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How can I put Tn(n+1) and Tn(n-1) values into diff equations?

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Martin Pecha
Martin Pecha 2018년 5월 4일
편집: Martin Pecha 2018년 5월 4일
I need to calculate system of equations for transport of heat between the cells - total number of cells is Ncell=19. Problem is that every cell in calculation is taking heat from cell(n-1) and cell(n+1). How can I write it down if these values are basically not calculated before? Is it possible to write it as a matrix where I choose specific values for Tn+1 and Tn-1?
dTdt(3) and dTdt(3+ncell+1) are the edge cells where one part interacts with T of air dTdt(4:3+ncell) are the one I need to write correctly where ncell are the inner cells (Ncell-2)
%parameters
Tinp=T(1);
Tinn=T(2);
T1=T(3);
Tn=T(4:3+ncell);
TN=(3+ncell+1);
Toutp=(4+ncell+1:4+2*ncell)';
Toutn=(4+2*ncell+1:4+3*ncell)';
Ttp=(4+3*ncell+1);
Ttn=(4+3*ncell+2);
TSoutp=1/ncell*(+sum(Toutp));
TSoutn=1/ncell*(+sum(Toutn));
Tnplus1=[Tn(2:17);TN]; %This is how I tried to write it
Tnminus1=[T1;Tn(1:16)]; %This is how I tried to write it
cTV2=y(1);
cTV3=y(2);
cTV4=y(3);
cTV5=y(4);
cCV2n=y(5:4+Ncell);
cCV3p=y(4+Ncell+1:4+2*Ncell);
cCV3n=y(4+2*Ncell+1:4+3*Ncell);
cCV4p=y(4+3*Ncell+1:4+4*Ncell);
cCV4n=y(4+4*Ncell+1:4+5*Ncell);
cCV5p=y(4+5*Ncell+1:4+6*Ncell);
dTdt=zeros(4+3*ncell+4,1);
% mass tank balance
dTdt(1)=(rho*Cp*QS*(Ttinp-Tinp)+Up*Ncell*Ap*(Tair-Tinp)+Wpump)/(rho*Cp*Vp*Ncell);
dTdt(2)=(rho*Cp*QS*(Ttinn-Tinn)+Up*Ncell*Ap*(Tair-Tinn)+Wpump)/(rho*Cp*Vp*Ncell);
%mass cell balance
dTdt(3)=(rho*Cp*QC*(Tinp-T1)+rho*Cp*QC*(Tinn-T1)+Ux*Ax*(Tn(1)-T1)+Uend*Ax*(Tair-T1)+2*Uy*Ay*(Tair-T1)+Uz*Az*(Tair-T1)+k2*cCV2n(1,:)/d*S*(-H24)+k3*cCV3n(1,:)/d*S*(-H34)+k4*cCV4p(1,:)/d*S*(-H43)+k5*cCV5p(1,:)/d*S*(-H53)+i*i*r*Ax)/(rho*Cp*VC);
dTdt(4:3+ncell)=(rho*Cp*QC*(Tinp-Tn)+rho*Cp*QC*(Tinn-Tn)+Ux*Ax*(Tnplus1-Tn)+Ux*Ax*(Tnminus1-Tn)+2*Uy*Ay*(Tair-Tn)+Uz*Az*(Tair-Tn)+k2*cCV2n(2:Ncell-1,:)/d*S*(-H24)+k3*cCV3n(2:Ncell-1,:)/d*S*(-H34)+k4*cCV4p(2:Ncell-1,:)/d*S*(-H43)+k5*cCV5p(2:Ncell-1,:)/d*S*(-H53)+i*i*r*Ax)/(rho*Cp*VC);
dTdt(3+ncell+1)=(rho*Cp*QC*(Tinp-TN)+rho*Cp*QC*(Tinn-TN)+Ux*Ax*(Tn(:,ncell)-TN)+Uend*Ax*(Tair-TN)+2*Uy*Ay*(Tair-TN)+Uz*Az*(Tair-TN)+k2*cCV2n(:,Ncell)/d*S*(-H24)+k3*cCV3n(:,Ncell)/d*S*(-H34)+k4*cCV4p(:,Ncell)/d*S*(-H43)+k5*cCV5p(:,Ncell)/d*S*(-H53)+i*i*r*Ax)/(rho*Cp*VC);
dTdt(4+ncell+1:4+2*ncell)=(rho*Cp*QC*(Tn-Toutp)+Up*Ap*(Tair-Toutp))/(rho*Cp*VC);
dTdt(4+2*ncell+1:4+3*ncell)=(rho*Cp*QC*(Tn-Toutn)+Up*Ap*(Tair-Toutn))/(rho*Cp*VC);
dTdt(4+3*ncell+1)=(rho*Cp*QC*(TSoutp-Ttp)+Ut*At*(Tair-Ttp))/(rho*Cp*VC);
dTdt(4+3*ncell+2)=(rho*Cp*QC*(TSoutn-Ttn)+Ut*At*(Tair-Ttn))/(rho*Cp*VC);

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