Total heat flux

Choose the characteristic velocity m so, that total heat flux on the wall is fully expended for liquid evaporation (the heating without any losses of heat r = 1). We conclude that... 

Figure 128 shows a simple heat exchanger that exchanges heat supplied by fluid 2 to heat up fluid 1 while flowing along the heat exchanger surface. For such heat exchangers, it is known that the total heat flux from fluid 2 to... 

The latent heat transport accounts for only 2% of the total heat flux in this case. However, it was observed by several investigators that the total heat transfer rate is proportional to this value, <7, lenl, because it is proportional to the bubble volume and the number of bubbles that cause intense agitation of the liquid layer close to the surface. This agitation, termed microconvection, together with the liquid-vapor exchange, were considered to be the key to excellent characteristics of boiling heat transfer (Forster and Greif, 1959). 

The total heat flux from the entire boiling surface can be expressed as... 

The other parameters in Eqs. (67) and (68) are evaluated in the same manner as in Section II,B,3, with the single exception of qwn. The evaluation of the wall heat flux for nucleate boiling in flowing systems has been described briefly in the reviews by Westwater (W4, W5) and Leppert and Pitts (L2). Less quantitative information is available for this case than for pool boiling. According to these authors, the heat flux in forced-convection nucleation is independent of the fluid velocity. Westwater (W5) and Roh-senow (R1) have presented a number of correlations for calculating the total heat flux in forced-convection nucleation the general form of these correlations is... 

It is clear that in this microcalorimeter, only a fraction of the outside wrall of the inner vessel is covered by thermoelectric elements. Consequently, only a part of the total heat flux emitted by the cell is detected. This may be the cause of a systematic error which, however, can be avoided if the heat transfer via the thermoelectric elements constitutes a constant fraction of the total, irrespective of the process taking place in the calorimeter cell. The present version of the Petit microcalorimeter can be used only at moderate temperatures (<100°C), mainly because some components of the thermoelectric elements wrould be damaged at higher temperatures. 

The total heat flux emitted by the area (S + S ), is therefore ... 

For n identical thermoelectric junctions, the total heat flux is... 

However, an effect of total heat flux was also noted by these latter authors, who ascribed this variation to a contribution due to nucleate boiling, and therefore proposed the following over-all equation (S4),... 

When writing the boundary conditions for the above pair of simultaneous equations the heat transferred to the surroundings from the reactor may be accounted for by ensuring that the tube wall temperature correctly reflects the total heat flux through the reactor wall. If the reaction rate is a function of pressure then the momentum balance equation must also be invoked, but if the rate is insensitive or independent of total pressure then it may be neglected. 

The frequency dependent derivation of Jq and p is somewhat lengthy and is therefore discussed here only qualitatively (see [36] for a full discussion). Essentially, one has to write the heat flux and the pressure at the polymer-air interface in terms of reflectivities and transmittances of all three interfaces (all of which are a function of the phonon frequency). The total heat-flux and interfacial pressure are then obtained in a self-consistent way by an integration over the Debye density of states [36],... 

In Fig. 1.13a the experimentally determined instability wavelength X (e.g. determined from Fig. 1.11) is plotted versus the total heat flux /q. The linear l//q dependence of Eq. (1.22) describes well the experimental data. A second verification of the experimental model stems from the value of Q that is determined by a fit to the data. Rather than a different value of 0 for each data-set, we find a universal value of 0 that depends only on the materials used (substrate, polymer), but not on any of the other experimental parameters (sample geometry, temperature difference). A value of Q = 6.2 described all data sets for PS on silicon in Fig. 1.13a, with a value of Q = 83 for PS on gold. This allows us, in similarity to the electric field experiments in the previous section to introduce dimensionless... 

Tmf Characteristic length at minimum fluidization % Total heat flux vector of fluctuation energy... 

More detailed examination and sampling allows association of hydrothermal circulation with specific vent fields. In such waters samples in the Galapagos Rift by the Alvin deep submersible, Jenkins, Edmond, and Corliss (1978) report juvenile He enrichments which dwarf the normal saturation concentrations by factors up to 11 for 4He and 60 for 3He (Figure 4.6). A particularly significant feature of this report is that added He occurs roughly in proportion to added heat AT up to 12°C in sampled water), corresponding to about 7.6 x 10 xcal/atom of 3He (Figure 4.7). Jenkins et al. note that if this value is representative, hydrothermal circulation may indeed account for the depression of conductive heat flow relative to models for total heat flux. As... 

The above results were for a rectangular duct with a wall temperature that is uniform around any section of the duct but in which the total heat flux from the wall around the section of the duct is not changing with distance, z, along the duct. A few results for ducts with other thermal boundary conditions [2],[10] are given in Table 4.1. 

Figure 3. Radiative, convective, and total heat flux to the combustor wall. (Reproduced with permission from Ref. 11. Copyright 1979, Science Applications, Inc.)...

The sidewalls act as near-adiabatic surfaces since the heat loss through each sidewall is only about 2.7 percent of the total heat flux originating at the source. 

Fig. 9a and b. Effect of oxygen concentration on the total heat flux (heat transfer from the flame to the poly(methyl methacrylate) surface through the gas and condensed (qj phase a) 25 vol %, b) 40 vol % Oj (After Ref. 

The absolute specific enthalpy of the mixture is then= u- -p/p. The total heat-flux vector is defined as... 

In the absence of any electrical input, it is clear that the temperature of the sample cavity will decrease until the total heat flux, qa, from the room to the sample cavity is balanced by heat flow, qs, from the cavity to the liquid nitrogen. The vast majority of this latter flux is carried by the thermal shunt and the heat sink. To a good approximation the thermal resistance of the heat sink is negligible compared to the shunt. If we lump the effective thermal conductance of the... 

Another interesting question that arises is whether there will be a temperature difference between the back and front side of a (silicon) wafer. Consider the situation at 500 mTorr and refer to Table 7.2. The total heat flux towards the wafer is 50xl0"2 Watt/cm2. In a steady state this same energy flux will also leave the front side of the wafer. Now we can apply Fouriers law ... 

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