Energy balance defined

The energy balance defining the temperature is given by Eq. (3-18). It is convenient for numerical solution to write this in terms of the rates of reaction instead of the conversion. This can be done by substituting for dxjdV the quantities in Eqs. (A) and (B). If we take both reactions into account and note that F, dx = F dx, Eq. (3-18) becomes ... 

Starting from the energy conservation equation of the gas phase, we may restore the energy balance defined in the EMMS model. Note that Fjc is defined in the whole dense phase, while Ugc applies only in the gas part of the dense phase, then, for the averaged energy consumption for suspending and transporting particles in any cell. 

Having explored the major degrees of freedom, the material and energy balance is now fixed, and hence the hot and cold streams which contribute to the heat exchanger network are firmly defined. The remaining task is to complete the design of the heat exchanger network. 

In liquid-phase sintering, densification and microstmcture development can be assessed on the basis of the liquid contact or wetting angle, ( ), fonned as a result of the interfacial energy balance at the solid-liquid-vapour intersection as defined by the Young equation ... 

Because of this heat generation, when adsorption takes place in a fixed bed with a gas phase flowing through the bed, the adsorption becomes a non-isothermal, non-adiabatic, non-equilibrium time and position dependent process. The following set of equations defines the mass and energy balances for this dynamic adsorption system [30,31] ... 

Often in plant operations condensate at high pressures are let down to lower pressures. In such situations some low-pressure flash steam is produced, and the low-pressure condensate is either sent to a power plant or is cascaded to a lower pressure level. The following analysis solves the mass and heat balances that describe such a system, and can be used as an approximate calculation procedure. Refer to Figure 2 for a simplified view of the system and the basis for developing the mass and energy balances. We consider the condensate to be at pressure Pj and temperature tj, from whence it is let down to pressure 2. The saturation temperature at pressure Pj is tj. The vapor flow is defined as V Ibs/hr, and the condensate quality is defined as L Ibs/hr. The mass balance derived from Figure 2 is ... 

A common process task involves heating a slurry by pumping it through a well-stirred tank. It is useful to know the temperature profile of the slurry in the agitated vessel. This information can be used to optimize the heat transfer process by performing simple sensitivity studies with the formulas presented below. Defining the inlet temperature of the slurry as T, and the temperature of the outer surface of the steam coil as U then by a macroscopic mass and energy balance for the system, a simplified calculation method is developed. 

A model can be defined as a set of relationships between the variables of interest in the system being investigated. A set of relationships may be in the form of equations the variables depend on the use to which the model is applied. Therefore, mathematical equations based on mass and energy balances, transport phenomena, essential metabolic pathway, and physiology of the culture are employed to describe the reaction processes taking place in a bioreactor. These equations form a model that enables reactor outputs to be related to geometrical aspects and operating conditions of the system. 

The quantity aAp is defined separately for each type of cooling tower. It depends on many variables jet pressure, jet division, airflow velocity, and others. The total energy balance for a cooling tower is (see Fig. 4.19)... 

Before energy balance is calculated, we need to make mass balance. Figure 9.1 shows the material balance for ethanol and glycerol fermentation. Put simply, mass into the system is equal to mass out of die system. The mass of carbon dioxide is calculated by adding mass of dry cell, mass of glycerol, mass of edianol and mass of water at product stream and then subtracting die sum from die feed stream. As a result, die mass of carbon dioxide is defined. The heat of the reaction is calculated by the following equation ... 

Using the digital simulation approach to steady-state design, the design calculation is shown to proceed naturally from the defining component balance and energy balance equations, giving a considerable simplification to conventional text book approaches. 

The RNG model provides its own energy balance, which is based on the energy balance of the standard k-e model with similar changes as for the k and e balances. The RNG k-e model energy balance is defined as a transport equation for enthalpy. There are four contributions to the total change in enthalpy the temperature gradient, the total pressure differential, the internal stress, and the source term, including contributions from reaction, etc. In the traditional turbulent heat transfer model, the Prandtl number is fixed and user-defined the RNG model treats it as a variable dependent on the turbulent viscosity. It was found experimentally that the turbulent Prandtl number is indeed a function of the molecular Prandtl number and the viscosity (Kays, 1994). 

When conjugate heat transfer through solid particles in the tube is to be included, the energy balance must be solved in the solid particles, in addition to the fluid flow regions. The energy balance for a solid region is defined by ... 

Among the above-defined thermodynamic entities, the individual ionic activity coefficients are particularly useful, because they allow practical calculation of the speciation state of an aqueous phase, linking individual ionic molalities to the energy balance. We will see in the following section how these coefficients may be derived. 

These different interpretations of the momentum or energy balances are shown pictorially in Fig. 6. Defining a pressure drop due to interaction of the two phases affords a link between these subdivisions. In Fig. 6, the interesting fact is shown that the total pressure drop may be less than the weight of the contents of the tube because of a negative... 

Before we develop the energy balances for our reactors, it is worthwhile to define some quantities from thermocfynamics because the energy balances we need are thermal energy balances. We begin with the First Law of Thermodynamics,... 

We want to find solutions of these equations. It will be convenient to make the energy-balance equation dimensionless before solving it. As introduced in the previous chapter, we define an almost dimensionless rate of heat generation as... 

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