Energy continued dissipation rate

In the process of calculation, determine flow field whether arrive at convergence according turbulent kinetic energy, turbulence dissipation rate, velocity and residual of continuity equation (Han, Z.Z et al. 2004, Fan, J.R et al. 2001). Suppose residual of the above physical quantity is 1.0 x 10" , flow field arrive at convergence in this numerical simulation. 

This equation expresses the fact that in a process with the various flow rates /, work is continuously dissipated to overcome the barriers, the resistance, or the friction that all the processing such as heat and mass transfer and chemical conversion introduce. In Chapter 5, we refer to this as the result of the "magic triangle." There is no clearer way to illustrate the origin of the process s energy bill, nor a better way to calculate it. This relation also defines the challenge that in order to keep the energy bill as low as possible one should find, as Bejan calls it, "the path of least resistance" [6]. 

As an example, for steady, incompressible, and isothermal turbulent flows using the k- model, the independent equations are (1) the continuity equation, Eq. (5.61) (2) the momentum equation, Eq. (5.65) (3) the definition of the effective viscosity, /xeff (combination of Eq. (5.64) and Eq. (5.72)) (4) the equation of turbulent kinetic energy, Eq. (5.75) and (5) the equation for the dissipation rate of turbulent kinetic energy, Eq. (5.80). Thus, for a three-dimensional model, the total number of independent equations is seven. The corresponding independent variables are (1) velocity (three components) (2) pressure (3) effective viscosity (4) turbulent kinetic energy and (5) dissipation rate of turbulent kinetic energy. Thus, the total number of independent variables is also seven, and the model becomes solvable. 

The value of k a, a being the gas-liquid contact area per unit volume, k the corresponding liquid side mass transfer coefficient, is considerably higher in the pulsing than in the gas-continuous flow regime. It has been tried in the past, and partially success-full, to correlate the mass transfer data to the energy dissipation rate in the bed. We made the premise, that pulses are parts of the bed already in the dispersed bubble flow regime and therefore must accredit for an increase in the transfer rate proportional to their presence in the bed. 

When an enzyme-catalyzed biochemical reaction operating in an isothermal system is in a non-equilibrium steady state, energy is continuously dissipated in the form of heat. The quantity J AG is the rate of heat dissipation per unit time. The inequality of Equation (4.13) means that the enzyme can extract energy from the system and dissipate heat and that an enzyme cannot convert heat into chemical energy. This fact is a statement of the second law of thermodynamics, articulated by William Thompson (who was later given the honorific title Lord Kelvin), which states that with only a single temperature bath T, one may convert chemical work to heat, but not vice versa. 

B. Solid, neutrally buoyant particles, continuous phase coefficient JVS = AA = 2 + 0.471V04 E> d tank/ Graphical comparisons are in Ref. 88, p. 116. [E] Use log mean concentration difference. Density unimportant if particles are close to neutrally buoyant. Also used for drops. Geometric effect (tiimp/titank) is usually unimportant. Ref. 102 gives a variety of references on correlations. [E] E = energy dissipation rate per unit mass fluid PgC AT = TT, P = power, F c V [88] p. 115 [102] p. 132 [152] p. 523... 

Subscript 1 indicates continuous phase and 2 indicates dispersed phase. Cd is a parameter of the standard k-s model (0.09), k is turbulent kinetic energy and si is turbulent energy dissipation rate. The eddy lifetime seen by dispersed phase particles will in general be different from that for continuous phase fluid particles due to the so-called crossing-trajectory effect (Csnady, 1963). This can be expressed in the form ... 

Average energy dissipation rate (or power draw) per mass of mixture, W/kg Maximum energy dissipation rate (or power draw) per mass of mixture, W/kg Volume fraction of dispersed phase, i.e., ratio of the volume of dispersed phase to the volume of dispersed and continuous phases... 

The continuous generation of heat by microbial cultures can also be used as a basis for an on-line monitoring of the microbial activity and metaboUsm. If the temperature increase in the cooling water, its flow rate, and the other relevant energy exchange terms such as agitation and evaporation rates are measured systematically, the heat dissipation rate of the cellular culture can quantitatively be monitored on-line in industrial fermenters. The information contained in this signal can be used to optimize the bioprocess and for on-line process control. 

In the presence of a dispersed phase (e.g., the monomer drops in the suspension polymerization), the turbulent intensity decreases due to the decrease of the velocity fluctuations of the continuous phase [24]. Doulah [25] proposed the following relation to account for the reduction of the energy dissipation rate in the presence of a second dispersed phase ... 

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