%print("Dynamic Model for Evaluating Mass and Concentration variation");
%Pre-alloacation of Arrays
XbFe=zeros(1,i);
XbCr=zeros(1,i);
XbO2=zeros(1,i);
XbFeO=zeros(1,i);
XbCr2O3=zeros(1,i);
CbFe=zeros(1,i);
CbCr=zeros(1,i);
CbO2=zeros(1,i);
CbFeO=zeros(1,i);
CbCr2O3=zeros(1,i);
keq_FeO=zeros(1,i);
keq_Cr2O3=zeros(1,i);
val=zeros(1,i);
XiFe=zeros(1,i);
XiCr=zeros(1,i);
CiFe=zeros(1,i);
CiCr=zeros(1,i);
JFe=zeros(1,i);
JCr=zeros(1,i);
MolesTransFe=zeros(1,i);
MolesTransCr=zeros(1,i);
MolesTransfFeO=zeros(1,i);
MolesTransfCr2O3=zeros(1,i);
MolesTransO2=zeros(1,i);
MFe=zeros(1,i);
MCr=zeros(1,i);
MO2InMetal=zeros(1,i);
Moxy=zeros(1,i);
MCr2O3=zeros(1,i);
MFeO=zeros(1,i);
MassOfFe=zeros(1,i);
MassOfCr=zeros(1,i);
MassofO2=zeros(1,i);
MassOfFeO=zeros(1,i);
MassOfCr2O3=zeros(1,i);
TotalMolesInMetal=zeros(1,i);
TotalMolesInSlag=zeros(1,i);
TotalMassOfMetal=zeros(1,i);
TotalMassOfSlag=zeros(1,i);
VolOfMetal=zeros(1,i);
VolOfSlag=zeros(1,i);
MolarVolumeofMetal=zeros(1,i);
MolarVolumeofSlag=zeros(1,i);
PerFeInMetal=zeros(1,i);
PerCrInMetal=zeros(1,i);
PerO2InMetal=zeros(1,i);
PerFeOInSlag=zeros(1,i);
PerCr2O3InSlag=zeros(1,i);
time=zeros(1,i);
%Input from User
TotalMassOfMetal(1) = input("Input Total Mass of Metal:" );
TotalMassOfSlag(1) = input("Input Total Mass of Slag: ");
DensityOfMetal(1) = input("Input Density of Metal: ");
DensityOfSlag(1) = input("Input Density of Slag: ");
PerFeInMetal(1) = input("Input Percentage of Fe in Metal: ");
PerCrInMetal(1) = input("Input Percentage of Cr in Metal: ");
PerO2InMetal(1)= input("Input Percentage of O2 in Metal: ");
PerFeOInSlag(1) = input("Input Percentage of FeO in Slag: ");
PerCr2O3InSlag(1) = input("Input Percentage of Cr2O3 in Slag: ");
O2AddedFromTop(1) = input("Input Oxygen added from Top: ");
O2AddedFromBottom(1) = input("Input Oxygen added from bottom: ");
Del_T = input("Input time step of each calculation: ");
Temp=input("Operating range of Temperature:" );
MassTransCoeffFe=input("Mass transfer Coefficients of Fe: ");
MassTransCoeffCr=input("Mass transfer Coefficients of Cr: ");
AssumedArea=input("Area Assumed: ");
%Standard Known Values/ Given Inputs
AtomicMassofFe= 56;
AtomicMassofCr= 52;
AtomicMassofO2= 16;
AtomicMassofFeO= 72;
AtomicMassofCr2O3= 152;
%Volume of Metal and Slag
VolOfMetal(1)=TotalMassOfMetal(1)/DensityOfMetal;
VolOfSlag(1)=TotalMassOfSlag(1)/DensityOfSlag;
%Initial Moles of Metal and Slag in kmoles
MFe(1)=TotalMassOfMetal(1)*(PerFeInMetal(1)/100)*(1/AtomicMassofFe);
MCr(1)=TotalMassOfMetal(1)*(PerCrInMetal(1)/100)*(1/AtomicMassofCr);
MFeO(1)=TotalMassOfSlag(1)*(PerFeOInSlag(1)/100)*(1/AtomicMassofFeO);
MCr2O3(1)=TotalMassOfSlag(1)*(PerCr2O3InSlag(1)/100)*(1/AtomicMassofCr2O3);
MO2InMetal(1)=TotalMassOfMetal(1)*(PerO2InMetal(1)/100)*(1/AtomicMassofO2);
%Moles of Oxygen Added in kmoles
MO2Added=((O2AddedFromBottom+O2AddedFromTop)*2*(273/298)/(22.4*60));
Moxy(1)=MO2InMetal(1)+MO2Added;
%Total Moles in Metal and Slag in kMoles
TotalMolesInMetal(1)=MCr(1)+MFe(1)+Moxy(1);
TotalMolesInSlag(1)=MCr2O3(1)+MFeO(1);
%Molar Volume
MolarVolumeofMetal(1)=TotalMolesInMetal(1)/VolOfMetal(1);
MolarVolumeofSlag(1)=TotalMolesInSlag(1)/VolOfSlag(1);
time(1)=0;
for i= 1:1200
%Mole Fractions of elements
XbFe(i)=MFe(i)/TotalMolesInMetal(i);
XbCr(i)=MCr(i)/TotalMolesInMetal(i);
XbO2(i)=Moxy(i)/TotalMolesInMetal(i);
XbFeO(i)=MFeO(i)/TotalMolesInSlag(i);
XbCr2O3(i)=MCr2O3(i)/TotalMolesInSlag(i);
%Bulk Concentration of elements
CbFe(i)=XbFe(i)*MolarVolumeofMetal(i);
CbCr(i)=XbCr(i)*MolarVolumeofMetal(i);
CbO2(i)=XbO2(i)*MolarVolumeofMetal(i);
CbFeO(i)=XbFeO(i)*MolarVolumeofSlag(i);
CbCr2O3(i)=XbCr2O3(i)*MolarVolumeofSlag(i);
%Equilibriium Constant Identfication
keq_FeO(i)=exp((-121009.9+(53.114*Temp)+ (8.314* Temp*log(0.5585/16)))/(-8.314*Temp));
keq_Cr2O3(i)=exp((-274347+(120.55*Temp)+ (8.314* Temp*log(0.5585/16)))/(-8.314*Temp));
%Interface concentration calculation of Fe and Cr
val(i)=keq_Cr2O3(i)*XbO2(i);
XiFe(i)=XbFeO(i)/(keq_FeO(i)*XbO2(i));
XiCr(i)=(XbCr2O3(i)^(0.5))/(val(i)^(1.5));
CiFe(i)=XiFe(i)*MolarVolumeofMetal(i);
CiCr(i)=XiCr(i)*MolarVolumeofMetal(i);
%Mass Flux Balance
JFe(i)=-MassTransCoeffFe*(CbFe(i)-CiFe(i));
JCr(i)=-MassTransCoeffCr*(CbCr(i)-CiCr(i));
%Moles Transfered
MolesTransFe(i)=JFe(i)*Del_T*AssumedArea;
MolesTransCr(i)=JCr(i)*Del_T*AssumedArea;
MolesTransfFeO(i)=MolesTransFe(i);
MolesTransfCr2O3(i)=0.5*MolesTransCr(i);
MolesTransO2(i)=MolesTransFe(i)+1.5*MolesTransCr(i);
%Moles of elements after this iteration
MFe(i+1)=MFe(i)+MolesTransFe(i);
MCr(i+1)=MCr(i)+MolesTransCr(i);
MO2InMetal(i+1)=MO2InMetal(i)+MolesTransO2(i);
Moxy(i+1)=Moxy(i)+MolesTransO2(i)+MO2Added;
MCr2O3(i+1)=MCr2O3(i)-MolesTransfCr2O3(i);
MFeO(i+1)=MFeO(i)-MolesTransfFeO(i);
%Mass of each elements
MassOfFe(i+1)=MFe(i+1)*AtomicMassofFe;
MassOfCr(i+1)=MCr(i+1)*AtomicMassofCr;
MassofO2(i+1)=Moxy(i+1)*AtomicMassofO2;
MassOfFeO(i+1)=MFeO(i+1)*AtomicMassofFeO;
MassOfCr2O3(i+1)=MCr2O3(i+1)*AtomicMassofCr2O3;
%Total Moles in metal and Slag
TotalMolesInMetal(i+1)=MCr(i+1)+MFe(i+1)+Moxy(i+1);
TotalMolesInSlag(i+1)=MCr2O3(i+1)+MFeO(i+1);
%Total Mass of Metal and Slag
TotalMassOfMetal(i+1)=MassOfFe(i+1)+MassofO2(i+1)+MassOfCr(i+1);
TotalMassOfSlag(i+1)=MassOfCr2O3(i+1)+MassOfFeO(i+1);
%Molar Volumes
VolOfMetal(i+1)=TotalMassOfMetal(i+1)/DensityOfMetal;
VolOfSlag(i+1)=TotalMassOfSlag(i+1)/DensityOfSlag;
MolarVolumeofMetal(i+1)=TotalMolesInMetal(i+1)/VolOfMetal(i);
MolarVolumeofSlag(i+1)=TotalMolesInSlag(i+1)/VolOfSlag(i);
%Percentage of elements
PerFeInMetal(i+1)=(MFe(i+1)*100*AtomicMassofFe)/TotalMassOfMetal(i+1);
PerCrInMetal(i+1)=(MCr(i+1)*100*AtomicMassofCr)/TotalMassOfMetal(i+1);
PerO2InMetal(i+1)=(Moxy(i+1)*100*AtomicMassofO2)/TotalMassOfMetal(i+1);
PerFeOInSlag(i+1)=(MFeO(i+1)*100*AtomicMassofFeO)/TotalMassOfSlag(i+1);
PerCr2O3InSlag(i+1)=(MCr2O3(i+1)*100*AtomicMassofCr2O3)/TotalMassOfSlag(i+1);
time(i+1)=time(i)+i/10;
%temperature iterations
Temp=Temp+0.02;
end
I am constantly getting :
Error using zeros
Size vector must be a row vector with real elements.
Error in dynamic_model (line 5)
XbFe=zeros(1,i);
Best Answer