For heat transfer

Figure 6.6 illustrates what happens to the cost of the system as the relative position of the composite curves is changed over a range of values of AT ir,. When the curves just touch, there is no driving force for heat transfer at one point in the process, which would require an... 

Were we can give these equations for the heat transfer process along radius R. The other processes of heat transfer can be simulated analogously by changing formula for heat transfer area and distances between centers of cells. For Dirichlet cells, bordering a gas medium, an equation of heat balance can be written in the form ... 

A simple cooling cycle serves to illustrate the concepts. Figure 1 shows a temperature—entropy plot for an actual refrigeration cycle. Gas at state 1 enters the compressor and its pressure and temperature are increased to state 2. There is a decrease in efficiency represented by the increase in entropy from state 1 to state 2 caused by friction, heat transfer, and other losses in the compressor. From state 2 to states 3 and 4 the gas is cooled and condensed by contact with a heat sink. Losses occur here because the refrigerant temperature must always be above the heat sink temperature for heat transfer to take... 

Table 5. Correlations for Heat-Transfer and Darcy Friction Coefficients for Noncircular Laminar Duct Flow ...

The LMTD, ie, logarithmic mean temperature difference, is an effective overall temperature difference between the two fluids for heat transfer and is a function of the terminal temperature differences at both ends of the heat exchanger. 

Several companies offer oils for heat-transfer service. Physical characteristics are summarized in Table 1. The oils discussed herein are widely used. Product brochures on the fluids are available from the manufacturers (3—12). 

Monsanto Chemical Company Oils. Monsanto Chemical Co. manufactures two oils for heat-transfer appHcations. Therminol HEP is a solvent refined paraffinic oil Therminol XP is a clear white mineral oil essentially identical to Multitherm PG-1 and Paratherm NE. 

DropletHea.tup, A relation for the time required for droplet heatup, T can be derived based on the assumption that forced convection is the primary heat-transfer mechanism, and that the Ran2-MarshaH equation for heat transfer to submerged spheres holds (34). The result is... 

Fig. 34. Internal cod configurations for heat-transfer surfaces (a) hehcal cod where = 0.02T, = 0.15T, and = 0.65Z (b) baffle cod...

The primary reformer is essentially a process furnace in which fuel is burned with air to indirectiy provide the heat of reaction to the catalyst contained within tubes. This area of the furnace is usually referred to as the radiant section, so named because this is the primary mechanism for heat transfer at the high (750—850°C) temperatures required by the process. Reforming pressures in the range 3 —4 MPa (30,000—40,000 atm) represent a reasonable compromise between cost and downstream compression requirements. 

AP ptim m (power dissipated/volume) correlation for heat transfer iu a 1.5-cm diameter tube. The correction for costs is... 

In the macroscopic heat-transfer term of equation 9, the first group in brackets represents the usual Dittus-Boelter equation for heat-transfer coefficients. The second bracket is the ratio of frictional pressure drop per unit length for two-phase flow to that for Hquid phase alone. The Prandd-number function is an empirical correction term. The final bracket is the ratio of the binary macroscopic heat-transfer coefficient to the heat-transfer coefficient that would be calculated for a pure fluid with properties identical to those of the fluid mixture. This term is built on the postulate that mass transfer does not affect the boiling mechanism itself but does affect the driving force. 

Approximately 1 kg of biphenyl per 100 kg of benzene is produced (6). Because of the large scale, HD A operations provide an ample source of cmde biphenyl from which a technical grade of 93—97% purity can be obtained by distillation (35). Zone refining or other crystallization techniques are requited to further refine this by-product biphenyl to the >99.9% purity requited for heat-transfer appHcations. 

Rehable estimates of annual production of biphenyl in the United States are difficult to obtain. The 1990 figure is probably on the order of 16 million kg/yr of which about half is derived from hydrodealkylation sources. About 10% of the biphenyl derived from HD A sources is consumed, as 93—95% grade, in textile dye carrier appHcations. The remainder is used for alkylation or upgraded to >99.9% grades for heat-transfer purposes. Essentially all of the high purity biphenyl produced by dehydrocondensation of ben2ene is used as alkylation feedstock or is utili2ed directly in heat-transfer appHcations. 

Biphenyl, terphenyl, and their alkyl or hydrogenated derivatives generally serve markets where price and performance, rather than composition, is the customer s primary concern. Performance standards for heat-transfer appHcations are usually set by the fluid suppHer. The biphenyl—diphenyl oxide eutectic (26.5% biphenyl, 73.5% DPO) represents a special case. This composition has become a widely recogni2ed standard vapor-phase heat-transfer medium. It is sold throughout the world under various trademarks. In the United States, Dow (Dowtherm A) and Monsanto (Therminol VP-1) are the primary suppHers. Alkylated biphenyls and partially hydrogenated terphenyls serving the dielectric and carbonless copy paper dye solvent markets likewise are sold primarily on the basis of price and performance characteristics jointly agreed on by producer and user. 

Exothermicity. The catalytic reactions are often exothermic bond-forming reactions of small molecules that give larger molecules. Consequendy, the reactors are designed for efficient heat removal. They may be jacketed or contain coils for heat-transfer media, or the heat of reaction may be used to vaporize the products and aid in the downstream separation by distillation. 

Elevated pressures are required to keep water in the Hquid state. Liquid water cataly2es oxidation so that reactions proceed at relatively lower temperatures than would be required if the same materials were oxidi2ed in open flame combustion. At the same time, water moderates oxidation rates by providing a medium for heat transfer and removing excess heat by evaporation. 

Sindlady, heating surface area needs are not direcdy proportional to the number of effects used. For some types of evaporator, heat-transfer coefficients decline with temperature difference as effects are added the surface needed in each effect increases. On the other hand, heat-transfer coefficients increase with temperature level. In a single effect, all evaporation takes place at a temperature near that of the heat sink, whereas in a double effect half the evaporation takes place at this temperature and the other half at a higher temperature, thereby improving the mean evaporating temperature. Other factors to be considered are the BPR, which is additive in a multiple-effect evaporator and therefore reduces the net AT available for heat transfer as the number of effects is increased, and the reduced demand for steam and cooling water and hence the capital costs of these auxiUaries as the number of effects is increased. 

J Ordinate, Colburn j factor, equals f/2 for heat transfer for inner wall of annulus /h2 for outer wall of annulus jy for heat transfer for ideal tube bank Dimensionless Dimensionless... 

Fourier s law is the fundamental differential equation for heat transfer by conduction ... 

The analogy has been reasonably successful for simple geometries and for fluids of very low Prandtl number (liquid metals). For high-Prandtl-number fluids the empirical analogy of Colburn [Trans. Am. Tn.st. Chem. Ting., 29, 174 (1933)] has been veiy successful. A J factor for momentum transfer is defined asJ =//2, where/is the friction fac tor for the flow. The J factor for heat transfer is assumed to be equal to the J factor for momentum transfer... 

Metzner and Friend [Ind. Fng. Chem., 51, 879 (1959)] present relationships for turbulent heat transfer with nonnewtouiau fluids. Relationships for heat transfer by natural convection and through laminar boundaiy layers are available in Skelland s book (op. cit.). 

Jh /m Chilton-Colbum factor for heat transfer See /D Dimensionless Dimensionless... 

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