Special Heat-Transfer Coefficients

Vessel with heating jacket. In Fig. 4.13-la a vessel with a cooling or heating jacket is shown. When heating, the fluid entering is often steam, which condenses inside the jacket and leaves at the bottom. The vessel is equipped with an agitator and in most cases also with baffles (not shown). 

Correlations for the heat-transfer coefficient from the agitated Newtonian liquid inside the vessel to the jacket walls of the vessel have the following form  

4 Principles of Steady-State Heat Transfer 

Flat-blade turbine agitator with no baffles (B4) 

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Equation (F.l) shows that each stream makes a contribution to total heat transfer area defined only by its duty, position in the composite curves, and its h value. This contribution to area means also a contribution to capital cost. If, for example, a corrosive stream requires special materials of construction, it will have a greater contribution to capital cost than a similar noncorrosive stream. If only one cost law is to be used for a network comprising mixed materials of construction, the area contribution of streams requiring special materials must somehow increase. One way this may be done is by weighting the heat transfer coefficients to reflect the cost of the material the stream requires. 

Maintenance of isothermal conditions requires special care. Temperature differences should be minimised and heat-transfer coefficients and surface areas maximized. Electric heaters, steam jackets, or molten salt baths are often used for such purposes. Separate heating or cooling circuits and controls are used with inlet and oudet lines to minimize end effects. Pressure or thermal transients can result in longer Hved transients in the individual catalyst pellets, because concentration and temperature gradients within catalyst pores adjust slowly. 

Work in connection with desahnation of seawater has shown that specially modified surfaces can have a profound effect on heat-transfer coefficients in evaporators. Figure 11-26 (Alexander and Hoffman, Oak Ridge National Laboratory TM-2203) compares overall coefficients for some of these surfaces when boiling fresh water in 0.051-m (2-in) tubes 2.44-m (8-ft) long at atmospheric pressure in both upflow and downflow. The area basis used was the nominal outside area. Tube 20 was a smooth 0.0016-m- (0.062-in-) wall aluminum brass tube that had accumulated about 6 years of fouhng in seawater service and exhibited a fouling resistance of about (2.6)(10 ) (m s K)/ J [0.00015 (fF -h-°F)/Btu]. Tube 23 was a clean aluminum tube with 20 spiral corrugations of 0.0032-m (lA-in) radius on a 0.254-m (10 -in)... 

Of these special surfaces, only the double-fluted tube has seen extended services. Most of the gain in heat-transfer coefficient is due to the condensing side the flutes tend to collect the condensate and leave the lauds bare [Caruavos, Proc. First Int. Symp. Water Desalination, 2, 205 (1965)]. The coudeusiug-film coefficient (based on the actual outside area, which is 28 percent greater than the nominal area) may be approximated from the equation... 

The heavy-duty jacketed type (Fig. ll-62a) is a special custom-built adaptation of a heavy-duty vibratory conveyor shown in Fig. 11-60. Its apphcation is continuously to cool the crushed materi [from about 177°C (350°F)] produced by the vibratoiy-type caster of Fig. 11-53. It does not have the liqmd dam and is made in longer lengths that employ L, switchback, and S arrangements on one floor. The capacity rate is 27,200 to 31,700 kg/h (30 to 35 tons/h) with heat-transfer coefficients in the order of 142 to 170 W/(m °C) [25 to 30 Btii/(h ft °F)]. For heating or drying applications, it employs steam to 414 kPa (60 IbFin ). 

Product Quality Considerations of product quahty may require low holdup time and low-temperature operation to avoid thermal degradation. The low holdup time eliminates some types of evaporators, and some types are also eliminated because of poor heat-transfer charac teristics at low temperature. Product quality may also dic tate special materials of construction to avoid met hc contamination or a catalytic effect on decomposition of the product. Corrosion may also influence evaporator selection, since the advantages of evaporators having high heat-transfer coefficients are more apparent when expensive materials of construction are indicated. Corrosion and erosion are frequently more severe in evaporators than in other types of equipment because of the high hquid and vapor velocities used, the frequent presence of sohds in suspension, and the necessary concentration differences. 

Equation 12.105 is often referred to as the Lewis Relation. It provides an approximate method for evaluating a mass transfer coefficient if the heat transfer coefficient is known. The assumption that the turbulent eddies can penetrate right up to the surface is justified however only in special circumstances and the problem is considered further in the next section. 

Gasses due to their low heat capacity do not store and transport as much heat as similar volumes of a liquid. Therefore their low heat transfer coefficients are often not a special problem. From analytical model for a simple heat storage given previously, we know that the temperature of the heat transfer fluid on the outlet of the storage model was... 

A sufficient condition that the RI be determined by a vertex critical point is that the feasible region R be convex. (Of course, a special case of this is when all the feasibility constraints are linear see Section III,B.) Unfortunately, when flow rates or heat transfer coefficients are included in the uncertainty range, the feasible region can be nonconvex (see Examples 1 and 2 and Section III,C,3). Thus, current algorithms for calculating the RI are limited to temperature uncertainties only. 

Control of bed temperature provides some special challenges. As the load is varied, either the heat transfer coefficient or immersed tube area must be varied correspondingly. This may be achieved over a moderate load change by varying the area of tubes immersed in the bed by varying the height of the bed. 

It is proposed to construct a heat exchanger to condense 7.5 kg/s of -hexane at a pressure of 150 kN/m2, involving a heat load of 4.5 MW. The hexane is to reach the condenser from the top of a fractionating column at its condensing temperature of 356 K. From experience it is anticipated that the overall heat transfer coefficient will be 450 W/m2 K. Cooling water is available at 289 K. Outline the proposals that you would make for the type and size of the exchanger, and explain the details of the mechanical construction that you consider require special attention. 

Due to the lack of published data on the special flow field generated in the LDPE tubular reactor by the end pulsing valve, the development of the mathematical model was preceded by a fluiddynamic study, with the aim of evidencing the influence, if any, of the pulsed motion on the axial mixing, the heat transfer coefficient and the pressure drop in the reactor. 

A solution may come from the ability to realize a large heat-transfer coefficient, for example U = 1000W/m2/K. This means that special attention must be paid to scaling and the thermal resistance of the metal wall must be reduced, as discussed in Section 13.2.1. The minimum temperature difference becomes AT4, = 0.8ATmm = 50.4K. This might offer a feasible solution, but the robustness of the reactor is questionable. 

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