The heat balance

Tte rate of heat transfer through an element of width w of die plane 1-2, of thickness dy at a distance y from the surface is  

It is shown in Section 11,2 that there is a mass rate of flow of fluid through plane. 2-4, out of the element equal to pw(9/ar)(/Q % dy) ck. 

Since the plane, 2-4, lies outside the boundary layers, the heat leaving the elemeni through the plane as a result of this flow is  

The heat transferred by thermal conduction into the element through plane, 1-3 is  

If the temperature 6s of the main stream is unchanged, a heat balance on the element gives  

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When the heat duty requirement, is specified and the fluid temperature change, AT, is fixed, as a result of operating or equipment limitations, the required volumetric pumping rate from the heat balance is... 

No external heat source is required. In all types of steelmaking that employ pig iron, which melts at temperatures well below low carbon steel, the heat balance between exothermic oxidation of elements, such as C, Si, and Mn, and the cooling provided by scrap or sometimes other endothermic coolants, such as iron ore, are critical issues. The numerical factors are well understood and are routinely contained in computer programs used by operators. If the balance is such that the temperature after blowing is too high, refractory consumption is increased significantly. 

Thus the ECCU always operates in complete heat balance at any desired hydrocarbon feed rate and reactor temperature this heat balance is achieved in units such as the one shown in Eigure 1 by varying the catalyst circulation rate. Catalyst flow is controlled by a sHde valve located in the catalyst transfer line from the regenerator to the reactor and in the catalyst return line from the reactor to the regenerator. In some older style units of the Exxon Model IV-type, where catalyst flow is controlled by pressure balance between the reactor and regenerator, the heat-balance control is more often achieved by changing the temperature of the hydrocarbon feed entering the riser. 

Thus the amount of heat that must be produced by burning coke ia the regenerator is set by the heat balance requirements and not directly set by the coke-making tendencies of the catalyst used ia the catalytic cracker or by the coking tendencies of the feed. Indirectly, these tendencies may cause the cracker operator to change some of the heat-balance elements, such as the amount of heat removed by a catalyst cooler or the amount put iato the system with the feed, which would then change the amount of heat needed from coke burning. 

If FCCU operations are not changed to accommodate changes ia feed or catalyst quaUty, then the amount of heat required to satisfy the heat balance essentially does not change. Thus the amount of coke burned ia the regenerator expressed as a percent of feed does not change. The consistency of the coke yield, arising from its dependence on the FCCU heat balance, has been classified as the second law of catalytic cracking (7). 

The impact that variations in coke content and burning conditions can have on the overall heat of coke combustion is shown in Table 2. Because the heat balance dictates the amount of heat that is required from burning coke, the heat of combustion then determines the amount of coke that must be burned. 

The heat balance shows that the heat loss from the furnace walls is only ca 11% of the energy suppHed by the fuel and just slightly more than the sensible heat loss with the slag. The principal heat loss is in the stack gases and is equivalent to ca 30% of the energy suppHed by the fuel. 

The heat balance of a reacdor is made up of three terms Heat of reaction -I- Heat transfer = Gain of sensible and latent heats by the mixture. This estabhshes the temperature as a function of the composition... 

Batch Reactions For a batch reaction, the heat balance is... 

In tubular reactors of only a few cm in diameter, the temperature is substantially uniform over the cross section so only an axial gradient occurs in the heat balance. 

The sparger design can be based on all vapor flow, but the heat balance must include the liquid. 

The small value of the entropy change reflects the fact that only liquids are involved in tlris reaction. The heat balance in canying out tlris reaction may be calculted, according to Hess s law, by calculating tire heat change at room temperarnre, and subtracting tire heat required to raise the products to the hnal teirrperamre. The data for tlris reaction are as follows ... 

Now assume that U and S are not large and that AT = 20 K is needed to keep the heat balance. In this case when something causes the temperature to rise even for a very short time by one K, the reaction rate will increase, just as before, by 15%. The heat transfer rate will increase by a ratio of (21-20)720, that is by 5 %. The 5 % increase cannot restore the heat balance and the reaction temperature will keep rising. A temperature runaway will occur. 

The turbine firing temperature based on the heat balance can be also computed and must be within about 2-6 °F (1-3 °C) of each other. The heat balance relationships as they apply to the gas turbine... 

Consider the heat balance over a time (dt) during which there is a flow of mobile phase (dv) and a temperature change (d0), then... 

Consider the heat balance of the cell. However, as opposed to the GC column, the heat capacity of the liquid mobile phase in an in LC column is relatively large. Consequently, heat convected from the cell by the mobile phase must also be taken into account. It follows that... 

The problem is different from typical heat transfer problems. The heat balance is not straightforward because the outlet temperatures are unknown. A trial-and-error procedure is therefore required. 

Since the reaction is endothermic (+AH[ /a), then the heat balance for the first stage is ... 

At the adiabatic condition, Q = 0, as no heat is added to or removed from the system. The heat balance becomes... 

The first order reaction is represented by (-r ) = kC, and applying the mass balance Equation 6-120 and the heat balance Equation 6-121, respectively, gives the fractional conversion in terms of the mass balance equation ... 

The feed temperature Tg for the adiabatic operation at the optimal temperature T p is determined from the heat balance, -GAli + Q = 0, where G = pu and... 

The heat balance to the three-zone jacket can be expressed by... 

When a damp cloth is laid in an air flow, it settles after a certain time ic an equilibrium temperature, the so-called wet bulb temperature (0 ), which is determined through heat and mass transfer. Negotiating the heat flow obtained by radiation and conduction, the heat balance of the wet cloth in a stationary situation can be expressed as... 

Existing methods for evaluation of the general thermal state of the body, both in comfort and under heat or cold stress, are based on an analysis of the heat balance for the human body ... 

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