Heat capacity transfer coefficient

Stream Supply temp. T, rc) Target temp. Tr rC) AH (MW) Heat capacity flow rate CP (WN C- ) Heat transfer coefficient h(MW... 

Amplitude of controlled variable Output amplitude limits Cross sectional area of valve Cross sectional area of tank Controller output bias Bottoms flow rate Limit on control Controlled variable Concentration of A Discharge coefficient Inlet concentration Limit on control move Specific heat of liquid Integration constant Heat capacity of reactants Valve flow coefficient Distillate flow rate Limit on output Decoupler transfer function Error... 

Time constants. Where there is a capacity and a throughput, the measurement device will exhibit a time constant. For example, any temperature measurement device has a thermal capacity (mass times heat capacity) and a heat flow term (heat transfer coefficient and area). Both the temperature measurement device and its associated thermowell will exhibit behavior typical of time constants. 

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 ). 

Circffiation and heat transfer in this type of evaporator are strongly affected by the liquid level. Highest heat-transfer coefficients are achieved when the level, as indicated by an external gauge glass, is only about halfway up the tubes. Shght reductions in level below the optimum result in incomplete wetting of the tube walls with a consequent increased tendency to foul and a rapid reduction in capacity. When this type of evaporator is used with a liquid that can deposit salt or scale, it is customary to operate with the liquid level appreciably higher than the optimum and usually appreciably above the top tube sheet. 

Economic and process considerations usually dictate that agitated thin-film evaporators be operated in single-effect mode. Veiy high temperature differences can then be used many are heated with Dowtherm or other high-temperature media. This permits achieving reasonable capacities in spite of the relatively low heat-transfer coefficients and the small surface that can be provided in a single tube [to about 20 m" (200 ft")]. The structural need for wall thicknesses of 6 to 13 mm (V4 to V2. in) is a major reason for the relatively low heat-transfer coefficients when evaporating water-like materials. 

Control of an evaporator requires more than proper instrumentation. Operator logs snould reflect changes in basic characteristics, as by use of pseuao heat-transfer coefficients, which can detect obstructions to heat flow, hence to capacity. These are merely the ratio of any convenient measure of heat flow to the temperature drop across each effect. Dilution by wash and seal water should be monitored since it absorbs evaporative capacity. Detailed tests, routine measurements, and operating problems are covered more fuUy in Testing Procedure for Evaporators (loc. cit.) and by Standiford [Chem. Eng. Prog., 58(11), 80 (1962)]. 

Tests on plant-scale dryers are usually carried out to obtain design data for a specific material, to select a suitable diyer type, or to check present performance of an existing diyer with the objective of determining its capacity potential. In these tests overall performance data are obtained and the results used to make heat and material balances and to estimate overall drying rates or heat-transfer coefficients. 

Circulation of air at velocities of I to 10 m/s is desirable to improve the surface heat-transfer coefficient and to eliminate stagnant air pockets. Proper air flow in tray dryers depends on sufficient fan capacity, on the design of ductwork to modify sudden changes in direction, and on properly placed baffles. Nonuniform airflow Is one of the most serious problems in the operation of tray di yers. 

In general, this equipment offers an economical heat-transfer area for first cost as well as operating cost. Capacity is hmited primarily by the air velocity which can be used without excessive dust entrainment. Table 12-32 shows hmiting air velocities suitable for various sohds particles. Usually, the equipment is satisfactory for particles larger than 100 mesh in size. [The use of indirect-heated conveyors eliminates the problem of dust entrainment, but capacity is limited by the heat-transfer coefficients obtainable on the deck (see Sec. 11)]. 

By virtue of its chemical and thermal resistances, borosilicate glass has superior resistance to thermal stresses and shocks, and is used in the manufacture of a variety of items for process plants. Examples are pipe up to 60 cm in diameter and 300 cm long with wall tliicknesses of 2-10 mm, pipe fittings, valves, distillation column sections, spherical and cylindrical vessels up 400-liter capacity, centrifugal pumps with capacities up to 20,000 liters/hr, tubular heat exchangers with heat transfer areas up to 8 m, maximum working pressure up to 275 kN/m, and heat transfer coefficients of 270 kcal/hz/m C [48,49]. 

In the case of a temperature probe, the capacity is a heat capacity C == me, where m is the mass and c the material heat capacity, and the resistance is a thermal resistance R = l/(hA), where h is the heat transfer coefficient and A is the sensor surface area. Thus the time constant of a temperature probe is T = mc/ hA). Note that the time constant depends not only on the probe, but also on the environment in which the probe is located. According to the same principle, the time constant, for example, of the flow cell of a gas analyzer is r = Vwhere V is the volume of the cell and the sample flow rate. 

For heat exchangers in true counter-current (fluids flowing in opposite directions inside or outside a tube) or true co-current (fluids flowing inside and outside of a tube, parallel to each other in direction), with essentially constant heat capacities of the respective fluids and constant heat transfer coefficients, the log mean temperature difference may be appropriately applied, see Figure 10-33. ... 

Providing that the flow rates are steady, the heat transfer coefficients do notvary and the specific heat capacities are constant throughout the working range, the average temperature difference over the length of the curve is given hy ... 

In general, the temperature 0S at the axis is not known, and the heat transfer coefficient is related to the temperature difference between the walls and the bulk fluid. The bulk temperature of the fluid is defined as the ratio of the heat content to the heat capacity of the fluid flowing at any section. Thus the bulk temperature 9S is given by ... 

A vessel contains 1 tonm (I Mg) of a liquid of specific heat capacity 4.0 kj/kg K. The vessel is heated by steam at 393 K which is fed to a cod immersed in the agitated liquid and heat is lost to the surroundings at 293 K from the outside o." the vessel. How long dots it take to heat the liquid from 293 to 353 K and what is the maximum temperature to which the liquid can be heated When the liquid temperature has reached 353 K, the steam supply is tinned off for 2 hours (7.2 ks and the vessel cools. How long will it take to reheat the material to 353 K The surface area of the coil is 0 5 m2 and the overall coefficient of heat transfer to the liquid may be taken as 600 W/m2 K. The outside area of Lie vessel is 6 m2 and the coefficient of heat transfer to the surroundings may be taken as 10 W/m2 K. 

A process requires a flow of 4 kg/s of purified water at 340 K to be heated from 320 K by 8 kg/s of untreated water which can be available at 380, 370, 360 or 350 K. Estimate the heat transfer surfaces of one shell pass, two tube pass heat exchangers suitable for these duties. In all cases, the mean heat capacity of the water streams is 4.18 kJ/kg K and the overall coefficient of heat transfer is 1.5 kW/m2 K. 

A stirred reactor contains a batch of 700 kg reactants of specific heat 3.8 kJ/kg K initially at 290 K, which is heated by dry saturated steam at 170 kN/m2 fed to a helical coil. During the heating period the steam supply rate is constant at 0.1 kg/s and condensate leaves at the temperature of the steam. If heat losses arc neglected, calculate the true temperature of the reactants when a thermometer immersed in the material reads 360 K. The bulb of the thermometer is approximately cylindrical and is 100 mm long by 10 mm diameter with a water equivalent of 15 g, and the overall heat transfer coefficient to the thermometer is 300 W/m2 K. What would a thermometer with a similar bulb of half the length and half the heat capacity indicate under these conditions ... 

An open cylindrical tank 500 mm diameter and I m deep is three quarters filled with a liquid ol density 980 kg/mJ and of specific heat capacity 3 kj/kg K. If the heat transfer coefficient from the cylindrical walls and the base of the tank is 10 W/m2 K and front the surface is 20 W/m3 K, what area of heating coil, fed with steam at 383 K. is required to heat the contents from 288 K to 368 K in a half hour The overall heat transfer coefficient for the coil may be taken as 100 W/m2 K, the surroundings we at 288 K and the heal capacity of the tank itself may be neglected. 

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