Whenever a temperature gradient exists within a system, or when two systems at different temperatures are brought into contact, energy is transferred. The process by which the energy transport takes place is known as heat transfer. Because the heating surface of an evaporator represents the largest portion of the evaporator cost, heat transfer is the most important single factor in the design of an evaporation system. An index for comparing different types of evaporators is the ratio of heat transferred per unit of time per unit of temperature difference per dollar of installed cost. If the operating conditions are the same, the evaporator with the higher ratio is the more "efficient."
Three distinctly different modes of heat transmission are: conduction, radiation, and convection. In evaporator applications, radiation effects can generally be ignored. Most usually, heat (energy) flows as a result of several or all of these mechanisms operating simultaneously. In analyzing and solving heat transfer problems, it is necessary to recognize the modes of heat transfer which play an important role, and to determine whether the process is steady-state or unsteady-state. When the rate of heat flow in a system does not vary with time (i.e., 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 heat transferred to a fluid which is being evaporated can be considered separately as sensible heat and latent (or "change of phase") heat. Sensible heat operations involve heating or cooling of a fluid in which the heat transfer results only in a temperature change of the fluid. Change-of-phase heat transfer in an evaporation system involves changing a liquid into a vapor or changing a vapor into a liquid, i.e., vaporization or condensation. Boiling or vaporization is a convection process involving a change in phase from liquid to vapor. Condensation is the convection process involving a change in phase from vapor to liquid. Most evaporators include both sensible heat and change-of-phase heat transfer.
Energy is transferred due to a temperature gradient within a fluid by convection; the flow of energy from the heating medium, through the heat surface of an evaporator and to the process fluid occurs by conduction. Fourier observed that the flow or transport of energy was proportional to the driving force and inversely proportional to the resistance.
Flow = f (potential + resistance)
Conductance is the reciprocal of resistance and is a measure of the ease with which heat flows through a homogeneous material of thermal conductivity k.
Flow = f (potential * conductance)
A potential or driving force in a process heat exchanger or evaporator is a local temperature difference, AT. Figure 3 illustrates an example of conduction through composite walls or slabs having different thickness and composition. The conductance, also known as the wall coefficient, is given by: hw = k/xw (e.g. Btu/hr ft2 °F).[6] By selecting a conducting material, such as copper or carbon steel, which has a relatively high value of thermal conductivity, and by designing a mechanically rigid but thin wall, the wall coefficient could be large. Fouling problems at surfaces x0 and x3 must be understood and accounted for. A stagnant oil film or a deposit of inorganic salts must be treated as a composite wall, too, and can seriously reduce the performance of an evaporator or heat exchanger over time. This phenomenon has been accounted for in good evaporator design practice by assigning a fouling factor, f, for the inside surface and the outside surface based upon experience.17' The fouling coefficient is the inverse of the fouling factor:
hfo = 1 ¡fo outside fouling coefficient hft = \!f inside fouling coefficient
Distance, x
Figure 3. Heat conduction through a composite wall, placed between two fluid streams Ta and Tb. (From Transport Phenomena by R. B. Bird, W. E. Stewart, and E. N. Lightfoot, 1960, p. 284. Used with permission of John Wiley & Sons, Inc.)
Distance, x
Figure 3. Heat conduction through a composite wall, placed between two fluid streams Ta and Tb. (From Transport Phenomena by R. B. Bird, W. E. Stewart, and E. N. Lightfoot, 1960, p. 284. Used with permission of John Wiley & Sons, Inc.)
Note that the bulk fluid temperatures (designated Ta and Tb in Fig. 3) are different than the wall or skin temperatures (T0 and T3). Minute layers of stagnant fluid adhere to the barrier surfaces and contribute to relatively important resistances which are incorporated into a film coefficient.
ha = outside film coefficient ht = inside film coefficient
The magnitude of these coefficients is determined by physical properties of the fluid and by fluid dynamics, the degree of turbulence known as the Reynolds number or its equivalent. Heat transfer within a fluid, due to its motion, occurs by convection; fluid at the bulk temperature comes in contact with fluid adjacent to the wall. Thus, turbulence and mixing are important factors to be considered, even when a change in phase occurs as in condensing steam or a boiling liquid.
The development of heat transfer equations for the tubular surface in Fig. 4 is similar to that for the composite walls of Fig. 3 except for geometry. It is quite important to differentiate between the inner surface area of the tubing and the outer surface area, which could be considerably greater, particularly in the case of a well-insulated pipe or a thick-walled heat exchanger tubing. Unless otherwise specified, the area/I, used in determining evaporator sizes or heat transfer coefficients, is the surface through which the heat flows, measured on the process or inside surface of the heat exchanger tubing.
The derivation of specific values for the inside and outside film coefficients, ht and h0, is a rather involved procedure requiring a great deal of applied experience and the use of complex mathematical equations and correlations; these computations are best left to the staff heat transfer specialist, equipment vendor, or a consultant. Listed are four references that deal specifically with evaporation and the exposition and use of semi-empirical equations for heat transfer coefficients.[8HU]
If steady-state conditions exist (flow rates, temperatures, composition, fluid properties, pressures), Fourier's equation applies to macro-systems in which energy is transferred across a heat exchanger or an evaporator surface:
The term U is known as the overall heat transfer coefficient and is defined by the following equation:
Example:
ha = 1000 Btu/hr fl2 °F Condensing steam hf = very large Clean steam hw = 39,000 1" #16 BWG copper tubing hf. - 500 Inside fouling coefficient hj = 600 Aqueous solution of inorganic salt
U = (0.001 + 0.0 + 0.003 + 0.002 + 0.0016)"1 = 213 Btu/hr ft2 °F
Fluid at temperature Tb outside tube
T.12
Figure 4. Head conduction through a laminated tube with fluid at temperature T„ inside and fluid temperature Tb outside. (From Transport Phenomena by R. B. Bird, W. E. Stewart, andE. N. Lightfoot, p. 287, John Wiley & Sons, Inc., 1960. Used with permission.)
The evaporator design engineer determines the heat load, Q, and the driving force, AT, from the Heat Exchanger Specification Sheet. If an overall coefficient, U, can be obtained from operating or pilot plant data (or can be calculated, as in the example above), the required evaporator surface area, A, can be obtained. In most types of evaporators, the overall heat transfer coefficient can be a strong function of the temperature difference, AT. Because the driving force is not constant at every point along a heat exchanger or evaporator surface, a LMTD (Log Mean Temperature Difference) and LMTD correction factors are used in the Fourier equation to represent AT. Figure 5 shows how the LMTD can be calculated using terminal temperatures (i.e., inlet and outlet temperatures) for a heat exchanger in the simple case where no change of phase occurs.
In a steam-heated evaporator, both the heating medium and the process fluid undergo a phase change and most of the energy transferred is latent heat. Some sensible heat may be involved if the feed stream is to be preheated and if the condensate undergoes some subcooling. Further, some types of evaporators (for example, a submerged tube forced-circulation evaporator) involve the concept of boiling point elevation, due to the hydrostatic pressure of the liquid phase. The point to be emphasized is that the representative driving force, AT, utilized in the proper design of an evaporator involves some rather complicated computations and correction factors, compared with a simple problem of the transfer of sensible heat in the tubular exchanger illustrated in Fig. 5.
The temperature difference used in computing heat transfer in evaporators is usually an arbitrary figure, since it is really quite impossible to determine the temperature of the liquid at all positions along the heating surface (for example, see Fig. 6). The condensing temperature of steam, the more common heating medium, can usually be determined simply and accurately from a measurement of pressure in the steam side of the heating element, together with use of the steam tables. In a similar manner, a pressure measurement in the vapor space above the boiling liquid will give the saturated vapor temperature which, assuming a negligible boiling-point rise, would be substantially the same as the boiling liquid temperature. Temperature differences calculated on the basis ofthis assumption are called apparent temperature differences and heat-transfer coefficients are called apparent coefficients.
Figure 6. Temperature variations in a long-tube vertical evaporator. (1) Feed not boiling at tube inlet. (2) Feed enters at boiling point. (3) Same as curve 2, but feed contains 0.01% surface active agent. (From Chemical Engineers'Handbook, edited by R. H. Perry and C. H. Chilton, 5th ed., p. 11-29. ©1973, McGraw-Hill. Used with permission.)
Figure 6. Temperature variations in a long-tube vertical evaporator. (1) Feed not boiling at tube inlet. (2) Feed enters at boiling point. (3) Same as curve 2, but feed contains 0.01% surface active agent. (From Chemical Engineers'Handbook, edited by R. H. Perry and C. H. Chilton, 5th ed., p. 11-29. ©1973, McGraw-Hill. Used with permission.)
Boiling-point rise is the difference between the boiling point of a solution and the boiling point of water at the same pressure. Figure 7 can be used to estimate the boiling-point rise for a number of common aqueous solutions. When the boiling-point rise is deducted from the apparent temperature difference, the terms temperature difference corrected for boiling-point rise and heat-transfer coefficient correctedfor boiling-point rise are used. This is the most common basis of reporting evaporator heat transfer data, and is the basis understood in the absence of any qualifying statement.'121
Was this article helpful?