clear; clc; // Illustration 2.7 // Page: 116 printf('Illustration 2.7 - Page: 116\n\n'); // solution //*****Data*****// // a-benzene b-nitrogen T = 300; // [K] P = 101.3; // [kPa] v =10; // [m/s] R = 8.314; // [cubic m.Pa/mole.K] //*****// // Combining the given correlation with the definitions of j-H, and St_H, from Table 2.1 yields // j_H = h*Pr^(2/3)/(Cp*row*v) = h*Pr^(2/3)/(Cp*Gy) = f(Re) // Therefore // h = Cp*Gy*f(Re)/(Pr)^(2/3) = 20*(Gy)^0.5 for carbon dioxide // Since Re = row*v*l/u = Gy*l/u, where 'l' is a characteristic length, the function f(Re) must be compatible with 20*Gy^0.5 .Therefore, let f(Re) = bRe^n, where 'b' and 'n' are constants to be evaluated. Then, // h = (Cp*Gy*b/Pr^(2/3))*(l*Gy/u)^n = 20*Gy^0.5 // Comparing both sides of equation, we get // n+1 =0.5 // Therefore n = -0.5; // Data on the properties of C02 at 300 K and 1 bar u = 1.5*10^-5; // [viscosity, P] Pr = 0.77; // [Prandtl number] Cp = 853; // [J/kg.K] // Therefore // b = 5.086*l^0.5 // j_D = j_H = f(Re) = 5.086*(l^0.5)*Re^-0.5 // From Table 2.1 // F = j_D*c*v/Sc^(2/3) = 5.086*(l^0.5)*c*v/(Re^0.5*Sc^(2/3)) = 5.086*(row*v*u)^0.5/(Mavg*Sc^(2/3)) // Vapor pressure of benzene P_a = exp(15.9008-(2788.51/(T-52.36))); // [mm of Hg] P_a = P_a*101.3/760; // [kPa] // Parameter for a-benzene, b-nitrogen yi_a = 0.07; yi_b = 0.93; Tc_a = 562.2; Tc_b = 126.2; // [K] Pc_a = 48.9; Pc_b = 33.9; // [bar] M_a = 78.1; M_b = 28; // [gram/mole] V_a = 259; V_b = 89.8; // [cubic cm/mole] Z_a = 0.271; Z_b = 0.290; sigma_a = 5.349; sigma_b = 3.798; // [Angstrom] ek_a = 412.3; ek_b = 71.4; // [E/k, K] // From equation 2.52 and 2.53 Tcm = yi_b*Tc_b+yi_a*Tc_a; // [K] Pcm = 10^6*R*Tcm*(yi_b*Z_b+yi_a*Z_a)/((yi_b*V_b+yi_a*V_a)*100000); // [bar] M_avg = yi_b*M_b+yi_a*M_a; // [kg/kmole] printf("Average molecular weight is %f kg/kmole\n\n",M_avg); row = P*M_avg/(R*T); // [kg/cubic m] printf("Density of mixture is %f kg/cubic m\n\n",row); // From equation 2.50 Em = 0.176*(Tcm/(M_avg^3*Pcm^4))^(1/6); // [uP]^-1 // From equation 2.51 Trm = T/Tcm; f_Trm = (0.807*Trm^0.618)-(0.357*exp(-0.449*Trm))+(0.340*exp(-4.058*Trm))+0.018; // From equation 2.49 u = f_Trm/Em; // [uP] u = u*10^-7; // [viscosity, kg/m.s] printf("Average viscosity of mixture is %e kg/m.s\n\n",u); // Calculating diffusivity of benzene using equation 1.49 D_ab = 0.0986; // [square cm/s] Sc = u/(row*D_ab*10^-4); // [Schmidt number] F = 5.086*(row*v*u)^0.5/(M_avg*Sc^(2/3)); // [kmole/square m.s] printf("The required mass transfer coefficient is %e kmole/square m.s\n\n",F);