Document QXLpDyNyZKK0GxXdKx996VBZk

716 CHAPTER 53 1959 Guide transfer of mass as vapor and internal liquid. These two proc esses occur simultaneously, and the factors governing the rate of each process determine the rate of drying. In any commercial drying problem, a principal objective is to supply the required heat in the most efficient manner. Consequently, heat transfer may occur by convection, con duction, or radiation, or by any combination of these mecha nisms. The various types of industrial dryers may be shown to differ fundamentally with respect to the method used for transferring heat to the solid. In general, heat must flow first to the outer surface of the solid and then into the interior. An important exception is drying with high frequency electrical currents where heat is generated within the solid, producing a higher temperature at the interior than at the surface, and consequently, causing heat to flow from inside the solid to the outer surfaces. Mass transfer in drying occurs as liquid or vapor flow, or both, within the solid, and as vapor flow from the external wet surfaces. The nature of liquid-concentration gradients in solids during drying depends on the mtwhftntgm of internal liquid flow, and this mechanism, in turn, depends to a large extent upon the physical and chemical characteristics of the solid being dried. Infernal and External Conditions A study of how a solid dries may be based on the internal mpyhanism of liquid flow, or on the effect of the external conditions of temperature, humidity, air flow, state of sub division, etc., on the drying rate of the solid. The former pro cedure involves a fundamental study of the liquid flow condi tions within a solid during drying. The latter procedure, although less fundamental, is more generally used because the effects are easier to establish and the results have greater im mediate application in dryer design and operation. Internal Mechanism of Liquid Flow. Internal liquid flow may occur by several mechanisms, depending on the structure of the solid. Several mechanisms of flow are as follows: 1. Diffusion in continuous, homogeneous solids. 2. Capillary flow in granular and porous solids. 3. Flow caused by shrinkage and pressure gradients. 4. Flow caused by a vaporization-condensation sequence. 5. Flow caused by gravity. 6. Flow caused by an electrical potential, electro-osmosis. 7. Flow caused by temperature gradients, thermal diffusion. Although more than one of these mechanisms of flow may. be effective at one time, only one predominates as a rule at a given time, in a solid during drying. However, a different mechanism may predominate at a different time in the cycle. The mechanism of moisture flow is usually established experi mentally from a study of moisture gradients. External Variables. The principal external variables in volved in any drying problem are: temperature, humidity, air flow, state of subdivision of the solid, agitation of the solid, method of supporting the solid, and the contact between hot surfaces and wet solid. All these variables do not necessarily occur simultaneously in one problem. Periods of Drying1 A typical drying time curve for a wet solid is shown in Fig. 1. This curve is a plot of the moisture content at any time in a solid undergoing drying. It is the usual method of present ing experimental drying data. Although Ftg. 1 shows that the moisture content is subject to a continuous variation with time, a more precise illustration of the nature of this varia- Fig. 1 .... Moisture Content w vs. Drying Time 0 tion can be obtained by differentiating the curire and plotting the drying rate in pounds of water per (hour) (pound of dry material) against the moisture content in pounds of water per pound of dry material as shown in Fig. 2. The rate curve shows- that the drying process is not a smooth, continuous one in which a single mechanism controls throughout. Section BA on each curve represents a constant-rote period. In Fig. 1, it is shown by a straight line of constant slope dw/d$, which becomes a horizontal line on the rate curve in Fig. 2. The curved portion of Fig. 1 is termed the falling-rate period, and, as shown in Fig. 2, it is typified by a continuously changing rate. Point A, where the constant rate ends and the drying rate begins to decrease, is termed the critical moisture content. The portion of the curve designated by CB in Figs. 1 and 2 represents a warming-up period, and it may, or may not, be a significant item depending on the total time involved. Constant-Rate Period. Drying during the constant-rate pe riod is equivalent to evaporation from a free-water surface on the surface of the solid. The rate of drying in this period is determined by the rate of diffusion of water vapor through an air film at the wet surface of the solid. A constant rate of evap oration on the surface of the solid maintains the surface at a Fig. 2 i... Rote of Drying ^ vs. Moisture Content w Industrial Drying Systems 717 constant temperature, which, in the absence of other heat effects, is very nearly the wet-bulb temperature of the air. If heat flows to the surface of evaporation by radiation and conduction, or both, in addition to convection, the surface temperature will be constant at some value between the air temperature and the wet-bulb temperature. This higher temperature in turn produces a higher constant rate of evaporation. In those dryers in which heat is transferred to a wet solid by conduction through hot surfaces, and heat.transfer by convection is not a factor, the wet surfaces approach the boiling point temperature rather than a wet-bulb tempera ture. When all the heat for evaporation in the constant-rate period is supplied by a hot gas, a dynamic equilibrium is established between the rate of heat transfer to the material and the rate of vapor removal from the surface. This equilib rium between heat and mass transfer rates can be expressed as follows: where dto h,Ai do " H ktA&p (1) -- " drying rate, pounds of water per (hour) (pound of. - bone-dry material). h, TM total heat transfer coefficient, Btu per (hour) (square foot) (Fahrenheit degree). A a area of heat transfer and evaporation, square feet per pound of bone-dry material. H = enthalpy of evaporation at < , Btu per pound. kf -- mass transfer coefficient, pounds per (hour) (square foot) (atmosphere). hi = (t* -- I,) -- temperature difference between air and surface of evaporation, Fahrenheit degrees. U -- air temperature, Fahrenheit. t, - temperature'of surface of evaporation, Fahrenheit. Ap " (p, -- p.) = vapor-pressure difference, atmospheres. p, -- vapor pressure of water at t,, atmospheres. p = partial pressure of water vapor in air, atmospheres- When ht = he, the coefficient of heat transfer by convection only, then t, under equilibrium conditions becomes , the wet-bulb temperature of the air, and p, is the vapor pressure at this temperature. If heat is also'supplied by radiation, then ht is the sum (4C + K) where hr is the radiation coefficient . and he is the convection coefficient, and t, becomes higher than the wet-bulb temperature. A similar result occurs when heat reaches the surface of evaporation by convection and con duction. Effect of Air Velocity. The principal effect of air velocity is on he and k, , since the rate of transfer'of heat and mass in the constant-rate period depends mainly on the rate of diffusion of heat and vapor through the air film at the surface of the solid, and air velocity is the chief factor affecting the thinlmawi of this film. The influence of direction of air flow on the heat transfer coefficient hc and on the. corresponding drying rate dw jg is shown in Table 1. Effect of Temperature or Humidity. Temperature or humidity enters the drying rate equation as a driving force across the air film. The wet-bulb depression, which is the difference be tween the dry-bulb temperature and the wet-bulb tempera ture, is directly proportional to the drying rate in thl* period. Table \ .... Convection Heat Transfer (hj and Rates of Drying y Coefficients for Constant-Rate Period Direction of Air flow h. dw dd 0.01286*-M , Parallel to plane surfaces* 001286** H Perpendicular to plane sur faces1 0076*n Through circulation* (for 0-376* "c. Reynolds number > 300) 0/- 0.37c,o6*-*AA Letter Symbols for Table ) (oof piwfowfy defined) h. " convection heat transfer coefficient, Btu per (hour) (square foot) (Fahrenheit degree). G mass velocity of dry air, pounds per (hour) (square " foot). U = wet-bulb temperature of drying air, Fahrenheit, o -- drying area, square feet per cubic foot of bed volume. , = bulk density of dry granular bed, pounds per cubic foot. D, = average diameter of particle, feet. Atm " logarithmic mean difference between air temperature entering and leaving the bed and the wet-bulb tem perature, Fahrenheit. , = humid heat, Btu per (pound of dry air) (Fahrenheit degree). When dealing with heat transfer coefficients the wet-bulb depression is the driving force, whereas with w transfer coefficients the driving force is.expressed in terms of humidity or vapor-pressure differential ' Fig. 3 permits a ready estimate of the constant drying rate for various air temperatures and humidities. The chart is based on the difference between the dry-bulb and wet-bulb temperatures of the entering stream of air, and on an air velocity of 300 fpm. It may be assumed satisfactory for tray drying of any material in the constant-rate drying period. It does not apply to rotary or through-circulation drying. A curve for correcting toe air velocity is incorporated in Fig. 3. This curve is based on the variation of drying rate with the 03 power of the velocity. Evaporation from Liquid Drops. For the important problem of spray drying, evaporation rates of liquid drops must be estimated. Below a value of Reynolds number (DpG/p) of 10 for spherical particles, the heat transfer coefficient across the gas film surrounding the drop is given by h TM filmheat transfer coefficient, Btu per (hour) (square foot) (Fahrenheit degree). kf =* thermal conductivity of gas film, Btu per (hour) (square foot) (Fahrenheit degree per foot).