Document a454MeKNnB31j3jLODjwRaOZM

974 CHAPTER 46 1952 Guide /- At: = total heat transfer coefficient, Btu per (hour) (square foot) (Fahrenheit degree). ... ;. A ~ area of heat transfer and evaporation, square feet. : !> x = latent heat of evaporation at t,, Btu per pound, fc, = mass transfer coefficient; pounds per (hour) (square-foot) (atmosphere)V ,. = (t, -- l.) = temperature difference between air and surface of evaporation, Fahrenheit degrees. , . U = air temperature, Fahrenheit.' '. U = temperature of surface of evaporation. Fahrenheit. Ap = (p. -- p.) = vapor pressure difference, atmospheres, p, = vapor pressure of water at U, atmospheres, p, = partial pressure of water vapor in air, atmospheres. : When ht = he, the coefficient of heat transfer by convection only, then under equilibrium conditions becomes ta, 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 (hc + hr) where hr is the radia tion coefficient and'A. is the convection coefficient, and l, becomes higher than the wet-bulb temperature. A similar result occurs when heat reaches the surface of evaporation by convection and conduction, When the surface is at the wet-bulb temperature, the value of Ap in millimeters of mercury, is almost exactly one-half the wet-bulb depression [ta -- f), in Centigradedegrees. Effect of Air Velocity. The principal effect of air velocity is on hc and ke, 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 thickness.rtf this film. The influence of air velocity may be expressed by the following relationship ? A, = 0.0128 G0-* ; (2) where Ac = convection heat transfer coefficient, Btu per (hour) (square foot) (Fahren heit degree). G = mass velocity of dry air, pounds per (hour) (square foot). For estimating the constant rate in drying from plane surfaces with air flow parallel to the surface of evaporation and with no radiation or conduction effects;'the following heat transfer expression can be used: . ^,o0.0128G0M(<>_u (3) where t,, = wet-bulb temperature of the drying air, Fahrenheit degrees. . Heat transfer coefficients, rather than mass transfer coefficients, should be used to estimate drying rates, because heat transfer coefficients are generally more reliable, and, unless the temperature of the drying surface is measured, it must be calculated from heat transfer considerations before mass transfer coefficients can be applied for drying-rate predictions. The assumption that the surface of drying is at the wet-bulb temperature of the air, introduces a more serious error in the computation of mass transfer than of heat transfer. Determination of True Surface Temperature. Frequently, radiation and conduction are of sufficient magnitude to cause the temperature of evap oration to exceed the wet-bulb temperature of the air. When this occurs, it is necessary to estimate the true surface temperature in order to calculate Industrial Drjfing Systems 975 the constant rate. This may be done by means of a heat balance equating the total heat transferred by convection, conduction, and radiation to the latent heat of evaporation. Constant-Rate Period in Through-Circulation Drying. The equation for estimating the rate of evaporation when air flows across a free water surface must be modified for the case of air-flow through a permeable bed of solids. The constant rate in through-circulation drying depends on the air rate, air temperature, air humidity, size of the particles milking up the permeable bed, and physical characteristics of these particles.4 The following general expression for the constant rate in through-circula tion drying for the system water and air, was developed5 from experiments on the rate of evaporation of water from the. surface of wet spheres and5, cylindrical particles with through-circulation of air : dW _ 0.42aG-ss(Aff)m 0.37c.a(?"Af d0 Dp41 Xp.D",-41 W where aw constant rate, pounds of water per (hour) (pound of dry stock). a =. drying area, square feet per cubic foot of bed yolume. G = superficial mass velocity, pounds of dry air per (hour) (square foot), m = logarithmic mean of inlet and outlet humidity driving force, across^ the ; air film adjacent to the particle through which the water, vapor diffuses, pounds per pound (the surface humidity is taken as the hunudity. corres ponding to the wet-bulb temperature of the idiying air).' ~ ---i = bulk density of dry granular bed, pounds per cubic foot. Dp = average diameter of particle, feet. Aim = logarithmic mean difference between temperature entering and leaving the bed and the wet-bulb temperature, Fahrenheit degrees. c8 = humid beat, Btu per (pound of dry air) (Fahrenheit degree). X = latent heat of evaporation, Btu per pound. Equation 4 applies w;hen the Reynolds number DpG/n js greater than 300, where /x is the viscosity of the air. stream. For values less than 300, a modification of Equation 4 has been presented.6 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/u) of 10 for spherical particles, tbe: heat ' transfer coefficient across the gas filin surrounding the drop is given by ' (5) where A = film heat transfer coefficient, Btu per (hour) (square foot) (Fahrenheit de-. gree). - ki = thermal conductivity of gas film, Btu per (hour) (square foot) (Fahrenheit degree per foot). Equation 5 is applicable when the Reynolds number for liquid drops is less than 10. Drop diameters are almost always less than 500 microns, and usually in the range of 20 to 150 microns. The rate of evaporation of drops may be expressed in tenias of heat transfer or mass transfer. In terms of heat transfer, the evaporation rate is given by the equation: ? ,. .