Document bbRm4rg2qGy8g57raaMVGQw1

HEATINC VENTILATINC AIR CONDITIONING CUIDE 1944 0.8 fiower of the air velocity. For practical calculations the wet surface is assumed to attain the wet-bulb temperature of the air passing over it, and evaporation takes place at constant rate under equilibrium condi tions. The equation may then be expressed in three forms: where R = C A F- (AP) R = C' A V (AH) R = C A V - (AT) (1) (2) (3) R = rate of drying during constant-rate period, pounds of moisture per hour. A *= area of bed or material in contact with air, square feet. V = air velocity over material, feet per minute. AP = difference between vapor pressure at wet-bulb (surface) temperature and at dew-point of air. AH = difference between humidity ratio of saturated air, at the surface temperature, and the actual humidity ratio of the air stream, pounds of water per pound of dry air. &T = difference between dry-bulb and wet-bulb temperatures of air, i.e.t the wet-bulb depression. C, C\ C" proportionality constants (for numerical values consult references). These equations are useful mainly for computing the effects of changes in operating conditions, such as changes in air velocity, air temperature, humidity and surface area. The equations assume that the material is in equilibrium at the wet-bulb temperature of the air. If equilibrium has not been reached, or if heat is being added to the charge by. radiation or conduction, such conditions must be taken into account. For large tray dryers or continuous surfaces, the logarithmic mean difference should be substituted for the simple difference in AP, AH and A T. When tiie constant of proportionality is known for a given set of con ditions, Equations 1, 2 or 3 may be applied for basic design, as illustrated in Example I." Example 1. Compute the rate of drying of a granular material-initially 35 per cent moisture (dry basis), if the material is spread in trays and is to be dried by blowing air horizontally over the surface at 1000 fpm. The air is 140 F dry-bulb, 90 F wet-bulb. Density of the dry material is 85 lb per. cubic foot, and the drying constant C", in Equation 3,' has been found to be about 1/25,000. Find the size of dryer for a capacity of one ton per hour (dry basis), and the time required for drying each batch from 35 to 10 per cent moisture content, if the material is spread in trays, in a layer one' inch thick. (The. critical moisture content of the material is below 10 per cent, hence the drying is at constant rate.) Solution: Assume that the surface of the material attains the wet-bulb temperature of the air, then AT = 140 -- 90 = 50 F. The rate of drying by Equation 3 is: R = C" A F08 AT ==0.50lb of water per hour per square foot of surface: a5|UUU The total water evaporated per-square foot of surface is: OK W = (0.35 - 0.10) = 1.77 lb (per batch). Then the time required per batch is: T 1.77 0.50 w 3.54 hr. 74? CHAPTER 41. DRYINC SYSTEMS The size of dryer required to dry the material at the rate of one ton of dried material per operating hour will be: A. = -2-0--0-n0,X. 3-.-5--4 = 1000 sq ft, tota,l area o,f t. rays. o5/lZ Falling-Rate Period The critical moisture content marks the end of the constant rate period and the beginning of the falling-rate period. This falling rate may be due to the fact that the surface is no longer completely wetted, or it may result from a condition in which the moisture cannot reach the surface as fast as it can be evaporated. When this high resistance to capillary flow and diffusion is the governing factor in the drying process, the time of drying increases rapidly with the thickness of the material. During constant. rate drying the time required is directly proportional to the thickness of the bed (see Example 1), while the time required for drying during the falling-rate period is often proportional to the.square of the thickness of the material. Actual calculations of drying during the falling-rate period are not highly satisfactory because of the number' of variables. It has been demonstrated empirically tiiat the rate of drying is approximately pro portional to the free water content of the material. An approximate vqlue of the critical moisture content which marks the beginning of the falling-rate period may be obtained from Table 3. DESIGN In all drying problems, data regarding temperatures, time, and hu midity must be obtained by experiment or previous experience. Experi ments are best performed at the temperatures, humidities, and velocities to be actually used in the full sized dryer, and with full size samples. The following nomenclature and explanation of terms will be used in the discussion of design calculations: ff = humidity ratio of air, pounds of water vapor per pound of dry air. G = pounds of dry air supplied to the dryer per unit of time, 5 = pounds of stock dried per unit of time in a continuous dryer, S' = pounds of stock charged per batch to a discontinuous.dryer, e = time. Q = total heat supplied to the dryer, t = air temperature, t> = stock temperature. l". = average stock temperature over short time interval, in a batch dryer, lw = wet-bulb, temperature, S' = specific heat of the stock. B = total radiation and conduction losses per unit time, to = pounds of water per pound of dry stock, heat of evaporation of water. humid heat of air, i.e., heat necessary to raise 1 ib of dry air -f- II lb of steam i F. Subscript (1) designates conditions at the point where -the material in question (air. or stock)' enters, and (2) where it leaves the dryer. 743