Energy Balances for Steady-State Flow Processes

Energy Balances for Steady-State Flow Processes... 

The general energy balance for steady-state flow processes is given by Eq. (7.8) ... 

Energy Balances for Steady-State Flow Processes Flow processes for which the first term of Eq. (4-149) is zero are said to occur at steady state. As discussed with respect to the mass balance, this means that the mass of the system within the control volume is constant it also means that no changes occur with time in the properties of the fluid within the control volume or at its entrances and exits. No expansion of the control volume is possible under these circumstances. The only work of the process is shaft work, and the general energy balance, Eq. (4-149), becomes... 

For step 1, a steady-state flow process, the energy balance is... 

Process energy balances are established using the first law of thermodynamics. It has the following form for a steady-state flow process where kinetic and potential energy contributions are neglected ... 

The energy balance for a steady-state steady-flow process resulting from the first law of thermodynamics is... 

We now take up the problem of estimating the heat transfer coefficients and the energy flux E in turbulent flow in a tube. As in our analysis of the corresponding mass transfer problem (Chapter 10), we consider the transfer processes between a cylindrical wall and a turbulently flowing n-component fluid mixture. We examine the phenomena occurring at any axial position in the tube, assuming that fully developed flow conditions are attained. For steady-state conditions, the differential energy balance (Eqs. 11.1.1 and 11.1.2) takes the form... 

A typical set of the required five variables would be the temperatures and pressures of the inlet and outlet water streams, T, Tg, P, and Pg, plus the inlet water flow rate N. With values for these five variables, we can solve the steady-state material balance for the outlet water flow rate (the inlet and outlet mass flow rates are equal here) and we can solve the steady-state energy balance for Q. In this example the value computed for the heat duty is the actual value for the real process, regardless of reversibility, because the process is workfree. However, in the general case, when heat and work both cross a system boundary, the energy balance gives only their sum. Variations on this problem are also possible for example, if we knew values for the five variables T, Tg, P, Pg and Q, then we could solve the energy balance for the required water flow rate. Or, if we knew T, P, P , Q, and N, then we could solve for the outlet water temperature Tg. 

The common shower presents us with the opportunity to present a simple example to highlight the operability issue. Although simple, this example of mixing two streams of hot and cold water is very representative of a typical industrial blending operation. For this process, the inputs Ui and 2 are the flow of cold water Qi and hot water q2, and the outputs yi and are the total flow F and the combined temperature T. For steady-state analysis, it is assumed that the temperatures of the input streams are constant at Ti of 15°C and T2 of 50"C. The energy and material balance equations are written as... 

Additionally, there is process simulation steady-state flow sheet simulators and dynamic flow sheet simulators. Steady-state flow sheet simulators have been widely used in chemical process engineering since the 1960s. Steady-state simulators describe the process as a set of modules connected by flows of material and energy between them. The modules correspond to mass and energy balances together with physical and thermodynamic data necessary for calculations. The calculations may be performed using one of two basic techniques. The sequential approach computes modules one by one, in a direction that generally follows that of the physical flows in the system (Leiviska, 1996). 

A useful interpretation of feedforward control is that it continually attempts to balance the material or energy that must be delivered to the process against the demands of the disturbance (Shinskey, 1996). For example, the level control system in Fig. 15.3 adjusts the feedwater flow so that it balances the steam demand. Thus, it is natural to base the feedforward control calculations on material and energy balances. For simplicity, we will first consider designs based on steady-state balances using physical variables rather than deviation variables. Design methods based on dynamic models are considered in Section 15.4. 

This forms the basis of constructing an enthalpy budget in which the total enthalpy flux is compared with the scalar heat flux, 7q(W m-3), obtained from dividing heat flow by size (volume or mass) of the living matter. If account is made of all the reactions and side reactions in metabolism, the ratio of heat flux to enthalpy flux, the so-called energy recovery ( Yq/H = Jq/Jh) will equal 1. If it is more than 1, then the chemical analysis has failed fully to account for heat flux and if it is less than 1, then there are undetected endothermic reactions. Account for all reactions may seem a formidable task, but it should be borne in mind that anabolic processes dissipate insignificant amounts of heat compared with those of catabolism and that ATP production and utilization are balanced in cells at steady-state. Catabolism is generally limited to a relatively few well-known pathways with established overall molar enthalpies. So, as will be seen later, the task is by no means mission impossible. ... 

The general form of the mechanical energy balance can be derived starting with the open-system balance and a second equation expressing the law of conservation of momentum, a derivation beyond the scope of this book. This section presents a simplified form for a single incompressible liquid flowing into and out of a process system at steady state. 

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