Heat term energy balance

In terms of the average specific heat, this energy balance can be rewritten as ... 

The analysis of the heat exchanger network first identifies sources of heat (termed hot streams) and sinks (termed cold streams) from the material and energy balance. Consider first a very simple problem with just one hot stream (heat source) and one cold stream (heat sink). The initial temperature (termed supply temperature), final temperature (termed target temperature), and enthalpy change of both streams are given in Table 6.1. 

Referring to the schematic diagram in Figure 2-81, it is clear that the thermal energy balance should include terms AH and AH, which represent the sensible heats necessary to raise the temperatures of reactants and products from to T,. Thus,... 

Finally, the energy available from the above reaction might be used to operate a fuel cell such as those involved in the space program. In that case, as much as 818 kj/mol of useful electrical work could be obtained relatively litde heat is evolved. Summarizing this discussion in terms of an energy balance (per mole of methane reacting) ... 

This section is concerned with the UA xtiT — Text) term in the energy balance for a stirred tank. The usual and simplest case is heat transfer from a jacket. Then A xt refers to the inside surface area of the tank that is jacketed on the outside and in contact with the fluid on the inside. The temperature difference, T - Text, is between the bulk fluid in the tank and the heat transfer medium in the jacket. The overall heat transfer coefficient includes the usual contributions from wall resistance and jacket-side coefficient, but the inside coefficient is normally limiting. A correlation applicable to turbine, paddle, and propeller agitators is... 

A heat exchange term is added to the energy balance. Equation (5.30), to give... 

Separating the energy balance into heat loss and heat generation terms Rate of heat loss (Hl) = Rate of heat generation (Hq)... 

The energy aspects can be considered in terms of the enthalpy change of the process, AH to produce 1 mole of product. The energy balance for the process is as follows, assuming all the energy is initially provided by heat ... 

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). 

The input and output terms of equation 1.5-1 may each have more than one contribution. The input of a species may be by convective (bulk) flow, by diffusion of some kind across the entry point(s), and by formation by chemical reaction(s) within the control volume. The output of a species may include consumption by reaction(s) within the control volume. There are also corresponding terms in the energy balance (e.g., generation or consumption of enthalpy by reaction), and in addition there is heat transfer (2), which does not involve material flow. The accumulation term on the right side of equation 1.5-1 is the net result of the inputs and outputs for steady-state operation, it is zero, and for unsteady-state operation, it is nonzero. 

Equations similar to 12.3-10 to -15 may be written in terms of internal energy, U, with Cv, the heat capacity at constant volume, replacing CP. For liquid-phase reactions, the difference between the two treatments is small. Since most single-phase reactions carried out in a BR involve liquids, we continue to write the energy balance in terms of H, but, if required, it can be written in terms of U. In the latter case, it is usually necessary to calculate AU from AH and Cv from CP, since AH and CP are the quantities listed in a database. Furthermore, regardless of which treatment is used, it may be necessary to take into account the dependence of AH (or AU) and CP (or C,) on T ... 

Equation 12.3-16 is valid whether heat is transferred to or from the system, and whether the reaction is exothermic or endothermic. Note that each term on the left side of equation 12.3-16 may be an input or an output. Furthermore, CP is the molar heat capacity of the system, and is given by equation 12.3-13 as such, it may depend on both T and composition (through /A). The right side of equation 12.3-16 may also be expressed on a specific-mass basis (12.3-11). This does not affect the consistency of the units of the terms in the energy balance, which are usually J s-1. 

For nonadiabatic operation and an exothermic reaction, the overall situation is similar, but is complicated by the inclusion of the heat transfer term for Q in the energy balance in equation 14.3-10. 

To relate fA and T, we require the energy balance (15.2-9). From this equation, for adiabatic operation (the heat transfer term on right side vanishes),... 

For reactions involving heat effects, the total and component material balance equations must be coupled with a reactor energy balance equation. Neglecting work done by the system on the surroundings, the energy balance is expressed by where each term has units of kj/s. For steady-state operation the accumulation... 

With high concentrations, heat effects in the chromatographic column may be important. This would require the simultaneous application of an energy balance and the introduction of a term reflecting the influence of temperature on the adsorption equilibrium. 

In general, the cell energy balance states that the enthalpy flow of the reactants entering the cell will equal the enthalpy flow of the products leaving the cell plus the sum of three terms (1) the net heat generated by physical and chemical processes within the cell, (2) the dc power output from the cell, and the rate of heat loss from the cell to its surroundings. 

In this work, the goal is to design a control function in such a manner that neither the reaction heat nor kinetic nor mass transfer terms are required for stabilizing temperature. The scheme provides an estimated value of the heat generation from energy balance. Alkylation isobutane/propylene using sulfuric... 

Among the three heat-generation terms, the irreversible and reversible heat sources of ORR are dominant. For a straight-channel cell shown in Figure 12, the total amount of heat release is 2.57 W, of which the irreversible heat is 55.3%, the reversible heat 35.4%, and the Joule heat only 9.3% The total heat released from the fuel cell can also be estimated from the overall energy balance, i.e. 

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