Heat transfers

Heat tranfer processs time constants are formulated as 

U is the heat transfer coefficient, M the mass, Cp the heat capacity and A the heat transfer area. A knowledge and understanding of the appropriate time constants is important in interpreting many of the simulation examples. 

Heat transfer (heat transmission) is an important unit operation in chemical and bioprocess plants. In general, heat is transferred by one of the three mechanisms, namely, conduction, convection, and radiation, or by their combinations. However, we need not consider radiation in bioprocess plants, which usually operate at relatively low temperatures. The heating and cooling of solids rarely become problematic in bioprocess plants. 

The term heat exchanger in the broader sense means heat transfer equipment in general. In the narrower sense, however, it means an equipment in which colder fluid is heated through use of the waste heat of a hotter fluid. For example, in milk pasteurization plants the raw milk is usually heated in a heat exchanger by pasteurized hot milk, before the raw milk is heated by steam in the main heater. 

Heat transfer The basic concepts of mass transfer can be readily extended to heat transfer by writing the rate of heat transfer (from phase 1 to phase 2) across a surface as 

Heat is transferred from points of high temperature to points of lower temperature by direct contact of particles of matter or the emission and absorption of radiant energy. The three classifications of heat transfer are  

Conduction. The transfer of heat from one body to another by physical contact. The rate of heat flow by conduction is proportional to the area available for the heat transfer and the temperature gradient in the direction of the heat flow path. The rate of heat flow in a given direction can be expressed as  

Shell and tube Bundle of tubes encased in a cylindrical shell. Always the first type exchanger to consider. 

Air cooled heat exchanger Rectangular tube bundles mounted on frame, with air used as the cooling medium Economic where cost of cooling water is high. 

Double pipe Pipe within a pipe inner pipe may be finned or plain. For small units. 

In most situations heat flows not by one, but by several of these mechanisms simultaneously. 

Conduction is the transfer of heat from one part of a body to another part of the same body, or from one body to another in physical contact with it, without appreciable displacement of the particles of the body. Conduction can occur in solids, liquids, or gases. 

Convection is the transfer of heat from one point to another within a fluid, gas or liquid, by the mixing of one portion of the fluid with another. In natural convection, the motion of the fluid is entirely the result of differences in density resulting from temperature differences in forced convection, the motion is produced by mechanical means. When the forced velocity is relatively low, it should be realized that free-convection factors, such as density and temperature difference, may have an important influence. 

In the solution of heat-transfer problems, it is necessary not only to recognize the modes of heat transfer which play a role, but also to determine whether a process is Steady or Unsteady. When the rate of heat flow in a system does not vary with time-when it is constant-the temperature at any point does not change and steady-state conditions prevail. Under steady-state conditions, the rate of heat input at any point of the system must be exactly equal to the rate of heat output, and no change in internal energy can take place. The majority of engineering heat-transfer problems are concerned with steady-state systems. 

The transfer of heat between two adjacent passages is a combination of transfer at the two surfaces of the wall between them and of conduction through the wall. The rate of transfer can be expressed in the form h X (area) X (difference of temperatures in the passages on one side and the other). We call h the overall heat transfer coefficient. 

If the material at the junction of the walls is neglected, the temperature in the wall varies linearly with distance, and the addition of resistances gives 

In the limit e — 0, A e does not approach zero otherwise an infinite number of resistances would be found in a finite space. Equation (15) can be written 

Nu = Nusselt number (of magnitude 3-4 for many shapes of cross section) 

The transfer of heat to and from process fluids is an essential part of most processes. In general, heat flows from one location to another by three distinct mechanisms  

In this part we will concentrate on heat transfer in SCF reactors. For this, we wiU look at the mechanisms that govern heat transfer from the inside of the reactor (bulk) toward the coolant in the jacket. Many expressions and correlations have been developed for stirred vessels, depending on the vessel geometry, the stirrer type and geometry, and the liquid medium [8-10]. However, none of them have been specifically derived for supercritical fluids. 

This unique position for heat is the reason why heat, of all the forms of energy, needs to be studied in further detail. 

Heat transfer is thus important to biological organisms. Excess heat must be removed and heat deficiencies must be filled. Otherwise, organisms will not survive. 

Conduction, convection, and radiation heat transfer happen according to 

This relation is somewhat different for the three different heat transfer modes, but dependence on these parameters is important for each. 

All heat is transferred due to a difference in temperature. As the temperature difference increases, more heat can be transferred from the stuff at higher temperature to the stuff at the lower temperature. 

There are at least three ways to heat a wafer in a cold wall reactor  

Since the most important industrial CVD-W reactors essentially use hot plate heating we will direct most of our attention to this type of wafer heating. 

Generally speaking, there are at least four different routes for transporting heat from one body (the hot plate) to another (the wafer)  

The heat transport by physical contact between the wafer and the hot plate is very marginal as is the case for free convection (certainly at low pressures). Therefore, we will concentrate on the two main pathways, namely radiation and gas conduction (see also figure 7.1). 

Heat transport by radiation is described by the Stefan-Boltzmann equation (for two parallel planes)  

In considering heat transfer in gas-solid fluidization it is important to distinguish between, on the one hand, heat transfer between the bed and a heat transfer surface (be it heated bed walls or heat transfer coils in the bed) and, on the other hand, heat transfer between particles and the fluidizing gas. Much of the fluidization literature is concerned with the former because of its relevance to the use of fluidized beds as heterogeneous chemical reactors. Gas-particle heat transfer is rather more relevant to the food processing applications of fluidization such as drying, where the transfer of heat from the inlet gas to the wet food particle is crucial. 

Correlations for heat transfer coefficients generally take the form 

The Nusselt number Nu contains the heat transfer coefficient h and is defined as 

Consider steady heat transfer across a slab of material that extends infinitely in two directions and has thickness L. In the thin direction, x, the equation for steady heat conduction is 

The temperature, T, is a function of position, x. Notice that one condition is at x = 0 and the other at x = L. This makes it a two-point boundary value problem. The thermal conductivity k can depend upon temperature, and when it does the problem is nonlinear. The rate of energy generation is Q. 

Diffusion across a flat slab is very similar to Eq. (9.1)  

Many chemical reactions take place inside a catalyst pellet, which is a porous material (such as AI2O3 impregnated with the catalyst, usually metals of various kinds). The equation for a spherical catalyst pellet with radius is 

In most cases, this problem is nonlinear. Again, this problem is a two-point boundary value problem because the boundary conditions are at two different spatial positions. At r = 0 there is no flux (center of the pellet), and at r = Rp the concentration takes a specified value equal to the external concentration. 

ThcrL uie three distinet ways in which heat may pass from a source to a receiver, although most engineering applications are combinations of two or three. These are conduetion, convection, and radiation 

The rate of flow of heat is proportional to the difference in temperature through the solid and the heat transfer area of the solid, and uiverse) proportional to the thickness of the solid. The proportionality coiislain. f. is known as the thermal conductivity of the solid. Thus, the rjiiaiility o heat l lo may he CNpressed by the following equation  

A f = temperature difference, F k = thermal conductivity, Btu/hr ft-°F L = distance heat energy is conducted, ft 

The thermal conductivity of solids has a wide range of numerical values, depending upon whether the solid is a relatively good conductor of heat, such as metal, or a poor conductor, such as glass-fiber or calcium silicalc. The laUer serves as insulation. 

The transfer of heat within a fluid as the result of mixing of the warmer and cooler portions of the fluid is convection. For example, air in contact with the hot plates of a radiator in a room rises and cold air is drawn off the floor of the room. The room is heated by convection. It is the mixing of the warmer and cooler portions of the fluid that conducts the heat from the radiator on one side of a room to the other side. Another example is a bucket of water placed over a flame. The water at the bottom of the bucket becomes heated and less dense than before due to thermal expansion. It rises through the colder upper portion of the bucket transferring its heat by mixing as it rises. 

In practice, the heat transfer rate to a cryogenic fluid may be limited by the nature of the contacting surface, fluid, or vapor. For example, when the fluid contacts an insulating material, the heat transfer rate 

When a solid is heated or cooled, heat is transferred through the structure. The equations of heat transfer were initially formulated by Fourier. They predate and are of identical mathematical form to Pick s laws of diffusion (Sections 7.1 and 7.3). In the case of steady-state heat transfer, the one-dimensional heat transfer equation is  

In the case of nonsteady-state heat transfer, the equation is analogous to the diffusion equation  

Examples are provided from heat transfer mass transfer simultaneous diffusion and convection simultaneous diffusion and chemical reaction simultaneous diffusion, convection, and chemical reaction and viscous flow. 

Some examples may be worked out in more detail than others. Those worked-out examples with missing details provide an opportunity for the readers to check their knowledge of the mathematical techniques used. 

Although we know from our experience that heat flows from regions of high temperature to regions of low temperature, one might want to know how the temperature in a solid changes with time and position. Assuming that the heat transfer is strictly by conduction, one can analyze this situation with reference to the sketch shown below. 

An energy balance on a small volume of the solid of cross-sectional area A and thickness Ax is 

The rate of heat conduction into the solid volume is given by Aq where q x is heat flux at position x (J/cm s) whereas Aq x+ x is the rate of heat conduction out. q x+i is the heat flux at position x + Ax. 

The approach to problems of heat transfer in agitated systems has been entirely analogous to that employed for heat transfer to fluids in pipes or in other physical situations. In studies of agitated systems, the general correlation technique has been to use a Nusselt number, an impeller Reynolds number, a Prandtl number, and a viscosity ratio in the usual heat-transfer relation  

Some workers have modified this equation to include certain characteristic dimension ratios of the agitation system. 

The results of the more extensive experimental investigations are outlined in Table VI. Except for scattered early data (P6, R2), the work of Chilton et al. (C5) was the first study to use the conventional groups for correlating heat transfer to jackets or coils. In some cases the temperatures at different points in the liquid varied by as much as 5°F. They used a variety of liquids, and found values of h in the range of 20-2000 B.T.U./(hr.) (ft.2) (°F.), depending on the conditions used. 

Investigators Heat transfer surface System geometry Correlation Range of Reynolds number 

Rushton et al. (Rl5) Vertical tubes 4-ft. vessel— 4 ft. water depth. Mixing Equipment Co. flat blade turbines 16 in., 6 blades, heating. 16 in., 6 blades, cooling. 12 in., 4 blades, heating. 12 in., 4 blades, cooling. 1 1 1 1 poop UPPao 1 X l -5 X 10  

In order to increase the temperature of a substance, we have to supply heat. The heat that should be supplied to increase the temperature varies from one substance to another. So scientists have come up with a way to define this -the specific heat. The specific heat (J/g.C°) of a substance is the amount of heat that should be added to one gram of that substance to raise its temperature by one degree Celsius. The Heat capacity of a given sample substance is the amount of heat that is required to increase the temperature by one degree Celsius. Heat capacity, specific heat, and temperature are related according to the following relations  

Heat of fusion of a solid substance is the quantity of heat required to melt one gram of that substance at its melting point. The usual unit used is J/g. 

It is normal practice only to check out the heat transfer coefficient of the agitator system under consideration at its full-scale dimensions. 

During scale-up, it must be taken into account that the vessel volume increases proportionately to the cube of the scale-up factor while the vessel surface area available for heat transfer increases in proportion to its square. If the scale-up is performed with a criterion less than Oj = const due to process constraints (P/Vocthe heat transfer capability is diminished not only due to the higher heat flux per unit area but also by the lower values of a.  

This section describes irreversible and reversible heat transfer. Keep in mind that when this book refers to heat transfer or heat flow, energy is being transferred across the boundary on account of a temperature gradient at the boundary. The transfer is always in the direction of decreasing temperature. 

We may sometimes wish to treat the temperature as if it is discontinuous at the boundary, with different values on either side. The transfer of energy is then from the warmer side to the cooler side. The temperature is not actually discontinuous instead there is a thin zone with a temperature gradient. 

In this chapter, we briefly describe fundamental concepts of heat transfer. We begin in Section 20.1 with a description of heat conduction. We base this description on three key points Fourier s law for conduction, energy transport through a thin film, and energy transport in a semi-infinite slab. In Section 20.2, we discuss energy conservation equations that are general forms of the first law of thermodynamics. In Section 20.3, we analyze interfacial heat transfer in terms of heat transfer coefficients, and in Section 20.4, we discuss numerical values of thermal conductivities, thermal diffusivities, and heat transfer coefficients. 

This material is closely parallel to the ideas about diffusion presented in the rest of this book. This parallelism is not unexpected, for heat transfer and mass transfer are described with equations that are very similar mathematically. The material in Section 20.1 is like that in Chapter 2, and the general equations in Section 20.2 are conceptually similar to those in Chapter 3. The material on heat transfer coefficients in Section 20.3 closely resembles the mass transfer material in Chapters 9 through 15, and the numerical values in Section 20.4 are parallel to those in Chapters 5 and 8. 

Thus we are abstracting ideas of heat transfer in a few sections, whereas we detailed similar ideas of mass transfer over many chapters. This represents a tremendous abridgment. As those skilled in heat transfer recognize, the heat transfer literature is immense, of far greater size than the mass transfer literature. To be sure, this book is about diffusion, and so an emphasis on mass transfer is appropriate. But if the description of heat transfer is to be so terse, why include it at all  

I have included the description of heat transfer because I want to discuss simultaneous heat and mass transfer in the next chapter. This simultaneous transport process is important practically and is interesting intellectually, with implications ranging beyond the particular problems presented. However, to discuss this simultaneous process, we need to assure a background in heat transfer. I expect that many who read this book will not have such a background, for this topic is usually buried well inside the engineering curriculum. Accordingly, this chapter is a synopsis to provide this background. 

The mechanisms described above tell us how heat travels in systems, but we are also interested in its rate of transfer. The most common way to describe the heat transfer rate is through the use of thermal conductivity coefficients, which define how quiddy heat will travel per unit length (or area for convection processes). Every material has a characteristic thermal conductivity coefficient. Metals have high thermal conductivities, while polymers generally exhibit low thermal conductivities. One interesting application of thermal conductivity is the utilization of calcium carbonate in blown film processing. Calcium carbonate is added to a polyethylene resin to increase the heat transfer rate from the melt to the air surrounding the bubble. Without the calcium carbonate, the resin cools much more slowly and production rates are decreased. 

When two bodies having different temperatures are put in contact, there is a heat transfer from the higher-temperature body to the lower-temperature body. Heat transfer can be effected by three physical mechanisms conduction, convection, and radiation. 

Metals are the best heat conductors. On the other hand, air is a poor conductor of heat, and in general, biological materials (e.g., foods) are poor conductors. Materials that are poor conductors are called insulators (e.g., plastics, asbestos, rubber, cotton). 

Food materials (which depend not only on the t fpe of food but also its microstructure) 0.2-0.7 

Wood (depending on the type of wood and on the direction of the fibers) 0.1-0.3 

Adapted from http //web2.clarks(Hi.edii )rojects/subramaniaii/ch330/notes/ Introduction%20to%20Heat%20Transfer.pdf 

In simple cases, e.g. a tank containing hot liquid losing heat to its surroundings, the equation governing heat transfer may be written 

The overall heat transfer coefficient is normally made up of several terms arising from the various resistances to the flow of heat. In the simple example mentioned above, there will be terms for heat transfer through the liquid by conduction and convection, for conduction through the metal wall of the tank and through any layers of insulating material and for heat loss from the outer skin to the surrounding air. 

In a given situation, the value of h will depend on the mechcmism by which heat is transferred, on the properties of the materials through which heat transfer takes place and on the fluid mechanics of any heated and cooled fluids. The temperature difference and the absolute value of the temperatures may also affect h, though the value of h is usually taken to be constant over limited ranges of temperature. Table 9 gives the ranges of values of h to be expected in various situations. 

Approximate ranges of values of the overall heat transfer coefficient, h 

The ignition, burning, and extinguishment of fires can be explained in terms of classical heat transfer principles. Heat is transferred by one or more of three mechanisms  

Heat transfer is always from hot to cold. The main mechanisms of heat transfer in a hydrocarbon are thermal radiation and direct flame contact (convection). Heat transfer to personnel can cause burns. Heat transfer to equipment and structures can lead to failure of hydrocarbon-containing equipment that can further feed the fire. 

Bergles, Arthur E. Department of Mechanical Engineering, Rensselaer Polytechnical Institute (chap. 11, Techniques to Augment Heat Transfer), e-mail abergles aol.com 

Bergman, Theodore L. Department of Mechanical Engineering, University of Connecticut (chap. 18, Heat Transfer in Materials Processing), e-mail tberg eng2.uconn.edu 

Shriniwas Department of Chemical Engineering, Ohio State University (chap. 13, Heat Transfer in Fluidized and Packed Beds) 

Ping-Hai Department of Mechanical Engineering, National Taiwan University, Taiwan, ROC (chap. 16, Measurement of Temperature and Heat Transfer), e-mail phchen ccms.ntu.edu.tw 

Calculate the time taken for the distant face of a brick wall, of thermal diffusivity, DH = 0.0042 cm2/s and thickness l = 0.45 m, initially at 290 K, to rise to 470 K if the near face is suddenly raised to a temperature of O = 870 K and maintained at that temperature. Assume that all the heat flow is perpendicular to the faces of the wall and that the distant face is perfectly insulated. 

The temperature at any distance x from the near face at time t is given by  

Considering the first term only, 3471 05 = 1.0 and t = 1.204 x 105 s The second and higher terms are negligible compared with the first term at this value 

Calculate the time for the distant face to reach 470 K under the same conditions as Problem 9.1, except that the distant face is not perfectly lagged but a very large thickness of material of the same thermal properties as the brickwork is stacked against it. 

This problem involves the conduction of heat in an infinite medium where it is required to determine the time at which a point 0.45 m from the heated face reaches 470 K. 

Although the use of a relatively large amount of solvent is effective for a small scale laboratory experiment, it should be noted that the final removal of heat is, in principle, ascribed to heat transfer through the wall of the reactor. Therefore, heat transfer is especially important for a large-scale production in industry. 

The most straightforward method for effective temperature control is heat transfer. Efficient heat transfer to remove heat from the reaction system is the key to conducting highly exothermic reactions, although synthetic chemists have not paid significant attention to this issue. 

The rate of heat transfer is important for successfully conducting reactions. If heat transfer is slow, the energy liberated by a reaction is accumulated in the system and the temperature in the reactor increases, causing undesired side reactions. Efficient heat transfer is essential for the conduction of highly exothermic reactions in a controlled way in flash chemistry. 

Heat transfer is the passage of thermal energy from a hot body to a cold body. It occurs through conduction, convection, and radiation, or a combination of these. 

Conduction is the thermal energy transfer through direct molecular contact. Conduction occurs between molecules, both solute and solvent molecules in solution. Conduction in solution is analogous to molecular diffusion in solution. The amount of heat transferred by conduction is expressed by  

at different points of any gas in a closed volume for a short time, a different temperature is created and the gas is then left to itself, the temperature at all gas points is equalized owing to the process of heat transfer. From a macroscopic point of view, the phenomenon of heat transfer in gases consists of temperature transport from hotter to colder places. Within the framework of the molecular kinetic theory, the process of heat transfer consists of the fact that molecules from a heated site of the gas, where they have large kinetic energy, transfer the energy to cooler areas via collisions a flow of heat is thus created. 

In reality, in gases and liquids this phenomenon is usually accompanied by heat transport by the steam of a gas or a liquid initiated by their density difference, i.e., so-called convection. However, we will now consider heat transfer exclusively from the point of view of molecular kinetics. By the way, it is very difficult to subdivide these two processes. 

The transfer of heat caused by the thermal (chaotic) movement of microparticles is referred to as a heat transfer phenomenon. Thus, in the general transport formula (3.7.10), Aq is the flux of heat. The transferable value in this case is the amount of heat Q or G(x) = CyT x) where Cy is the heat capacity of a substance. This heat is produced by the total kinetic energy of the molecules. Hence the heat transport description can be given as  

From a microscopic point of view, the driving force is the molecular averaged kinetic energy gradient d e) dx. Taking into account that s)=(U2)kT, we obtain  

From the other side a value of the particle s flux is equal to (dqldt)X(llS)= 

Having described the electrical paraneters which control the current density and power dissipation within the ceramic material and having outlined various applicator structures, attention is now switched to the equation which controls the heat transfer. In the present context it will suffice to quote the following continuity equations for heat  

Many gas-solid reactions are sufficiently exothermic or endothermic that the progress of the reaction is markedly affected by the temperature change that accompanies the reaction. Moreover, many reactions will take place at measurable rates only at elevated temperatures it follows that both heat transfer between a pellet and a moving gas stream and conductive heat transfer within a pellet itself need to be discussed. 

Since the subject of heat transfer is extensively covered in many engineering texts [1, 79, 80] only a very brief survey of topics that are of particular relevance to gas-solid reaction systems will be presented here. 

CONVECTIVE HEAT TRANSFER BETWEEN A SINGLE PARTICLE 

Let us consider a solid particle the surface temperature of which is maintained at in contact with a moving gas stream, which has a bulk temperature Tq, as sketched in Fig. 2.9. 

The heat flux from the solid surface may be related to Tq and in the following manner  

For a pure component droplet evaporating into a stagnant gaseous medium in the continuum regime, the quasi-steady rate of change of droplet radius a with time is given by an equation attributed to Maxwell (1890), 

If the vapor is removed by flowing a purge gas through the balance chamber during the evaporation process, and/or if the chamber volume is 

Continuum theory applies when the mean free path of the vapor A,- is small compared with the droplet radius, that is, when the Knudsen number Kn is small (Kn = A,/a 1). From the kinetic theory of gases (Jeans, 1954), the mean free path of the vapor in a binary system is given by 

Values of djj for common gases have been tabulated by Hirschfelder et al. (1967) and by Bird et al. (1960). 

Rapid evaporation introduces complications, for the heat and mass transfer processes are then coupled. The heat of vaporization must be supplied by conduction heat transfer from the gas and liquid phases, chiefly from the gas phase. Furthermore, convective flow associated with vapor transport from the surface, Stefan flow, occurs, and thermal diffusion and the thermal energy of the diffusing species must be taken into account. Wagner 1982) reviewed the theory and principles involved, and a higher-order quasisteady-state analysis leads to the following energy balance between the net heat transferred from the gas phase and the latent heat transferred by the diffusing species  

Increasing rate of transport of the gas molecules across the interface 

Heating and cooling of reactants and products are generally carried out in tubular or coil heat exchangers. Two fluids at different temperatures flow in the tube and shell sides of the exchanger, and heat transfer takes place from the hot to the cold fluid. The rate of heat transfer (Q) is the product of the heat transfer area (A), the temperature difference between the two fluids (AT), and the overall heat transfer coefficient (U). In other words Q = UA AT. 

The overall heat transfer coefficient is a composite number. It depends on the individual heat transfer coefficients on each side of the tube and the thermal conductivity of the tube material. The individual heat transfer coefficient in turn depends on the fluid flow rate, physical properties of the fluid, and dirt factor. The temperature along the tube is not uniform. The hot and the cold fluids may flow in the same (cocurrent) or in opposite (countercurrent) directions. Generally the hot and cold fluids come in contact only once, and such an exchanger is called single pass. In a multipass exchanger, the design of the 

Select a convection section with the same size tube as the radiant section, 4.5 inches OD (do) or 

The gas flow area is restricted by both the tube and the fins. The projected area of the finned tube 

The heat transfer rate can now be computed. First consider the radiation leakage through the shield coil. From the previous example, the factor of comparison between a tube bank and a plane, a = 0.74. 

The convective heat transfer coefficient for a bare tube is computed as follows  

The fin efficiency, E, = 0.84. The effective heat transfer coefficient for the finned tube is 

Compared to the use of reduced-order flow models, the porous-medium approach allows an even larger multitude of microchannels to be dealt with. Furthermore, for comparatively simple geometries with only a limited number of channels, it represents a simple way to provide qualitative estimates of the flow distribution. However, as a course-grained description it does not reach the same level of accuracy as reduced-order models. Compared to the macromodel approach as propagated by Commenge et al, the porous-medium approach has a broader scope of applicability and can also be applied when recirculation zones appear in the flow-distribution chamber. However, the macromodel approach is computationally less expensive and can ideally be used for optimization studies. 

The generalized energy equation for a polymerization system in convective or non-convective domain is (Bird et al., 2007) 

If the reaction domain is nonconvective, the substantial derivative becomes a partial derivative, or time derivative measured at each point in space. This approach is used for reactive spherical particulate systems in the next section. 

An important limiting case of interest in this monograph is the purely diffusive case (no convection and chemical reaction) in the radial direction (radius = ro) of a cylindrical geometry, which occurs when a fluid within a small tube is rapidly cooled. Thus, Eq. (2.2.9) reduces to 

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Even if the reactor temperature is controlled within acceptable limits, the reactor effluent may need to be cooled rapidly, or quenched, to stop the reaction quickly to prevent excessive byproduct formation. This quench can be accomplished by indirect heat transfer using conventional heat transfer equipment or by direct heat transfer by mixing with another fluid. A commonly encountered situation is... 

In fact, cooling of the reactor effluent by direct heat transfer can be used for a variety of reasons ... 

The liquid used for the direct heat transfer should be chosen such that it can be separated easily from the reactor product and so recycled with the minimum expense. Use of extraneous materials, i.e., materials that do not already exist in the process, should be avoided because it is often difficult to separate and recycle them with high efficiency. Extraneous material not recycled becomes an effluent problem. As we shall discuss later, the best way to deal with effluent problems is not to create them in the first place. 

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

Figure 2.5 Heat transfer to and from stirred tanks.

However, if high rates of heat transfer are required or the catalyst requires frequent regeneration, then fixed beds are not suitable, and under these circumstances, a fluidized bed is preferred, as we shall discuss later. 

Fluidized-bed catalytic reactors. In fluidized-bed reactors, solid material in the form of fine particles is held in suspension by the upward flow of the reacting fluid. The effect of the rapid motion of the particles is good heat transfer and temperature uniformity. This prevents the formation of the hot spots that can occur with fixed-bed reactors. 

In addition to the advantage of high heat transfer rates, fluidized beds are also useful in situations where catalyst particles need frequent regeneration. Under these circumstances, particles can be removed continuously from the bed, regenerated, and recycled back to the bed. In exothermic reactions, the recycling of catalyst can be... 

One disadvantage of fluidized heds is that attrition of the catalyst can cause the generation of catalyst flnes, which are then carried over from the hed and lost from the system. This carryover of catalyst flnes sometimes necessitates cooling the reactor effluent through direct-contact heat transfer hy mixing with a cold fluid, since the fines tend to foul conventional heat exchangers. 

Heat transfer. Once the basic reactor type and conditions have been chosen, heat transfer can be a major problem. Figure 2.11 summarizes the basic decisions which must be made regarding heat transfer. If the reactor product is to be cooled by direct contact with a cold fluid, then use of extraneous materials should be avoided. 

The temperature difference between stages can be manipulated by changing the heat transfer area. Figure 3.136 shows the effect of a decrease in heat transfer area. 

Reactor heat carrier. Also as pointed out in Sec. 2.6, if adiabatic operation is not possible and it is not possible to control temperature by direct heat transfer, then an inert material can be introduced to the reactor to increase its heat capacity flow rate (i.e., product of mass flow rate and specific heat capacity) and to reduce... 

The final restriction of simple columns stated earlier was that they should have a reboiler and a total condenser. It is possible to use materials fiow to provide some of the necessary heat transfer by direct contact. This transfer of heat via direct contact is known as thermal coupling. 

Specifying the hot utility or cold utility or AT m fixes the relative position of the two curves. As with the simple problem in Fig. 6.2, the relative position of the two curves is a degree of freedom at our disposal. Again, the relative position of the two curves can be changed by moving them horizontally relative to each other. Clearly, to consider heat recovery from hot streams into cold, the hot composite must be in a position such that everywhere it is above the cold composite for feasible heat transfer. Thereafter, the relative position of the curves can be chosen. Figure 6.56 shows the curves set to ATn,in = 20°C. The hot and cold utility targets are now increased to 11.5 and 14 MW, respectively. 

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... 

Rgura 6.8 Three forms of crosspinch heat transfer. 

The overlap in the shifted curves as shown in Fig. 6.15a means that heat transfer is infeasible. At some point this overlap is a maximum. This maximum overlap is added as a hot utility to correct the overlap. The shifted curves now touch at the pinch, as shown in Fig. 6.156. Since the shifted curves just touch, the actual curves are separated by AT ,in at this point (see Fig. 6.156). 

Find a way to overcome the constraint while still maintaining the areas. This is often possible by using indirect heat transfer between the two areas. The simplest option is via the existing utility system. For example, rather than have a direct match between two streams, one can perhaps generate steam to be fed into the steam mains and the other use steam from the same mains. The utility system then acts as a buffer between the two areas. Another possibility might be to use a heat transfer medium such as a hot oil which circulates between the two streams being matched. To maintain operational independence, a standby heater and cooler supplied by utilities is needed in the hot oil circuit such that if either area is not operational, utilities could substitute heat recovery for short periods. 

The shaded areas in Fig. 6.24, known as pockets, represent areas of additional process-to-process heat transfer. Remember that the profile of the grand composite curve represents residual heating and cooling demands after recovering heat within the shifted temperature intervals in the problem table algorithm. In these pockets in Fig. 6.24, a local surplus of heat in the process is used at temperature differences in excess of AT ,in to satisfy a local deficit. ... 

Example 6.4 The process in Fig. 6.2 is to have its hot utility supplied by a furnace. The theoretical flame temperature for combustion is 1800°C, and the acid dew point for the flue gas is 160°C. Ambient temperature is 10°C. Assume = 10°C for process-to-process heat transfer but = 30°C for flue-gas-to-process heat transfer. A high value for for flue-gas-to-process heat... 

Most refrigeration systems are essentially the same as the heat pump cycle shown in Fig. 6.37. Heat is absorbed at low temperature, servicing the process, and rejected at higher temperature either directly to ambient (cooling water or air cooling) or to heat recovery in the process. Heat transfer takes place essentially over latent heat profiles. Such cycles can be much more complex if more than one refrigeration level is involved. 

The problem with Eq. (7.5) is that the overall heat transfer coefficient is not constant throughout the process. Is there some way to extend this model to deal with the individual heat transfer coefficients ... 

By constrast, Fig. 7.46 shows a diflFerent arrangement. Hot stream A with a low coefficient is matched with cold stream D, which also has a low coefficient but uses temperature diflferences greater than vertical separation. Hot stream B is matched with cold stream C, both with high heat transfer coefficients but with temperature differences less than vertical. This arrangement requires 1250 m of area overall, less than the vertical arrangement. 

By assuming a reasonable fluid velocity, together with fluid physical properties, standard heat transfer correlations can be used. 

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

Thus, for a given exchanger duty and overall heat transfer coefficient, the 1-2 design needs a larger area than the 1-1 design. However, the 1-2 design offers many practical advantages. These... 

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