% 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)