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COP coefficient of performance in refrigerationd diameter m; [L]D diameter m; [L]
diffusivity m2 s-1; [L]2 [t]-1
sieve aperture m ; [L]
e 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 100m), Ek kinetic energy, Ep potential energy, Er pressure energy
f friction factor; dimensionlessratio of actual drying rate to maximum drying rate, dimensionless
fc crushing strength of material kg m-1 s-2; [M] [L]-1 [t]-2
F 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
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time to sterilize at 121°C min; [t] (Fo) Fourier number (kt/cL2); 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 (D32gt/2); dimensionlessh 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 coefficientkg 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
KK Kick's constant m3 kg-1 ; [L]3 [M]-1
KR Rittinger's constant m4 kg-1; [L]4 [M]-1
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Ks rate constant for crystal surface reactions m s-1; [L] [t]-1
Kd mass transfer coefficient to the interface, m s-1; [L] [t]-1
Kg overall gas mass transfer coefficientKl overall liquid mass transfer coefficientL 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)
rotational frequency, revolutions/minute or s ; [t]-1
(Nu) Nusselt number (hcD/k); dimensionlessp 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
P constant in freezing formula; dimensionless;
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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/D5N); dimensionless(Pr) Prandtl number (cp/k); dimensionlessq 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
R constant in freezing formulae; dimensionlessresistance to flow through filter; dimensionless
R 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
(Re)RH
Reynolds number (Dv/) and (D2N/); dimensionlessrelative humidity p/p , % ; dimensionless
s compressibility of filter cake; dimensionless distance m ; [L] standard deviation of sample compositions
from the mean in mixing; dimensionlessso , sr
initial and random values of standard deviation in mixing; dimensionless
(Sc) Schmidt number (/D); dimensionless(Sh) Sherwood number (K'd/D); dimensionlessSG specific gravity; dimensionless
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t time s, h, min (from context) ; [t] tf , freezing time hT temperature °C or T K; [T] Tav mean temperature, Ta air, Ts surface, Tc
centre Tm mean temperature in radiationU 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
meanX 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, dimensionlessYYs, Ya
humidity, absolute kg kg-1; humidity difference; dimensionlesshumidity of saturated air, humidity of air
z height m; [L] temperature difference for 10-fold change in
thermal death time °C, [T]
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Z depth, height of fluid m; [L]
absorbtivity; dimensionlesscoefficient of thermal expansion m m-1 °C-1; [T]-1
1, 2 length ratios in freezing formula; dimensionlessthickness of layer for diffusion m; [L]difference
tm logarithmic mean temperature difference °C; [T]emissivity; dimensionless
roughness factor; dimensionlessefficiency of coupling of freezing medium to frozen foodstuff
Based on extracts, by permission, from ASHRAE Guide and Data Books.
Specific heats, latent heats of freezing and thermal conductivities of foodstuffs can be estimated if the percentage of water in the foodstuff is known. If this percentage is p then: (a) Specific heat = 4.19p/100 + 0.84(100- p)/100 kJ kg-1 °C-1 above freezing = 2.1 p/100 + 0.84(100- p)/100 kJ kg-1 °C-1 below freezing. (b) Latent heat = 335p/100 kJ kg-1
(c) Thermal conductivity = 0.55p/100 + 0.26(100 -p)/l00 J m-1 s-1 °C-1 above freezing = 2.4p/100 + 0.26(100 -p)/l00 J m-1 s-1 °C-1 below freezing. These equations represent a considerable over-simplification so they, and also the tabulated data, should be used with caution, particularly in the region between 0°C and -18°C. Freezing of foodstuffs occurs over a range of temperatures and not at any fixed point. For complete data the only really satisfactory source is a thermodynamic chart
such as those prepared by Riedel (for example, in DKV Arbeitsblatt 8-11, 1957 C. F. Muller, Karlsruhe) for lean beef, and also for egg yolk, potato and APPENDIX 8