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Equations energy equation

In the reactors studied so far, we have shown the effects of variable holdups, variable densities, and higher-order kinetics on the total and component continuity equations. Energy equations were not needed because we assumed isothermal operations. Let us now consider a system in which temperature can change with time. An irreversible, exothermic reaction is carried out in a single perfectly mixed CSTR as shown in Fig. 3.3. [Pg.46]

In order for a model to be closured, the total number of independent equations has to match the total number of independent variables. For a single-phase flow, the typical independent equations include the continuity equation, momentum equation, energy equation, equation of state for compressible flow, equations for turbulence characteristics in turbulent flows, and relations for laminar transport coefficients (e.g., fJL = f(T)). The typical independent variables may include density, pressure, velocity, temperature, turbulence characteristics, and some laminar transport coefficients. Since the velocity of gas is a vector, the number of independent variables associated with the velocity depends on the number of components of the velocity in question. Similar consideration is also applied to the momentum equation, which is normally written in a vectorial form. [Pg.179]

First, we shall assume the system is two-dimensional and that the physical properties, except surface tension and density (in the body force term of the momentum equations) are constant. With these assumptions the continuity equation, momentum equations, energy equations and the diffusion equation are given by... [Pg.51]

Derivation of continuity equation, momentum equations, energy equation, and continuity equations of species in this chapter is based on literature [1,2]. Detailed explanation of conservation equations is beyond the scope of this chapter but further information can be found in literature [1-4]. [Pg.198]

The fluid flow, heat, and mass transfer in fnel ceU are commonly expressed by Navier-Stokes equation, energy equation, mass conservation equation, the associated chemical reaction equations, the charge conservation equation for the current density distribution, and their derivatives [132]. The theoretical maximum electrochemical work that a fuel cell can do may be determined by the Nemst equation as follows ... [Pg.600]

Guffey and Wehe (1972) used excess Gibbs energy equations proposed by Renon (1968a, 1968b) and Blac)c (1959) to calculate multicomponent LLE. They concluded that prediction of ternary data from binary data is not reliable, but that quarternary LLE can be predicted from accurate ternary representations. Here, we carry these results a step further we outline a systematic procedure for determining binary parameters which are suitable for multicomponent LLE. [Pg.73]

Gibbs-Helmholtz equation This equation relates the heats and free energy changes which occur during a chemical reaction. For a reaction carried out at constant pressure... [Pg.190]

Ramsay-Shields equation An equation relating the molecular surface energy of a liquid with its temperature... [Pg.341]

The themiodynamic properties calculated by different routes are different, since the MS solution is an approximation. The osmotic coefficient from the virial pressure, compressibility and energy equations are not the same. Of these, the energy equation is the most accurate by comparison with computer simulations of Card and Valleau [ ]. The osmotic coefficients from the virial and compressibility equations are... [Pg.495]

The osmotic coefficients from the HNC approximation were calculated from the virial and compressibility equations the discrepancy between ([ly and ((ij is a measure of the accuracy of the approximation. The osmotic coefficients calculated via the energy equation in the MS approximation are comparable in accuracy to the HNC approximation for low valence electrolytes. Figure A2.3.15 shows deviations from the Debye-Htickel limiting law for the energy and osmotic coefficient of a 2-2 RPM electrolyte according to several theories. [Pg.497]

If these assumptions are satisfied then the ideas developed earlier about the mean free path can be used to provide qualitative but useful estimates of the transport properties of a dilute gas. While many varied and complicated processes can take place in fluid systems, such as turbulent flow, pattern fonnation, and so on, the principles on which these flows are analysed are remarkably simple. The description of both simple and complicated flows m fluids is based on five hydrodynamic equations, die Navier-Stokes equations. These equations, in trim, are based upon the mechanical laws of conservation of particles, momentum and energy in a fluid, together with a set of phenomenological equations, such as Fourier s law of themial conduction and Newton s law of fluid friction. When these phenomenological laws are used in combination with the conservation equations, one obtains the Navier-Stokes equations. Our goal here is to derive the phenomenological laws from elementary mean free path considerations, and to obtain estimates of the associated transport coefficients. Flere we will consider themial conduction and viscous flow as examples. [Pg.671]

By multiplying this result by a factor of-2, and adding the result to the conservation of energy equation, one easily finds g = gj = v j - vj. This result, taken together widi conservation of angular momentum, x.gb =... [Pg.679]

Th c total en ergy of th e system. called the Hamilton iari, is ih c sum of th e kin elic an d poten tial energies (equation 24). [Pg.69]

Classical mcchan ics involves studying motion (trajectories) on the poten lial surface vh ere the classical kin etic energy equates to th c temperature. The relationship is that the average k in etic cn ergy o f... [Pg.310]

VVe therefore return to the point-charge model for calculating electrostatic interactions. If sufficient point charges are used then all of the electric moments can be reproduced and the multipole interaction energy. Equation (4.30), is exactly equal to that calculated from the Coulomb summation. Equation (4.19). [Pg.205]

Assuming constant physical coefficients for simplicity, the steady-state energy equation is expressed as... [Pg.91]

In the finite element solution of the energy equation it is sometimes necessary to impose heat transfer across a section of the domain wall as a boundary condition in the process model. This type of convection (Robins) boundary condition is given as... [Pg.100]

Working equations of the streamline upwind (SU) scheme for the steady-state energy equation in Cartesian, polar and axisymmetric coordinate systems... [Pg.129]

Following the procedure described in in Chapter 3, Section 3 the streamlined-upwind weighted residual statement of the energy equation is formulated as... [Pg.129]

Similarly in an axisymmetric coordinate system the terms of stiffness and load matrices corresponding to the governing energy equation written as... [Pg.131]

The inconsistent streamline upwind scheme described in the last section is fonuulated in an ad hoc manner and does not correspond to a weighted residual statement in a strict sense. In tins seetion we consider the development of weighted residual schemes for the finite element solution of the energy equation. Using vector notation for simplicity the energy equation is written as... [Pg.131]

Temperature variations are found by the solution of the energy equation. I he finite element scheme used in this example is based on the implicit 0 time-stepping/continuous penalty scheme described in detail in Chapter 4, Section 5. [Pg.145]

Step 5 - the obtained velocity field is used to solve the energy equation (see Chapter 3, Section 3). [Pg.145]

Petrov-Galerkin scheme - to discretize the energy Equation (5.25) for the calculation of T. [Pg.166]


See other pages where Equations energy equation is mentioned: [Pg.325]    [Pg.149]    [Pg.1290]    [Pg.1295]    [Pg.149]    [Pg.304]    [Pg.315]    [Pg.702]    [Pg.485]    [Pg.494]    [Pg.665]    [Pg.722]    [Pg.753]    [Pg.266]    [Pg.465]    [Pg.155]    [Pg.362]    [Pg.3]    [Pg.3]    [Pg.90]    [Pg.91]    [Pg.91]    [Pg.92]    [Pg.92]    [Pg.93]    [Pg.99]    [Pg.100]    [Pg.129]    [Pg.129]    [Pg.146]    [Pg.163]   


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Activation energies from Arrhenius equation

Activation energy defining equation

Activation energy equations

Activation energy permeation equation

Activation energy rate equation parameters

Activation energy, apparent defining equation

Activation free energy Marcus equation

Approximations that further simplify the energy equation

Arrhenius equation activation energy

Arrhenius equation, potential energy surfaces

Balance equation for energy

Basal energy expenditure equations

Bond dissociation energies equation

Boundary layer equations energy

Boundary layer equations turbulent kinetic energy

CCSD energy equation

Chemical equations energy

Chemical equations energy requirement

Condensed-phase energy equation

Conduction equation energy systems

Conservation of Energy and Heat Equation

Conservation of energy equation for a rotating component

Continuity and Energy Equations

Convection energy equation

Conversion energy balance equation

Correlation energy equations estimating

Development of Microscopic Mechanical Energy Equation and Its Application

Differential Equation of Energy Change

Duality of Fundamental Equations Entropy Maximization versus Energy Minimization

Dyson equation, and self energy

Einstein equation vacuum energy

Einstein mass-energy conversion equation

Einstein mass-energy equation

Einstein, Albert energy equation

Einstein, Albert mass energy equation

Einstein’s mass-energy equation

Electrostatic free energies, Poisson-Boltzmann equation

Energy Balance, Bernoulli Equation

Energy Equation in Microgeometries

Energy Equation of the Boundary Layer

Energy Fanning equation

Energy Internal equation

Energy Schrodinger equation

Energy Transfer Equations in Multi-Component Quasi-Equilibrium Plasma-Chemical Systems

Energy balance /equation

Energy balance /equation 664 Subject

Energy balance equation (first law

Energy balance equation, incompressible fluid

Energy balance equation, steady-state

Energy balance equation, steady-state conversion

Energy balance equations equation

Energy budget equations

Energy conservation equation

Energy conservation model equations

Energy density, equations

Energy diffusion equation, generalization

Energy eigenvalues, orbital Schrodinger equation

Energy equation

Energy equation

Energy equation boundary layer, laminar

Energy equation boundary layer, turbulent

Energy equation cartesian coordinates

Energy equation cylindrical coordinates

Energy equation derivation

Energy equation flow work

Energy equation for general steady-state flow

Energy equation forced convection

Energy equation general formulation

Energy equation heat-transfer rate

Energy equation integral

Energy equation porous media

Energy equation specific forms

Energy equation, bubbles

Energy equation, general form

Energy local volume averaged equation

Energy minimization, Hartree-Fock equations

Energy natural variable equations

Energy relationships and the Bernoulli equation

Energy surfaces, model equations

Energy surfaces, model equations Subject

Energy surfaces, model equations quadratic equation

Energy surfaces, model equations shapes

Energy thermochemical equation

Energy transfer equations

Energy transport, wave equation

Energy valence-region, equations

Energy-mass equation

Enthalpy term, energy balance equation

Equation of energy

Equation of thermal energy

Equation, Arrhenius mass-energy

Equations energy dissipation

Equations for mass and energy balance

Equations tearing energy

Equations, mathematical dissociation energy

Excess Gibbs Energy and Activity Coefficient Equations

Excess Gibbs energy Margules equations for

Excess Gibbs energy NRTL equation for

Excess Gibbs energy Porter equation for

Excess Gibbs energy Wilson equations for

Excess Gibbs energy van Laar equations for

Exchange energy equations

Free Energy Equations for Equilibrium Curve Calculations

Free energy equation

Free energy for equation

Free energy relationships, classes equations

Free energy, Gibbs , equations

Free particle energy equation

Fundamental equation for the transformed Gibbs energy

Fundamental equations energy, differential form

Fundamental model equations energy equation

Gas-phase energy equation

Gibbs energies internal energy equation

Gibbs energy Eyring equation

Gibbs energy equation

Gibbs free energy equation, glass transition

Gibbs free energy equation, glass transition polymers

Governing equations of mass and energy balance

Ground state energy equations

Hamiltonian equation energy gradient calculations

Hamiltonian equation zero-point energy

Hammett free-energy equation

Hartree-Fock equation total energy

Hohenberg-Kohn-Sham equations electronic energy

Integral equations Internal energy

Interpretation of the Free Energy Perturbation Equation

Intramolecular energy transfer equations

Inverse Dyson Equation with MP2 Self Energy

Kinetic energy equations

Kinetic energy operator Hamiltonian equations

Kinetic energy operator nuclear motion Schrodinger equation

Kohn-Sham Energy Functional and Equations

Kohn-Sham equations exchange energy

Kohn-Sham equations total energy

Legendre transforms internal energy equation

Linear energy transfer equations

Linear free energy equations

Linear free energy relationship equations

Linear free energy relationships Hammett equation

Mass momentum and energy balance equation

Mechanical energy balance equation

Microscopic Equation of Change for Kinetic Energy

Microscopic Equation of Change for Total Energy

Mixture Properties from Helmholtz Energy Equations of State

Natural variables internal energy equation

Nonadditive kinetic energy functionals equations

Nondimensional energy equation

Nuclear energy Einstein equation

One-Temperature Approach to Vibrational Kinetics and Energy Balance of CO2 Dissociation in Non-Equilibrium Plasma Major Equations

Perturbed Energy Equation for Moderate Peclet Number

Perturbed Energy Equation for Small Peclet Number

Poisson-Boltzmann equation energy models

Potential energy surfaces quantum chemical equations

Potential energy, equation

Quadratic equation, energy surfaces

Quartic equation, energy surfaces

Re-Expressed Equation of Change for Kinetic Energy

Representation of the CCSD Energy Equation

Rotational Energy Equations for the Symmetric Rotor

Schrodinger equation dissociation energy

Schrodinger equation energy spectrum

Schrodinger equation energy transfer

Schrodinger equation lowest-energy wavefunction

Schrodinger equation potential energy

Self-Consistent Single-Particle Equations and Ground-State Energies

Simplified Forms of the General Energy Equation

Smoluchowski equation energy derivation

Solution of the Energy Equation

Some other formulations of the energy equation

Steady-flow energy equation

Steady-state energy equation

Sums in the Energy Equation Modes of Motion

Surface energy Laplace equation

Techniques that use the Laplace equation to measure surface energy

The Boltzmann Equation with Energy Dependence

The CCSD Energy Equation

The Continuity, Energy, and Momentum Equations

The Energy Balance Equation

The Energy Equation

The Energy Equation for Steady Flow

The General Energy Balance Equation

The General Energy Equation

The Gibbs free energy equation

The energy equation for general steady-state flow

Thermal aspects energy equations

Thermal energy conservation equation

Thermal energy equation

Thermal energy equation cylindrical

Thermal energy equation derivation

Thermal energy equation enthalpy form

Thermal energy equation incompressible

Thermal energy equation single component

Thermal transport general energy equation

Thermochemical equations internal energy

Thermodynamic Properties from Helmholtz Energy Equations of State

Thermodynamics internal energy equation

Total energy flow and phenomenological equations

Total energy, equation

Transport equation turbulent kinetic energy

Transport theorem energy equation

Turbulence kinetic energy equation

Turbulent flow energy equation

Turbulent kinetic energy equation

Two-dimensional Model of PBMR - The Energy-balance Equation

Virtual Work Equation, Variational Methods and Energy Principles

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