% characteristic transport values
% need these properties for air and water at
% (a) 1 bar and 300 K,
% (b) 10 bar and 300 K,
% (c) 1 bar and 500 K (for liquid water need P > 1 bar!)
% density
% dynamic viscosity
% diffusion coefficient (O2 or N2 in air, ethanol in water)
% thermal conductivity
% heat capacity
Rg = 8.3143; % (Pa m3)/(mol K)
% DENSITY - AIR
%
% Assume ideal gas law holds over this range: PV = NRT
% N/V = P/(RT)
% MW(kg/mol)*N(mol)/V(m3) = rho (kg/m3) = MW(kg/mol)*P/(RT)
MW = 0.029; % ave molecular wt of air, (kg/mol)
T = [300 300 500]; % K
P = 1e5*[1 10 1]; % Pa
rhoA = MW*P./(Rg*T); % kg/m3
% DENSITY - WATER
%
% From Perry's Chemical Engineers' Handbook (6th ed, p. 3-75)
% density of water changes from 1000 kg/m3 at 273 K to 958 kg/m3
% at 373 K (boiling point at 1 atm)
% to get to 500 K with liquid water, need P > 1 bar
% xxxx for now, neglect change in liquid water density with T and P xxxx
rhoW = 1e3*[1 1 1]; % kg/m3
% DYNAMIC VISCOSITY UNITS: 1 Poise = 0.1 (Pa s) = 0.1 kg/m/s
% DYNAMIC VISCOSITY - AIR
%
% From Properties of Liquids and Gases, 5th ed,
% by Poling, Prausnitz & O'Connell
% at low P, mu (or eta) independent of P
% and proportional to T^(1/2)
% muO2 = 207 microPoise at 300 K and low P (p. 9.42)
% muO2 = 213 microPoise at 300 K and 30 bar (p. 9.42)
% muN2 = 178 microPoise at 300 K and low P (p. 9.11)
% muN2 = 258 microPoise at 500 K and low P (p. 9.11)
% see Wilke method on p. 9.21 for gas mixtures
% muA = [180 180 180*(500/300)^0.5]; % microPoise
% muA = muA*1e-6*(0.1/1) % (Pa s), 0.1 (Pa s)/Poise
%
% From Physical Chemistry by P.W. Atkins (1978), p. 810
% air at 273 K, mu (eta) = 1.71e-5 kg/m/s
% air at 293 K, mu (eta) = 1.82e-5 kg/m/s
muA = 1.82e-5; % kg/m/s
muA = muA*(T/293).^0.5; % correct for T
% DYNAMIC VISCOSITY - WATER
%
% From Properties of Liquids and Gases, 5th ed,
% by Poling, Prausnitz & O'Connell
% mu (or eta) increases with P with liquids (p. 9.55)
% e.g., by 57% for methycyclohexane for increase of 500 bar
% ln(mu) approx. linear in reciprocal absolute T (p. 9.57)
% From Perry's Chemical Engineers' Handbook (6th ed p. 3-252)
% mu water 300 K = 0.93 centiPoise
% mu water 436 K = 0.1 centiPoise
muW = 1e-2*[0.93 0.93 0.1]; % Poise
muW = muW*(0.1/1); % (Pa s), 0.1 (Pa s)/1 Poise
% THERMAL CONDUCTIVITY - AIR
%
% From Properties of Liquids and Gases, 5th ed,
% by Poling, Prausnitz & O'Connell
% kt (or lambda) of low P gases increase with T
% dkt/dT ranges from 4e-5 to 1.2e-4 W/(m K2)
% with more complex and polar molec having the larger values (p. 10.18)
% kt of gases increase with P, in range 1e-3 to 10 bar, kt increases
% about 1% or less per bar (p. 10.18)
% From Perry's Chemical Engineers' Handbook
% kt air at 300 K = 2.62e-2 (J/s/m/K)
% kt air at 500 K = 4.07e-2 (J/s/m/K)
% From Physical Chemistry by P.W. Atkins (1978), p. 810
% air at 273 K, kt = 0.241e-3 J/cm/s/K
ktA = 0.241e-3; % J/cm/s/K
ktA = ktA*(100/1); % J/m/s/K = (100 cm/1 m)*J/cm/s/K
ktA = ktA*(T-273)*4e-5; % correct for change in T at 4e-5 J/m/s/K/K
ktA = ktA.*(1 + 0.01*(P/P(1) - 1)); % correct for P, 1% incr per bar
% THERMAL CONDUCTIVITY - WATER
%
% From Properties of Liquids and Gases, 5th ed,
% by Poling, Prausnitz & O'Connell
% at moderate P, up to 50-60 bar, effect of P on liquids usually neglected
% except near critical point (p. 10.52)
% From Perry's Chemical Engineers' Handbook
% at 273 K, kt = 0.343 Btu/(h ft2)(deg-F/ft)
% at 273 K, kt = 0.343*1.7307 (J/s/m/K)
% 500 K = 440 deg-F
% at 420 deg-F, kt = 0.376*1.7307 (J/s/m/K)
ktW = 1.7307*[0.343 0.343 0.376]; % (J/s/m/K)
% DIFFUSION COEFFICIENT - O2 in AIR
%
% From Properties of Liquids and Gases, 5th ed,
% by Poling, Prausnitz & O'Connell
% from kinetic theory of ideal gases, D for gases
% proportional to T^(3/2) and proportional to reciprocal of P (p. 11.5)
% D*P = air-CO2 at 276 K = 0.144 (cm2/s)*bar (p. 11.13)
% xxxx for now use air-CO2 xxxxx
Dair = 0.144; % cm2/s
Dair = Dair*(1/1e4); % m2/s, (1 m2/1e4 cm2)
Dair = Dair*(T/276).^(3/2); % correct for T
Dair = Dair*P(1)./P; % correct for P
% DIFFUSION COEFFICIENT - Ethanol in WATER
%
% From Properties of Liquids and Gases, 5th ed,
% by Poling, Prausnitz & O'Connell
% theory D for liquids independent of P and proportional to T (p. 11.21)
% for ethanol in water at 288 K, D = 1.00e-5 cm2/s (p. 11.31)
% for CO2 in water at 288 K, D = 2.00e-5 cm2/s (p. 11.31)
Detoh = 1e-5; % cm2/s
Detoh = Detoh*(1/1e4); % m2/s, (1 m2/1e4 cm2)
Detoh = Detoh*(T/288); % correct for T
% HEAT CAPACITY - AIR
%
% From Physical Chemistry by P.W. Atkins (1978), p. 70
% for O2 at 298 K, Cp = 29.33 J/K/mol
% for N2 at 298 K, Cp = 29.14 J/K/mol
CpA = 29.2*[1 1 1]; % J/K/mol
CpA = CpA*(0.029/1); % J/K/kg, 0.029 kg/1 mol
% HEAT CAPACITY - WATER
%
% for water at ambient conditions, Cp = 1 cal/g/K
% Cp = 1 cal/g/K *(4.184 J/cal) = 4.184 J/g/K
% Cp = 4.184 J/g/K * (1000 g/1 kg) = 4.184e3 J/kg/K
CpW = 4.184e3*[1 1 1]; % J/kg/K
% SCHMIDT NUMBER
%
% Sc = mu/(rho D)
ScA = muA ./ (rhoA .* Dair)
ScW = muW ./ (rhoW .* Detoh) % ethanol in water
% PRANDTL NUMER
%
% Pr = mu/(rho alpha)
% alpha = kt/(rho Cp)
% Pr = mu*Cp/kt
PrA = muA.*CpA./ktA
PrW = muW.*CpW./ktW
% my numbers for air come out a little lower than in Perry's
% Perry's Chemical Engineers' Handbook (6th ed, p. 3-254)
% Pr air, 300 K, 1 bar = 0.705
% Pr air, 300 K, 10 bar = 0.712
% Pr air, 500 K, 1 bar = 0.689
% FLOW RATE IN TUBE AT LAMINAR-TURB TRANSITION
d = 1; % m, diameter of tube
% Re = U*d*rho/mu
% U = Re*mu/(d*rho)
Re = 2200; % critical Re 2100-2300
Uair = Re*muA./(d*rhoA) % m/s
Uwater = Re*muW./(d*rhoW)
Vair = Uair*pi*(d/2)^2 % m3/s
Vwater = Uwater*pi*(d/2)^2
% multiply m3/s times 1e3 for liters/s
% DISTANCE FOR FLOW OVER FLAT PLATE AT LAMINAR-TURB TRANSITION
% Re = U*X*rho/mu
Re = 5e5; % take this as critical Re but ranges widely...
U = 1; % m/s
Xair = Re*muA./(U*rhoA)
Xwater = Re*muW./(U*rhoW)
% VELOCITY BOUNDARY LAYER THICKNESS AT LAMINAR-TURB TRANSITION
% thickness at which T reaches 99% of free-stream T
delVair = 5*sqrt(muA.*Xair./(rhoA*U)) % m
delVwater = 5*sqrt(muW.*Xwater./(rhoW*U)) % m
% CONCENTRATION BOUNDARY LAYER THICKNESS AT LAMINAR-TURB TRANSITION
% thickness of stagnant film with same flux at surface
delCair = 3*sqrt(muA.*Xair./(rhoA*U)).*ScA.^(-1/3)
delCwater = 3*sqrt(muW.*Xwater./(rhoW*U)).*ScW.^(-1/3)
% THERMAL BOUNDARY LAYER THICKNESS AT LAMINAR-TURB TRANSITION
% thickness of stagnant film with same flux at surface
delTair = 3*sqrt(muA.*Xair./(rhoA*U)).*PrA.^(-1/3)
delTwater = 3*sqrt(muW.*Xwater./(rhoW*U)).*PrW.^(-1/3)