Heat transfer reversible

As the amount of temperature cross increases, however, problems are encountered, as illustrated in Fig. 7i8c. Local reversal of heat flow may be encountered, which is wasteful in heat transfer area. The design may even become infeasible. 

Another design, shown ia Figure 5, functions similarly but all components are iaside the furnace. An internal fan moves air (or a protective atmosphere) down past the heating elements located between the sidewalls and baffle, under the hearth, up past the work and back iato the fan suction. Depending on the specific application, the flow direction may be reversed if a propeUer-type fan is used. This design eliminates floorspace requirements and eliminates added heat losses of the external system but requires careful design to prevent radiant heat transfer to the work. 

The work, W, can range from 2ero, if the engine is completely ineffective, to the limiting negative value attained for reversible operation. If IT = 0, then the process degenerates to one of simple heat transfer, for which... 

Convection heat transfer is dependent largely on the relative velocity between the warm gas and the drying surface. Interest in pulse combustion heat sources anticipates that high frequency reversals of gas flow direction relative to wet material in dispersed-particle dryers can maintain higher gas velocities around the particles for longer periods than possible ia simple cocurrent dryers. This technique is thus expected to enhance heat- and mass-transfer performance. This is apart from the concept that mechanical stresses iaduced ia material by rapid directional reversals of gas flow promote particle deagglomeration, dispersion, and Hquid stream breakup iato fine droplets. Commercial appHcations are needed to confirm the economic value of pulse combustion for drying. 

Heat transfer external to the control volume is reversible. 

Since heat transfer with respec t to the surroundings and with respect to the system are equal but of opposite sign, = —Q. Moreover, the second law requires for a reversible process that the entropy changes of system and surroundings be equalbut of opposite sign AS = —AS Equation (4-356) can therefore be written Q = TcAS In terms of rates this becomes... 

Adiabatic A process for which there is no heat transfer between a system and its surroundings. An adiabatic process that is reversible is isentropic. 

The inerts will blanket a portion of the tubes. The blanketed portion has very poor heat transfer. The column pressure is controlled by varying the percentage of the tube surface blanketed. When the desired pressure is exceeded, the vacuum system will suck out more inerts, and lower the percentage of surface blanketed. This will increase cooling and bring the pressure back down to the desired level. The reverse happens if the pressure falls below that desired. This is simply a matter of adjusting the heat transfer coefficient to heat balance the system. 

In the case of thermodynamics, the designer can investigate the nature of the reaction heat and whether the reaction is reversible. If these exothermic reactions are irreversible, attention may be focused on the influence of reactor design on conversion and with heat transfer control. An objective of reactor design is to determine the size and type of reactor and mode of operation for the required job. The choice... 

Consider first the steady flow of fluid through a control volume CV between prescribed stable states X and Y (Fig. 2.1) in the presence of an environment at ambient temperature Tj, (i.e. with reversible heat transfer to that environment only). The maximum work which is obtained in reversible flow between X and Y is given by... 

Fig. 2.1. Reversible process with heat transfer at temperature To (to the environment) (after Ref. 5 ).

Fig. 2.3 shows such a fully reversible steady flow through the control volume CV. The heat transferred [GrevIx. supplies a reversible heat engine, delivering external work [( c)rev]x and rejecting heat [(2o)rev1x to the environment. 

The above analysis has been concerned with heat transfer from the control volume. Consider next heat [AQ] = [d REvlx transferred to the control volume. Then that heat could be reversibly pumped to CV (at temperature T) from the atmosphere (at temperature To) by a reversed Carnot engine. This would require work input... 

A reversible recuperative a/s cycle, with the maximum possible heat transfer from the exhaust gas, qj = Cp(74 — 7y), is illustrated in the T,s diagram of Fig. 3.2, where 7y = 72. This heat is transferred to the compressor delivery air, raising its temperature to 7x = 74, before entering the heater. The net specific work output is the same as that... 

Clearly, if A is zero (no heat transfer), then the normal polytropic relation holds. A point of interest is that if Tjp = (1 — A) then rj = 1 and the expansion becomes isentropic (but not reversible adiabatic). 

Provision of pretreatment The initial fill volume and MU supply is almost always pretreated in some manner. Because of the large volume of water in these systems, even low-hardness waters can produce sufficient quantities of calcium carbonate scale to severely impede heat transfer thus, for MTHW pretreatment, the use of ion-exchange softeners is the norm. For HTHW, some form of demineralization such as reverse osmosis (RO) or deionization by cation-anion exchange is typically preferred. 

Under hot BW conditions this reaction is reversible, leading to a serious risk of carbonate scale depositing on heat transfer surfaces. Consequently, many large water utilities and industries around the world continue to use the old established, but effective lime (calcium hydroxide) and soda ash (sodium carbonate) processes to soften water by precipitating out insoluble hardness salts. 

As we have seen before, exact differentials correspond to the total differential of a state function, while inexact differentials are associated with quantities that are not state functions, but are path-dependent. Caratheodory proved a purely mathematical theorem, with no reference to physical systems, that establishes the condition for the existence of an integrating denominator for differential expressions of the form of equation (2.44). Called the Caratheodory theorem, it asserts that an integrating denominator exists for Pfaffian differentials, Sq, when there exist final states specified by ( V, ... x )j that are inaccessible from some initial state (.vj,.... v )in by a path for which Sq = 0. Such paths are called solution curves of the differential expression The connection from the purely mathematical realm to thermodynamic systems is established by recognizing that we can express the differential expressions for heat transfer during a reversible thermodynamic process, 6qrey as Pfaffian differentials of the form given by equation (2.44). Then, solution curves (for which Sqrev = 0) correspond to reversible adiabatic processes in which no heat is absorbed or released. 

Since the heat was transferred reversibly out of the high-temperature reservoir and into the low-temperature reservoir, we may use these quantities to calculate... 

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