Tank coils are not generally used for the continuous heating or cooling of a flowing stream, but are usually applied in the heating or cooling of a liquid contained in a tank on a batch basis. The flow of heat into or out of the liquid, involves unsteady or transient heat transfer.
The heating and cooling media can flow through a coil immersed in the liquid as shown in Figure 1, or the media can be made to flow through a coil fastened (welded) on the outside of the vessel as shown in Figure 2. The latter arrangement may be referred to as "limpet coils" whereas the former is usually termed "coil in tank". The limpet coil is an improvement on the simple arrangement where a jacket through which the heat transfer medium flows, fits onto the outside of the vessel as illustrated in Figure 3. The benefits of the limpet coil are due to the uniform fluid velocity through the channel and the good distribution of heat transfer medium around the vessel periphery.
The heat transfer is usually improved by agitation of the liquid contained in the tank. (See Agitated Vessel Heat Transfer, Agitated Vessel Mass Transfer and Agitation Devices.) Unless agitation is employed the heat transfer at the vessel wall or across the coil will depend on natural convection within the liquid in the tank, which is not particularly efficient (see Free Convection).
In some applications, for instance, the manufacture of phenol-formaldehyde resin, the coils or jacket will serve two purposes. Steam or some other heating medium will be used initially to raise the temperature of the mixture in the tank to the desired reaction temperature. At a later stage a cooling medium (usually water) will be introduced into the coils or jacket to control the temperature to avoid runaway exothermic reactions, and finally to cool the batch before discharge. In such processes the viscosity of the fluid will change as the reaction proceeds. Changes in viscosity will affect the degree of agitation imparted to the batch liquid and hence the rate of heat transfer will fall as the viscosity increases.
Fletcher (1987) has given some representative data on overall heat transfer coefficients that may be obtained in agitated vessels. The range of these data shown in Table 1 illustrates some of the differences in heat transfer rates that may be experienced.
A number of different techniques are available to promote agitation within the bulk liquid. In general, they involve the rotation of some kind of blade system that either stirs the fluid or circulates it within the confines of the vessel. Mixing within vessels is a subject in its own right and only a brief outline is given here. Large diameter agitators that rotate at relatively low speeds, are usually employed where the liquid is viscous, in order to keep the power consumption for agitation as low as possible. Where low viscosity liquids are involved, smaller impellers operating at high speeds are often used. Where large viscosity changes are experienced during the processing, it is usual to employ low speed agitation. (See also Agitation Devices.)
Five, distinctly different agitators have found application in stirred tanks and include:
Anchor impellers as illustrated in Figure 4 usually operate at low speed, much of the disturbance within the liquid occurs close to the vessel wall. This is beneficial for heat transfer across the wall to or from limpet coils or jacket.
Helical ribbon impellers may be used in certain applications where the cost may be justified. Agitation at the wall is achieved by the close clearances between the blade and the wall surface. The helical design also imparts turbulence within the core of liquid. The arrangement of a helical ribbon mixer is shown in Figure 5.
Paddle type impellers may be used at high or low speeds of rotation. The basic concept is illustrated in Figure 6. The blades may be flat or pitched. At low speed the flat blades produce a tangential motion to the liquid. Pitched blades operated at high speed establish a radial flow pattern. The ratio of paddle diameter to vessel diameter is usually in the range 1:3 to 2:3.
Propellers resembling ships' propellers as illustrated in Figure 7, usually operate at high speed and produce an axial flow pattern in the liquid. The ratio of propeller diameter to vessel diameter is generally about 1:3.
Turbine mixers operate at high speed in low viscosity liquids. To reduce capital cost and to facilitate cleaning, the design is usually simple. The blades may be flat or curved as illustrated in Figure 8. Radial flow is induced by flat blades, but an axial component can be obtained with curved blades. The number of blades will affect the degree of turbulence produced, but as the number of blades is increased, the power consumption will increase. The final choice is a compromise between the level of turbulence desired and the allowable energy cost. The dissipation of energy may also produce a temperature rise in the liquid. The ratio of turbine diameter to vessel diameter is generally of the order of 1:3.
In many vessel designs baffles are included to provide good mixing by modification of flow patterns. The increased turbulence assists the heat transfer. Fletcher (1987) reports that baffles may increase heat transfer by as much as 35% compared to a system without baffles.
The level of turbulence within the vessel may be assessed using the so-called "agitation" Reynolds number Rea defined as:
where N is the speed of rotation of impeller, Di is the impeller diameter, and ν is the kinematic viscosity.
Table 2 Hewitt et al. (1994) provides the range of application of different agitators together with some practical comments.
The transfer of heat in agitated vessels involves two aspects:
The heat transfer associated with the flow within a pipe or channel, i.e., the coil in tank, limpet coils or the jacket.
The heat transfer associated with the flow across the vessel surface or across the outside of the coil in tank.
Heat transfer coefficients for the inside of limpet coils may be obtained from correlations developed or tubular or pipe flow. It will be necessary, however, to use a hydraulic mean diameter for the particular cross section of channel in the estimation of the appropriate Reynolds numbers. It has to be remembered that the effective heat transfer area is limited to the contact area between the limpet coil and the vessel outside wall.
Because of the complex flow patterns in jackets it is difficult to provide suitable correlations for heat transfer from within the jacket, and it is usual to base calculations on previous experience. Except for condensing steam heat transfer coefficients inside jackets are relatively low.
Heat transfer correlations within coils located in vessels are also based on correlations for straight pipes, but because of the circular motion of the fluid through the coil the heat transfer is enhanced. (See Coiled Tubes, Heat Transfer In.) In general the diameter of a coil is very much less than the inside diameter of the vessel so that the enhancement is greater than for limpet coils.
Jeschke (1925) provided an empirical correlation that allows for the increased heat transfer inside the coil
Where αi coil and αi (straight pipe) are the heat transfer coefficients on the inside of the coil and the equivalent straight pipe, respectively, and di and dc are the internal diameter of the pipe and the diameter of the coil, respectively.
It will be seen that as the coil diameter is increased the ratio di:dc decreases so that the rotational effect on heat transfer reduces. Because of the degree of turbulence generated in agitated vessels it is usual to assume that the heat transfer mechanism will be similar for the inside surface of the vessel and across immersed coils. The geometry involved, the use of baffles and the complex flow patterns make it inevitable that the correlations are empirical. The usual form of the correlations is:
where Nuν = the Nusselt number (based on vessel inside diameter), which may be referred to the heat transfer on the outside, of the helical coil or on the vessel inside surface. Pr is Prandtl Number, ηb and ηw are the liquid viscosities in the bulk and at the wall respectively and K is the constant that applies to the simple heat transfer correlation for the particular system. (See also Agitated Vessel Heat Transfer.)
Fletcher, P. (1987) Heat transfer coefficients for stirred batch reactor design, Chem. Engn., 33 (April), 33–37.
Jeschke, D. (1925) Wärmeübergang und Druckverlust in Rohrschlangen, Z. Deutsch. Ing., 81, 123.
Penney, W. R. (1983) Agitated Vessels in Heat Transfer Design Handbook, S.3.14. Hemisphere Publishing.