Fluxes, heat

The reformer heat flux is t5q)ically defined as the heat input per unit of time per square unit of inside tube surface. For a given absorbed duty, the heat flux is therefore determined by the amoimt of tube surface. 

A low heat flux provides extra catalyst volume and lower tubewall temperatures. This provides several advantages The extra catalyst volume increases the reforming reaction conversion. The lower tubewall temperature reduces the tubewall thickness, which in turn reduces the cost per tube and increases the tube life. The lower tubewall temperature also reduces the fuel requirement. 

A high heat flux has the opposite effect, but has the advantage of reducing the number of tubes. 

Because of these trade-offs, commercial heat fluxes t5q)ically vary from 

The above fluxes are average values for the entire fiimace. The point flux is highest in the zone of maximum heat release, and then falls off to a relatively low value at the tube outlet. The maximum point flux is often 35,000 to 40,000 Btu/hr-ft2. 

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A proposal based on Onsager s theory was made by Landau and Lifshitz [27] for the fluctuations that should be added to the Navier-Stokes hydrodynamic equations. Fluctuating stress tensor and heat flux temis were postulated in analogy with the Onsager theory. Flowever, since this is a case where the variables are of mixed time reversal character, tlie derivation was not fiilly rigorous. This situation was remedied by tlie derivation by Fox and Ulilenbeck [13, H, 18] based on general stationary Gaussian-Markov processes [12]. The precise fomi of the Landau proposal is confimied by this approach [14]. 

The lack of correlation between the flucUiating stress tensor and the flucUiating heat flux in the third expression is an example of the Curie principle for the fluctuations. These equations for flucUiating hydrodynamics are arrived at by a procedure very similar to that exliibited in the preceding section for difllisioii. A crucial ingredient is the equation for entropy production in a fluid... 

Figure Bl.27.11. Schematic diagram of a Tian-Calvet heat-flux or heat-conduction calorimeter.

Figure 3.5 Virtual element layer for the imposition of boundary heat flux...

Also lefeiied to by many other symbols with various heat fluxes as reference. 

Fig. 4. Physical zones of ablators. Typical time-integrated heat flux, J/m, (a) 500, (b) 5000, (c) <50 maximum instantaneous heat flux, MW/m, (a) 0.5,...

The nonconvective energy flux across the boundary is composed of two terms a heat flux and a work term. The work term in turn is composed of two terms useful work deflvered outside the fluid, and work done by the fluid inside the control volume B on fluid outside the control volume B, the so-called flow work. The latter may be evaluated by imagining a differential surface moving with the fluid which at time 2ero coincides with a differential element of the surface, S. During the time dt the differential surface sweeps out a volume V cosdSdt and does work on the fluid outside at a rate of PV cos dS. The total flow work done on the fluid outside B by the fluid inside B is... 

NUh2 is the Nusselt number for uniform heat flux boundary condition along the flow direction and periphery. 

A second property, closely related to the first, is the abiHty of the heat pipe to effect heat-flux transformation. As long as the total heat flow is ia equiHbrium, the fluid streams connecting the evaporatiag and condensing regions essentially are unaffected by the local power densities ia these two... 

Seldom is the temperature difference across the wall thickness of an item of equipment known. Siace large temperature gradients may occur ia the boundary layers adjacent to the metal surfaces, the temperature difference across the wall should not be estimated from the temperatures of the fluids on each side of the wall, but from the heat flux usiag equation 27... 

Chemical Reaction Measurements. Experimental studies of incineration kinetics have been described (37—39), where the waste species is generally introduced as a gas in a large excess of oxidant so that the oxidant concentration is constant, and the heat of reaction is negligible compared to the heat flux required to maintain the reacting mixture at temperature. The reaction is conducted in an externally heated reactor so that the temperature can be controlled to a known value and both oxidant concentration and temperature can be easily varied. The experimental reactor is generally a long tube of small diameter so that the residence time is well defined and axial dispersion may be neglected as a source of variation. Off-gas analysis is used to track both the disappearance of the feed material and the appearance and disappearance of any products of incomplete combustion. 

The combustor is assembled of flanged, spool-shaped water-cooled metal components, each with its own water-cooling circuit and pressure shell. No ceramic linings are used. Gas pressure is contained by stainless steel outer shells and the internal surfaces subject to high heat fluxes are lined with low alloy water-cooled panels. 

Operation of a reactor in steady state or under transient conditions is governed by the mode of heat transfer, which varies with the coolant type and behavior within fuel assembHes (30). QuaHtative understanding of the different regimes using water cooling can be gained by examining heat flux, q, as a function of the difference in temperature between a heated surface and the saturation temperature of water (Eig. 1). 

Fig. 1. Variation of heat flux, with temperature difference between heated wall, and saturation temperature of water, in regions where A...

Larger-si2ed heaters are usually hori2ontal box heaters. The radiant coils can be located either on the side walls so that the units are fired from underneath, or in a center row of tubes in which the heater is fired from both sides to provide a higher heat flux for reducing the radiant surface. An access area at one end of the box is required in order to remove the tubes. Sometimes multiple coils are included in the same box, which may require access to both ends of the box. 

Artificial surfaces must be resistant to cigarette bums, vandaUsm, and other harm. Fire resistance is most critically evaluated by the NBS flooring radiant panel test (10). In this test, a gas-fired panel maintains a heat flux, impinging on the sample to be tested, between 1.1 W/cm at one end and 0.1 W/cm at the other. The result of the bum is reported as the flux needed to sustain flame propagation in the sample. Higher values denote greater resistance to burning results depend on material and surface constmction. Polypropylene turf materials are characterized by critical radiant flux indexes which are considerably lower than those for nylon and acryflc polymers (qv) (11). 

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