Time required for heating or cooling

In the case of a storage tank with liquor of mass m and specific heat Cp, heated by steam condensing in a helical coil, it may be assumed that die overall tr sfer coefficient U is constant. If Tg is the temperature of the condensing steam, T and T2 the initial and final temperatures of the liquor, and A the area of heat transfer surface, and T is the temperature of the liquor at any time t, then the rate of transfer of heat is given by  

From this equation, the time t of heating from Ti to T2, may be calculated. The same analysis may be used if the steam condenses in a jacket of a reaction vessel. 

This analysis does not allow for any heat losses during the heating, or, for that matter, cooling operation. Obviously the higher the temperature of the contents of the vessel, the greater are the heat losses and, in the limit, the heat supplied to the vessel is equal to the heat losses, at which stage no further rise in the temperature of the contents of the vessel is possible. This situation is illustrated in Example 9.25. 

A vessel contains 1 tonm (1 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 of 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 turned 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 m and the overall coefficient of heat transfer to the liquid may be taken as 600 W/m K. The outside area of tnc vessel is 6 m and the coefficient of heat transfer to the surroundings may be taken as 10 W/m K. 

If T K is the temperature of the liquid at time t s, then a heat balance on the vessel gives  

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This chapter reviews the various types of impellers, die flow patterns generated by diese agitators, correlation of die dimensionless parameters (i.e., Reynolds number, Froude number, and Power number), scale-up of mixers, heat transfer coefficients of jacketed agitated vessels, and die time required for heating or cooling diese vessels. 

Computer software (BATCH) was developed to determine the time required for heating or cooling process fluids in a batch system. Table 7-18 gives the computer results of Example 7-10. 

The stirred tank with a jacket for heating or cooling (also called autoclave or digester) is the workhorse of the pharmaceutical, fine-chemicals, mineral and paper industries. It is used as a reactor, mixer, decanter, heater and cooler. The bubble and slurry-bubble columns too are akin to the STR. It is used as a batch reactor or semi- or fed-batch reactor for those reactions requiring a large residence time, as the tubular reactor would be too long and unwieldy. The STR is bulky, and the yield and selectivity could be low. 

Heating or cooling of process fluids in a batch-operated vessel is common in the chemical process industries. The process is unsteady state in nature because the heat flow and/or the temperature vary with time at a fixed point. The time required for the heat transfer can be modified, by increasing the agitation of the batch fluid, the rate of circulation of the heat transfer medium in a jacket and/or coil, or the heat transfer area. Bondy and Lippa [45] and Dream [46] have compiled a collection of correlations of heat transfer coefficients in agitated vessels. Batch processes are sometimes disadvantageous because ... 

When the mixture has cooled to about 6o°, there are added from the separatory funnel, first, a solution of 114 g. (0.5 mole) of ethyl laurate (Note 3) in 150 cc. of absolute alcohol (Note 4), then 500 cc. more of alcohol, as rapidly as is possible (Note 5) without loss of material through the condenser. The time required for the addition of the ester solution and the alcohol is less than five minutes, usually two or three minutes. When the reaction has subsided, the flask is heated on a steam bath until the sodium is completely dissolved (Note 6). The mixture is then steam distilled to remove the toluene and ethyl alcohol. 

The thermal time constant of a reactor characterizes the dynamics of the evolution of the reactor temperature. In fact, since it contains the ratio of the mass proportional to volume with the dimension L3 to the heat exchange area with the dimension L2, it varies non-linearly with the reactor scale, as is explained in Section 2.4. Some values of the time constant obtained with normalized stainless steel reactors [1] are summarized in Table 9.3. The variation by a factor of about 7, over the range considered here, is critical during scale-up. The heating or cooling times are often expressed as the half-life, the time required for the temperature difference to be divided by two ... 

One or both blocks are equipped with holes to which tubes are soldered for the solvent inlet, including sample injection and eluate outlet. Figure 17 illustrates the case in which inlet and outlet capillaries are placed in the upper heated block. It is, however, more advantageous to situate these capillaries in the lower cooled block for the reason that the lower wall is the accumulation wall of the channel so that the sample, after being injected, is transferred to the vicinity of this wall. In this way equilibration at the head of the channel is facilitated and the time required for primary relaxation is reduced. At the channel end, the solute is concentrated at the accumulation wall, and its exit is easier if the capillary is situated in this block so that the sample does not have to overcome the field strength. 

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