BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 3, 2012 119
where: Φ is the quantity of interest which in this case is the energy or humidity
of the intergranular air, ρ a is the density of air, v is the superficial or Darcian
velocity of the air as opposed to the average velocity of the air flowing between
the grain kernels, Γ is the effective diffusion coefficient of Φ through a bed of
grains, t is time, ∇ is the del operator Eqs. (2), S Φ is a source term.
∂ ∂ ∂
∇ = + + . (2)
∂x
∂y
∂z
Eq. (1) refers to a differentially small region of grain and this implies that the
properties have been averaged over some finite volume, otherwise they would
be discontinuous at the boundaries of the malt kernels and intergranular air.
2.1. Heat Transfer
The variable, Φ, in the generalised transport Eq. (1) can also represent
energy. In the case of porous media, such as a bulk of malt, the enthalpies of the
fluid (air) and solid (malt kernels) phases must be considered. The computer
software used in this work solves an enthalpy balance that ultimately reduces to
⎛
⎛ ∂HW
⎞⎞∂T
⎜( ρεc
a a
+ ρs(1
− ε) ⎜cs + cwW + ca ( ρavT
)
T
⎟⎟
+ ∇ =
⎝
⎝
∂ ⎠⎠
∂t
(3)
2
= k ∇ T + S ,
eff
en
where: c a , c s and c w are the specific heats of air, malt and liquid water,
respectively, ρ s is the density of malt kernels on a dry basis, ε – void fraction of
the bed of malt (we assume that value 0,15) , W – malt moisture content , H W -
is the integral heat of wetting of the malt, T – temperature, k eff is the effective
thermal conductivity of the bulk of malt (0.157 W/m 2 K), S en is the thermal
source term that results from heat being liberated or extracted from the malt
when they adsorb or desorb moisture. (Thorpe, 2007) demonstrates that ∂H w /∂T
is negligibly small for grains compared with the specific heat of moist grain and
it can be ignored. A feature of FLUENT is that the specific heat of the porous
zone must be entered as a constant, but in this application the term equivalent to
specific heat, i.e. c g +c w W+(∂H w /∂T), varies with moisture content. For he
purposes of the simulation presented here we assume that the start value of the
malt moisture content, W, is 0.557, which corresponds to a moisture content of
49% wet basis and the grain has a temperature of 21 ºC. The source term, S en ,
takes the form
W
Sen =−hs(1 −ε) ρ ∂
s
,
∂t
(4)
where: h s is the heat of sorption of water on the malt. (Hunter, 1989)
demonstrates that the ratio of the heat of sorption to the latent heat of
vaporisation, h v , of free water is given by