Unit Operations in Food Processing
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a acceleration m s-2; [L] [t]-2
thickness m; [L]
aw water activity p/ps or Y/Ys ; dimensionless
A area m2; [L]2
b height of liquid in a centrifuge m; [L]
(Bi) Biot number hsL/k;hsD/k;hsr/k;hsa/k ; dimensionless
c specific heat kJ kg-1 °C-1; [F] [L] [M]-1 [T]-1,
cp specific heat at constant pressure, cs humid heat
C heat conductance J m-2 s-1 °C-1; [F] [L]-1 [t]-1 [T]-1
coefficients - discharge, drag, geometric; constant; dimensionless
COP coefficient of performance in refrigeration


diameter m; [L]

diameter m; [L]
diffusivity m2 s-1; [L]2 [t]-1
sieve aperture m ; [L]


small temperature difference °C; [T]

E energy J; [F] [L]
Ec mechanical pump energy, Ef friction energy, Eh heat energy, Ei Bond's work index in grinding (energy to reduce unit mass from infinitely large particle size to 100
mm), Ek kinetic energy, Ep potential energy, Er pressure energy
f friction factor; dimensionless
ratio of actual drying rate to maximum drying rate, dimensionless
fc crushing strength of material kg m-1 s-2; [M] [L]-1 [t]-2

force N, kg m s-2; [F], [M] [L] [t]-2
Fc centrifugal force, Fd drag force, Fe external force, Ff friction force, Fg gravitational force; Fs accelerating force in sedimentation,
Fl mass ratio of liquid to solid in thickener feed; dimensionless
time to sterilize at 121°C  min; [t]

(Fo) Fourier number (kt/crL2); dimensionless
(Fr) Froude number (DN2/g); dimensionless
F(D) Cumulative particle size distribution, F'(D) particle size distribution; dimensionless
g acceleration due to gravity m s-2; [L] [t]-2
G mass rate of flow kg m-2s-1 ; [M] [L]-2 [t]-1
(Gr) Grashof number (D3r2bgDt/m2); dimensionless
h heat transfer coefficient J m-2 s-1°C-1; [F] [L]-1 [t]-1[T]-1
hc convection, hh condensing vapours on horizontal surfaces, hr radiation, hs surface, hv condensing vapours on vertical surface
H enthalpy, kJ kg-1; [F] [L] [M]-1, Hs, enthalpy saturated vapour, Ha, Hb, Hc,enthalpy in refrigeration system
  Henry's Law constant, atm mole fraction-1, kPa mole fraction-1; [F] [L]-2
k constant
  constant of proportionality
  friction loss factor; dimensionless
  thermal conductivity J m-1 s-1 °C-1 ; [F] [L]-1 [t]-1 [T]-1
k'g mass-transfer coefficient
kg  gas mass-transfer coefficient, k'g mass-transfer coefficient based on humidity difference, kl liquid mass transfer coefficient (units and dimensions from context)
K constant, K', K'', etc.
K' mass-transfer coefficient through membrane, kg m-2 h-1; [M] [L]-2 [t]-1; for ultrafiltration m s-1, for reverse osmosis kg m-2 h-1 kPa-1


Kick's constant m3 kg-1 ; [L]3 [M]-1
KR Rittinger's constant m4 kg-1; [L]4 [M]-1
Ks rate constant for crystal surface reactions m s-1; [L] [t]-1


mass transfer coefficient to the interface, m s-1; [L] [t]-1
Kg overall gas mass transfer coefficient
Kl overall liquid mass transfer coefficient
L flow rate of heavy phase kg h-1 ; [M] [t]-1

half thickness of slab for Fourier and Biot numbers m; [L]

  length m; [L]
  ratio of liquid to solid in thickener underflow;
Lc thickness of filter cake, equivalent thickness of filter cloth and precoat m; [L]
(Le) Lewis number (hc/k'gcp) or (hc/kgcs) dimensionless
m mass kg; [M]
  number, general
(M) mixing index, dimensionless
M molecular weight; dimensionless
  molal concentration (kg) moles m-3 ; [M] [L]-3
n number, general
N number of particles in sample;
rotational frequency, revolutions/minute or s ; [t]-1
(Nu) Nusselt number (hcD/k); dimensionless
p partial pressure Pa; [F] [L]-2
  pa partial pressure of vapour in air, ps saturation partial pressure
  factor in mixing and in grinding, dimensionless; factor in particle geometry in grinding, fractional content in mixing; dimensionless

constant in freezing formula; dimensionless;
power N m s-l, J s-1; [F] [L] [t]-1

  pressure Pa; [F] [L]-2
Ps pressure on surface Pa; [F] [L]-2
(Po) Power number (P/D5N3r); dimensionless
(Pr) Prandtl number (cpm/k); dimensionless
q heat flow rate J s-1; [F] [L] [t]-1
  fluid flow rate m3 s-1; [L]3 [t]-1
  reduction ratio factor in particle geometry in grinding and mixing; dimensionless
Q quantity of heat J; [F] [L]
r radius m; [L]
  rn neutral radius in centrifuge
  specific resistance of filter cake kg m-1; r' specific resistance of filter cake under 1 atm pressure [M] [L]-1

constant in freezing formulae; dimensionless
resistance to flow through filter; dimensionless


Universal gas constant 8.314 kJ mole-1 K-1; m3kPa mole-1K-1 , [L]2 [t]-2 [T]-1 ; 0.08206 m3 atm mole-1 K-1


Reynolds number (Dvr/m) and (D2Nr/m); dimensionless
relative humidity p/p , % ; dimensionless

s compressibility of filter cake; dimensionless
  distance m ; [L]
  standard deviation of sample compositions from the mean in mixing; dimensionless
so , sr initial and random values of standard deviation in mixing; dimensionless
(Sc) Schmidt number (m/rD); dimensionless
(Sh) Sherwood number (K'd/D); dimensionless
SG specific gravity; dimensionless
t time s, h, min (from context) ; [t]
  tf , freezing time h
T temperature °C or T  K; [T]
  Tav mean temperature, Ta air, Ts surface, Tc centre
  Tm mean temperature in radiation
U overall heat-transfer coefficient J m-2 s-1 °C-1 ; [F] [L]-1 [t]-1 [T]-1
v velocity m s-1 ; [L] [t]-1
V flow rate of light phase kg h-1; [M] [t]-1
  volume m3; [L]3
  volumetric flow rate m3 s-1; [L]3 [t]-1
w solid content per unit volume kg m-3; [M] [L]-3
  mass of dry material kg [M]
  weight kg; [F]
W work N m ; [F] [L]
  mass of material dried kg; [M]
x concentration in heavy phase kg m-3; [M] [L]-3
  distance, thickness m; [L]
  fraction, mole or weight, dimensionless
X moisture content on dry basis ; dimensionless
  Xc critical moisture content, Xf final moisture content, Xo initial moisture content;
  thickness of slab m ; [L]
y concentration in light phase kg m-3; [M] [L]-3
  fraction, mole or weight, dimensionless
Ys, Ya
humidity, absolute kg kg-1; humidity difference; dimensionless
humidity of saturated air, humidity of air
z height m; [L]
  temperature difference for 10-fold change in thermal death time °C, [T]
Z depth, height of fluid m; [L]
a absorbtivity; dimensionless
b coefficient of thermal expansion m m-1 °C-1; [T]-1
  b1, b2 length ratios in freezing formula; dimensionless
d thickness of layer for diffusion m; [L]
D difference
  Dtm logarithmic mean temperature difference °C; [T]
e emissivity; dimensionless
  roughness factor; dimensionless
h efficiency of coupling of freezing medium to frozen foodstuff
  air-drying efficiency, % , dimensionless
l latent heat kJ kg-1; [F] [L] [M]-1
  shape factor for particles, dimensionless
m viscosity kg s-1 m-1; Pa s, N s m-2; [M] [t]-1 [L]-1 ; [F] [t] [L]-2
p ratio of circumference to diameter of circle , 3.1416
P total pressure Pa; [M] [L]-1[t]-2 , [F] [L]-2
  osmotic pressure kPa; [F] [L]-2
r density kg m-3; [M] [L]-3
s Stefan-Boltzman constant, 5,73 x10-8 kg m-2 s-3 °C-4 , J m-2 s-1 K-4 ; [M] [t]-3 [T]-4 or [F] [L]-1 [t]-1 [T]-4
t shear stress in a fluid Pa; [F] [L]-2
f fin efficiency; dimensionless
w angular velocity radians s -1, [t]-1

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Unit Operations in Food Processing. Copyright © 1983, R. L. Earle. :: Published by NZIFST (Inc.)
NZIFST - The New Zealand Institute of Food Science & Technology