Page 234 - Modelling in Transport Phenomena A Conceptual Approach

214 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

in Eq. (7.58) become
min = mout = 0
w, = 0

Qint = - (ro2p)(h)(Tm - (~a))
-- dPw - 0
dt
msys = AD$/^) pm
Hsys = CP.,, (Tm - Tmr)

where (Ta) is the average air temperature, i.e., [(Ta)i, + (T,),,t] /2. Hence, Eq.
(7.5-8) takes the form

dTm
(7.6-8)
-6(h)(Tm - (Ta)) =DPP~~P~~
Equation (7.6-8) is a separable equation and rearrangement yields

(7.6-9)

Integration of Eq. (7.69) gives the cooling time, tl, as

(7.6-10)

The average heat transfer coefficient, (h) in Eq. (7.610) can be calculated from
the Whitaker correlation, Eq. (4.3-30), Le.,
Nu = 2 4- (0.4Rey +0.06Re2’3 ) (PL,/Pw)”4 (7.6-11)
p
ii) Solidification period: During the solidification process, solid and liquid
phases coexist and temperature remains constant at T,. Considering the parti-
cle as a system, the terms appearing in Eq. (7.5-8) become

mi, = m,t = 0
w, = 0
Qint = - (4)(h)(Ts - (T,))
dP,W = 0
dt
mays = mz + m,