Heat flow entries

For the common problem of heat transfer between a fluid and a tube wall, the boundary layers are limited in thickness to the radius of the pipe and, furthermore, the effective area for heat flow decreases with distance from the surface. The problem can conveniently be divided into two parts. Firstly, heat transfer in the entry length in which the boundary layers are developing, and, secondly, heat transfer under conditions of fully developed flow. Boundary layer flow is discussed in Chapter 11. 

Comparison of the thermal conductivities of prolate (p) and oblate (o) nematic liquid crystals. The entries for zero field have been obtained by using the Green-Kubo relation (3.3). The entries for finite field have been obtained by applying the heat flow algorithm (3.5). Note that the EMD GK estimates and the NEMD estimates agree within the statistical error. 

Finally, the true mean heat transfer coefficient that also takes into account the laminar flow entry length effect is given by ... 

A reversible cycle with turbine expansion split into two steps (high pressure, HP, and low pressure, LP) is illustrated in the T, s diagram of Fig. 4.3. The mass flow through the heater is still unity and the temperature rises from T2 to Tt, = Tq hence the heat supplied (3b is unchanged, as is the overall isentropic temperature ratio (x). But cooling air of mass flow i//H is used at entry to the first HP turbine (of isentropic temperature ratio. xh) and additional cooling of mass flow is introduced subsequently into the LP turbine (of isentropic temperature ratio Xl)- The total cooling flow is then i/( = i/ h + >h.-... 

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,... 

Fig. 6.2 shows a simplified diagram of the basic STIG plant with steam injection S per unit air flow into the combustion chamber the state points are numbered. Lloyd 2 presented a simple analysis for such a STIG plant based on heat input, work output and heat rejected (as though it were a closed cycle air and water/steam plant, with external heat supplied instead of combustion and the exhaust steam and air restored to their entry conditions by heat rejection). His analysis is adapted here to deal with an open cycle plant with a fuel input/to the combustion chamber per unit air flow, at ambient temperature To, i.e. a fuel enthalpy flux of/7i,o. For the combustion chamber, we may write... 

Eq. (6.16) is essentially the same as Eq. (6.8) for the basic STIG plant which, on reflection, is not surprising. If the states 1,2, 3, 4 and 5 and the steam quantity S are all the same then expressions for the work output, the heat input (or fuel energy supply) and the heat rejected are all unchanged. The total amount of heat transferred from the exhaust is also unchanged, but two separate flows, of air and of water/steam, have been raised in enthalpy before entry to the combustion chamber, rather than one (water/steam) in the earlier analysis. 

Figure 26.3 shows the relationship between port diameter and fluid velocity at 4 and 7 m/s and highlights the nominal maximum velocities for various plates. As the flow through the machine increases, the entry and exit pressure losses also increase. The nominal maximum flow rate for a plate heat exchanger limits these losses to an acceptable proportion of the total pressure losses, and is therefore a function not only of the port diameter but... 

At the CISE Laboratories in Milan, where the phenomenon of fast and slow burn-out was first noted, the onset of random temperature oscillations has in itself been assumed to signify burn-out, the implication being that temperature oscillations always occur [Bertoletti et ah (BI9) and Alessandrini et al. (A5)]. However, the CISE experiments have in the past been carried out with preformed mixtures of steam and water at entry to a heated test channel, and it is possible that this feature, which is known to produce flow disturbances (see Section III), may be the reason for the fact that temperature oscillations always occur. 

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. 

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