Heat-transfer rates

The rate at which heat is transferred from Fig. 21.Ts S catalyst bed exit gas to its economizer water is calculated from  

Section 21.3.1 s heat transfer amount, MJ per kg-mole of 1 catalyst bed feed gas 

3 catalyst bed exit gas to economizer = heat transfer rate 

This chapter has examined a very simple acid plant. Its techniques are, however, readily extended to complex industrial acidmaking situations. 

Catalyst bed gas enthalpies are readily calculated on our heatup path-equilibrium curve intercept worksheets. 

Heat transfer rate is given by the following equation  

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In addition to the advantage of high heat transfer rates, fluidized beds are also useful in situations where catalyst particles need frequent regeneration. Under these circumstances, particles can be removed continuously from the bed, regenerated, and recycled back to the bed. In exothermic reactions, the recycling of catalyst can be... 

Equipment for food freezing is designed to maximize the rate at which foods are cooled to —18° C to ensure as brief a time as possible in the temperature zone of maximum ice crystal formation (12,13). This rapid cooling favors the formation of small ice crystals which minimize the dismption of ceUs and may reduce the effects of solute concentration damage. Rapid freezing requires equipment that can deHver large temperature differences and/or high heat-transfer rates. 

Ultrafast pyrolysis in the vortex reactor is capable of pyrolyzing biomass at high heat-transfer rates on the reactor wall by ablation and has been... 

Hot product char carries heat into the entrained bed to obtain the high heat-transfer rates required. Feed coal must be dried and pulverized. A portion of the char recovered from the reactor product stream is cooled and discharged as product. The remainder is reheated to 650—870°C in a char heater blown with air. Gases from the reactor are cooled and scmbbed free of product tar. Hydrogen sulfide is removed from the gas, and a portion is recycled to serve as the entrainment medium. 

Fourier s Law of Heat Conduction. The heat-transfer rate,, per unit area,, in units of W/m (Btu/(ft -h)) transferred by conduction is directly proportional to the normal temperature gradient ... 

The Plane Wall. To calculate the heat-transfer rate through a plane wall, Fourier s law can be appHed directly. 

When the plane wall is made of mote than one material (Fig. lb), the heat-transfer rate is given as... 

The Overall Heat-Transfer Coeffieient. For the design and sizing of heat exchangers, the heat-transfer rate is often expressed as... 

The Tube Wall Tubular heat exchangers are built using a number of circular (or noncircular) tubes thus, the heat-transfer rate across tubular walls, following Fourier s law of heat conduction, becomes... 

I ewton s Cooling L w of Heat Convection. The heat-transfer rate per unit area by convection is directly proportional to the temperature difference between the soHd and the fluid which, using a proportionaUty constant called the heat-transfer coefficient, becomes... 

The importance of equations 37—39 is that once the heat-exchanger effectiveness, S, is known for a given heat exchanger, one can compute the actual heat-transfer rate and outlet stream temperatures from specified inlet conditions. This process is known as rating a given heat exchanger. 

Direct Contact Heat Exchangers. In a direct contact exchanger, two fluid streams come into direct contact, exchange heat and maybe also mass, and then separate. Very high heat-transfer rates, practically no fouling, lower capital costs, and lower approach temperatures are the principal advantages. 

The cross-sectional area of the wick is deterrnined by the required Hquid flow rate and the specific properties of capillary pressure and viscous drag. The mass flow rate is equal to the desired heat-transfer rate divided by the latent heat of vaporization of the fluid. Thus the transfer of 2260 W requires a Hquid (H2O) flow of 1 cm /s at 100°C. Because of porous character, wicks are relatively poor thermal conductors. Radial heat flow through the wick is often the dominant source of temperature loss in a heat pipe therefore, the wick thickness tends to be constrained and rarely exceeds 3 mm. 

Heat Recovery and Seed Recovery System. Although much technology developed for conventional steam plants is appHcable to heat recovery and seed recovery (HRSR) design, the HRSRhas several differences arising from MHD-specific requirements (135,136). First, the MHD diffuser, which has no counterpart ia a conventional steam plant, is iacluded as part of the steam generation system. The diffuser experiences high 30 50 W/cm heat transfer rates. Thus, it is necessary to allow for thermal expansion of the order of 10 cm (137) ia both the horizontal and vertical directions at the connection between the diffuser and the radiant furnace section of the HRSR. 

Continuous polymerization systems offer the possibiUty of several advantages including better heat transfer and cooling capacity, reduction in downtime, more uniform products, and less raw material handling (59,60). In some continuous emulsion homopolymerization processes, materials are added continuously to a first ketde and partially polymerized, then passed into a second reactor where, with additional initiator, the reaction is concluded. Continuous emulsion copolymerizations of vinyl acetate with ethylene have been described (61—64). Recirculating loop reactors which have high heat-transfer rates have found use for the manufacture of latexes for paint appHcations (59). 

The quahty of feed water required depends on boiler operating pressure, design, heat transfer rates, and steam use. Most boiler systems have sodium zeohte softened or demineralized makeup water. Feed-water hardness usually ranges from 0.01 to 2.0 ppm, but even water of this purity does not provide deposit-free operation. Therefore, good internal boiler water treatment programs are necessary. 

Control of supersaturation is an important factor in obtaining crystal size distributions of desired characteristics, and it would be useful to have a model relating rate of cooling or evaporation or addition of diluent required to maintain a specified supersaturation in the crystallizer. Contrast this to the uncontrolled situation of natural cooling in which the heat transfer rate is given by... 

Flow of mother Hquor through the cooled tubes is initiated, and crystals are grown on the tube surfaces. The heat transfer rate should be controUed so as to moderate crystal growth, thereby producing a relatively uniform layer of high purity soHds. 

An equation representing an energy balance on a combustion chamber of two surface zones, a heat sink Ai at temperature T, and a refractory surface A assumed radiatively adiabatic at Tr, inmost simply solved if the total enthalpy input H is expressed as rhCJYTv rh is the mass rate of fuel plus air and Tp is a pseudoadiabatic flame temperature based on a mean specific heat from base temperature up to the gas exit temperature Te rather than up to Tp/The heat transfer rate out of the gas is then H— — T ) or rhCp(T f — Te). The... 

On occasion one will find that heat-transfer-rate data are available for a system in which mass-transfer-rate data are not readily available. The Chilton-Colburn analogy provides a procedure for developing estimates of the mass-transfer rates based on heat-transfer data. Extrapolation of experimental or Jh data obtained with gases to predict hquid systems (and vice versa) should be approached with caution, however. When pressure-drop or friction-factor data are available, one may be able to place an upper bound on the rates of heat and mass transfer, according to Eq. (5-308). 

FIG. 8-49 Heat-transfer rate in sensible-heat exchange varies nonlinearly with flow of the manipulated fluid. 

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