Steady-state energy equation

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

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

Conservation Equations The computational model consists of steady-state energy equation describing conductive and convective heat transfer from the hot and cold fluids to the solid part of the heat exchanger with the following... 

The next approach incorporates the energy equation (Wagner, 1976). By assuming no heat transfer at the inner surface the steady-state energy equation (Eq. 9.38) takes the following form (see also Eq. 9.47) ... 

In defining the thermal efficiency of the closed gas turbine cycle, such as the one shown in Fig. 1.2, we employed the first law of thermodynamics (in the form of the steady-flow energy equation round the cycle), which states that the heat supplied is equal to the work output plus the heat rejected, i.e. 

From the steady-flow energy equation, the work output in an actual (irreversible) flow through a control volume CV, between states X and Y in the presence of an environment at To (Fig. 2.2), is... 

For a real (irreversible) flow process through the control volume CV between fluid states X and Y (Fig. 2.4), with the same heat rejected at temperature T [Q x = [0rev]x)> the work output is [WcvJx. Heat [Qq x Iso be transferred from CV directly to the environment at Tq. From the steady-flow energy equation,... 

In the simplified a/s analysis of Section 4.2 we assumed identical and constant specific heats for the two streams. Now we assume semi-perfect gases with specific heats as functions of temperature but we must also allow for the difference in gas properties between the cooling air and the mainstream gas (combustion products). Between entry states (mainstream gas 3g, and cooling air, 2c) and exit state 5m (mixed out), the steady flow energy equation, for the flow through control surfaces (A + B) and C, yields, for a stationary blade row,... 

Consider a section of uniform cylindrical pipe of length L and radius R, inclined upward at an angle 0 to the horizontal, as shown in Fig. 6-2. The steady-state energy balance (or Bernoulli equation) applied to an incompressible fluid flowing in a uniform pipe can be written... 

Recall from Chapter 6 that the steady-state energy-balance equations in a CSTR can be reduced to a single equation, which we wrote by considering the rates of heat generation and removal. We wrote these as... 

Beginning with the full Navier-Stokes and thermal-energy equations equations in differential-equation form, eliminate all appropriate terms. Write out the steady-state differential equations that describe this situation. 

Determining the conversion of monomer can only be as accurate as the method of quantifying the heat liberated from the reaction. The usual method is to take the difference between the inlet and outlet jacket water temperatures multiplied by the specific heat and flow rate of the water. This steady-state energy balance equation is ... 

In this section, we implement the radial basis function method in the energy equation and apply the technique to an example problem. We begin with a steady-state energy balance given by... 

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. 

The steady-state energy balance equation may be obtained by setting dT/dt equal to zero in Equation 11.3-12. 

We will now consider flow systems that are operated at steady state. The steady-state energy balance is obtained by setting dE yJdt) equal to zero in Equation (S-9) in order to yield... 

Substituting Equation (8-26) into Equation (8-22), the steady-state energy balance becomes... 

For multiple reactions occurring in either a semibatch or batch reactor, Equation (9-18) can be generalized in the same manner as the steady-state energy balance, to give... 

The steady flow energy equation states that the upstream stagnation enthalpy, Hi = (h + + gz)i, differs from the downstream value H2 only... 

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