Analysis of the Decreasing Drying Rate Period of Granular and Powdered Materials (II)

Abstract

In our former report we discussed the relation between water content and material temperature at the decreasing drying rate period under the constant drying condition. The relations among the gas temperature, t, material temperature, tm, and water content, F, under the unsteady drying condition-in a dryer of continuous counter current or parallel current-were studied, too.For drying granular and powdered materials, the high temperature gas (400700°C) is frequently used. In such a case, as in the case of drying a material containing organic solvents, the sensible heat needed for heating the evaporated vapor from the evaporating temperature to the temperature of the main gas stream (the so-called Ackermann effect), cannot be overlooked.In this paper, the relations among t, tm and F shall be discussed, taking into consideration the presence of this effect in the decreasing drying rate period.I. Under the steady drying condition:The heat at the surface of the material, qnd, (Fig. 1) may be calculated by solving the differential equation, Eq. (11).qnd=h(t-tm)b/(eb-1) (15)b=RdCp/hThe decreasing drying rate, Rd, is shown by Eq. (20).Rd=W0(-dw)/A0dθ=Rc(F/Fc)=(h/Cp)(lnD)(F/Fc) (20)The heat transferred from the main gas stream to the boundary film, qtd, (Fig. 1) is represented by:qtd=h(t-tm)beb/(eb-1) (17)The heat, qnd, causes the drying and the rise of the temperature of the material.qnd=h(t-tm)b/(eb-1)=(W0/A0)(-dw/dθ)rm+(W0/A0)(c+cww)(dtm/dθ) (19)From Eqs. (19) and (20), (dtm/dw)={rm-Cp(t-tm)/(DF/Fc-1)}/(c+cww) (21)Eq. (21) shows the relation between tm and w in the decreasing drying rate period. This equation can be solved by the numerical method. When the sensible heat of water at critical water content (cwwc) is small as compared with the specific heat of the dried material (c>cwwc), and rm_??_rw, Eq. (21) can be solved analytically:(t-tm)=rwFc/cln, D∞Σk=11/n-k(DF/Fc-1/DF/Fc)k+(D/D-1)n(DF/Fc-1/DF/Fc)n{(t-tw)-rwFc/clnD)∞Σk=1(D/D-1)k} (23)n=(CpFc)/(clnD), D=Cp(t-tw)+rw}/rwUnder the ordinary drying condition, the terms below the third one may be discarded.II. Under the unsteady drying condition:The heat balance in the differential small area of a continuous counter or parallel current dryer is given by:±GCHdt=qtdAdθ (25)+ count. cur., - para. cur.From Eqs. (20)', (17) and (25)