APPENDICES
APPENDIX 1
SYMBOLS, UNITS AND DIMENSIONS
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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 |
|
d |
diameter m; [L] |
| D |
diameter 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 100mm), 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 |
| F |
force N, kg
m s-2; [F], [M] [L] [t]-2 |
| (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 |
|
KK |
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 |
|
Kd |
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 | |
| P |
constant in
freezing formula; dimensionless; |
| 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 | |
| R |
constant in
freezing formulae; 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) |
Reynolds number
(Dvr/m)
and (D2Nr/m);
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 | |
 |
mean |
| 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 | |
| Y 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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