author(s):  
A. A. M. Sayed ◽  
L. J. Campbell
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Stable Stratification ◽  
Internal Gravity Waves ◽  
Conservation Equation ◽  
Lower Atmosphere ◽  
Thermal Forcing ◽  
Energy Conservation Equation ◽  
Vertical Location ◽  
Convective Cells

Abstract A two-dimensional two-layer mathematical model is described representing internal gravity waves and convection generated by a thermal forcing in the lower atmosphere. The model consists of an upper layer with stable stratification, a lower layer with unstable stratification, and a thermal forcing in the form of a nonhomogeneous term in the energy conservation equation. Exact analytical solutions are derived for some simple configurations. Depending on the vertical location and depth of the thermal forcing, the model can be used to represent different configurations in which gravity waves are generated by diabatic heating. When the thermal forcing is centered in the lower layer, convective cells are generated in the lower layer, and gravity waves are forced and propagate upward from the interface between the two layers. When the thermal forcing is centered at the interface, the convection in the lower layer is weaker, and gravity waves are forced by the direct effect of the thermal forcing in the upper layer and the influence of the convective cells below. Steady-amplitude solutions for the vertical profile of the gravity waves and convection are derived and generalized to include cases where there is a spectrum of horizontal wavenumbers or vertical wavenumbers or frequencies present.

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