I am getting error while trying to generate data for qtot_eV through variation of "d".

Below is my code:

clear;
close all;

deld=(80E-9-10E-9)/100;
d=[10E-9:deld:80E-9]; %Distance between the emitter and TPV cell stacks
q=1.602E-19;
hbar=1.054571596E-34;
hbar_eV=hbar/q;    %eV s
kb=1.3806503E-23;
kb_eV=kb/q;
h=2*pi*hbar;
h_eV=h/q;         %  eVs
T1=1500; %Emitter temperature, in K
T2=300; %TPV cell temperature, in K
c=2.9979E8; %speed of light
V=0; 
%Wavelength over which the near field heat transfer spectrum is calculated.
lambda_min1=10000E-6;
lambda_max1=2.5E-6;
lambda_max2=1E-6;
%number frequency points in the two calculation ranges
res1=100; %between lambda_min1 and lambda_max1
res2=100; %between lambda_max1 and lambda_max2
%wavelength to frequency conversion, do not touch
w_min1=2*pi*3E8/lambda_min1;
w_max1=2*pi*3E8/lambda_max1;
del1=(w_max1-w_min1)/res1;
w_min2=w_max1+del1;
w_max2=2*pi*3E8/lambda_max2;
del2=(w_max2-w_min2)/res2;
w=[(w_min1:del1:w_max1) (w_min2:del2:w_max2)];
lambda=2*pi*c./w;
w_ev=w/1.5193E15;

qevan_p=zeros(1,length(w)); %vector initialization
qevan_s=zeros(1,length(w));
qprop_p=zeros(1,length(w));
qprop_s=zeros(1,length(w));

for a=1:length(w)
    betaevanmax=10./d; %upper limit of the parallel wavevector for evanescent wave integration
    betaevanmin=w(a)/c; %lower limit
    
    qevan_p(a)=(Theta(w(a), T1,0)-Theta(w(a), T2, V))*1/pi^2*integral(@(beta)sevan_p(w(a),beta, d),betaevanmin,betaevanmax,'Reltol',1E-6,'AbsTol',1E-10); %default abstol = 1E-10 reltol 1E-6
    qevan_s(a)=(Theta(w(a), T1,0)-Theta(w(a), T2, V))*1/pi^2*integral(@(beta)sevan_s(w(a),beta, d),betaevanmin,betaevanmax,'Reltol',1E-6,'AbsTol',1E-10);
    qprop_p(a)=(Theta(w(a), T1,0)-Theta(w(a), T2, V)).*1/pi^2.*integral(@(beta)(sprop_p(w(a),beta,d)),0,w(a)/c);
    qprop_s(a)=(Theta(w(a), T1,0)-Theta(w(a), T2, V)).*1/pi^2.*integral(@(beta)(sprop_s(w(a),beta,d)),0,w(a)/c); 
    a/length(w) % progress indicator 
end 
qtot=qevan_p+qevan_s+qprop_p+qprop_s; %total intensity spectum
qtot_eV=qtot*1.5193E15/10000; %in w/cm2/eV

The error is:

Error using integral (line 85)

A and B must be floating-point scalars.

Error in optimization (line 59)

qevan_p(a)=(Theta(w(a), T1,0)-Theta(w(a), T2, V))*1/pi^2*integral(@(beta)sevan_p(w(a),beta, d),betaevanmin,betaevanmax,'Reltol',1E-6,'AbsTol',1E-10); %default abstol = 1E-10

reltol 1E-6

Answer 1

[VBBV]

As the error states, you need to provide scalar values for integral limits

 betaevanmax=10./max(d); % use a scalar value for upper limit for integral function 

[Ambali Odebowale]

But in this case only one value of qtot_eV will be obtained. However, I want to calculate qtot_eV for each values values of "d".

Hope my question is clear now.

Thanks while I await your response

[VBBV]

In that case you need to use another for loop to consider each value in vector d.

clear;
close all;

deld=(80E-9-10E-9)/100;
d=[10E-9:deld:80E-9]; %Distance between the emitter and TPV cell stacks
q=1.602E-19;
hbar=1.054571596E-34;
hbar_eV=hbar/q;    %eV s
kb=1.3806503E-23;
kb_eV=kb/q;
h=2*pi*hbar;
h_eV=h/q;         %  eVs
T1=1500; %Emitter temperature, in K
T2=300; %TPV cell temperature, in K
c=2.9979E8; %speed of light
V=0; 
%Wavelength over which the near field heat transfer spectrum is calculated.
lambda_min1=10000E-6;
lambda_max1=2.5E-6;
lambda_max2=1E-6;
%number frequency points in the two calculation ranges
res1=100; %between lambda_min1 and lambda_max1
res2=100; %between lambda_max1 and lambda_max2
%wavelength to frequency conversion, do not touch
w_min1=2*pi*3E8/lambda_min1;
w_max1=2*pi*3E8/lambda_max1;
del1=(w_max1-w_min1)/res1;
w_min2=w_max1+del1;
w_max2=2*pi*3E8/lambda_max2;
del2=(w_max2-w_min2)/res2;
w=[(w_min1:del1:w_max1) (w_min2:del2:w_max2)];
lambda=2*pi*c./w;
w_ev=w/1.5193E15;

qevan_p=zeros(length(w),length(d)); %vector initialization
qevan_s=zeros(length(w),length(d));
qprop_p=zeros(length(w),length(d));
qprop_s=zeros(length(w),length(d));

for k = 1:length(d)
    for a=1:length(w)
        betaevanmax=10/d(k); %upper limit of the parallel wavevector for evanescent wave integration
        betaevanmin=w(a)/c; %lower limit
        
        qevan_p(a,k)=(Theta(w(a), T1,0)-Theta(w(a), T2, V))*1/pi^2*integral(@(beta)sevan_p(w(a),beta, d(k)),betaevanmin,betaevanmax,'Reltol',1E-6,'AbsTol',1E-10); %default abstol = 1E-10 reltol 1E-6
        qevan_s(a,k)=(Theta(w(a), T1,0)-Theta(w(a), T2, V))*1/pi^2*integral(@(beta)sevan_s(w(a),beta, d(k)),betaevanmin,betaevanmax,'Reltol',1E-6,'AbsTol',1E-10);
        qprop_p(a,k)=(Theta(w(a), T1,0)-Theta(w(a), T2, V)).*1/pi^2.*integral(@(beta)(sprop_p(w(a),beta,d(k))),0,w(a)/c);
        qprop_s(a,k)=(Theta(w(a), T1,0)-Theta(w(a), T2, V)).*1/pi^2.*integral(@(beta)(sprop_s(w(a),beta,d(k))),0,w(a)/c); 
        a/length(w) % progress indicator 
    end 
end
qtot=qevan_p+qevan_s+qprop_p+qprop_s; %total intensity spectum
qtot_eV=qtot*1.5193E15/10000; %in w/cm2/eV

Also, matrix dimensions need to be changed as below

qevan_p=zeros(length(w),length(d)); %vector initialization
qevan_s=zeros(length(w),length(d));
qprop_p=zeros(length(w),length(d));
qprop_s=zeros(length(w),length(d));

[Ambali Odebowale]

Thanks so much. This really helps me