# How to create array while using integral function?

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Ishani Prachchhak on 24 Apr 2023
Edited: VBBV on 24 Apr 2023
Following is the code, there are parameters - b,c,gama1,sigma. And r that is the radius of the sphere is varing, also the time is varying. I want to get at each radial point at given time the value of I(integral) What am I doing is wrong?
K1=6;%(W/m.K)Thermal conductivity of Fe3O4 nanoparticle
K2=0.598; %Thermal conductivity of water-https://thermtest.se/thermal-conductivity-of-water
k1= 1.82E-06; %(m^2/s) Diffusivity of Fe3O4 nanoparticle
k2=2.29e-9; %at 25C (m^2/s) diffusivity of water- https://en.wikipedia.org/wiki/Molecular_diffusion
Vol= (4/3)*3.14*a^3;%Volume of nanoparticle
A=8.68E-05; %(W)heatproduced/ unit volume
b=(K2/K1)*((k1/k2)^1/2);
r=linspace(15e-9,17e-9,10);
c=1-(K2/K1);
t=linspace(1e-12,100e-12,10);
gama1=(a^2)/k1;
sigma=((r/a)-1)*((k1/k2)^1/2);
for t = 1e-12:100e-12
r = 15e-9:17e-9;
fun = @(y,gama1,sigma,b,c,t) ((exp(((-y.^2).*t)./gama1)).*(sin(y)-(y.*cos(y))).*((b.*y.*sin(y).*cos(sigma.*y))-((c.*sin(y)-y.*cos(y)).*sin(sigma.*y))))./((y.^3).*((((c.*sin(y))-(y.*cos(y))).^2)+((b.^2).*(y.^2).*(sin(y).^2))));
I=integral(@(y) fun(y,gama1,sigma,b,c,t),0,inf); %integration wrt y with other constants
end

VBBV on 24 Apr 2023
Edited: VBBV on 24 Apr 2023
K1=6;%(W/m.K)Thermal conductivity of Fe3O4 nanoparticle
K2=0.598; %Thermal conductivity of water-https://thermtest.se/thermal-conductivity-of-water
k1= 1.82E-06; %(m^2/s) Diffusivity of Fe3O4 nanoparticle
k2=2.29e-9; %at 25C (m^2/s) diffusivity of water- https://en.wikipedia.org/wiki/Molecular_diffusion
Vol= (4/3)*3.14*a^3;%Volume of nanoparticle
A=8.68E-05; %(W)heatproduced/ unit volume
b=(K2/K1)*((k1/k2)^1/2);
r=linspace(15e-9,17e-9,10);
c=1-(K2/K1);
t=linspace(1e-12,100e-12,10);
gama1=(a^2)/k1;
sigma=((r/a)-1)*((k1/k2)^1/2);
syms y
for J = 1:length(sigma)
for K = 1:length(t)
fun = ((exp(((-y.^2).*t(K))./gama1)).*(sin(y)-(y.*cos(y))).*((b.*y.*sin(y).*cos(sigma(J).*y))-((c.*sin(y)-y.*cos(y)).*sin(sigma(J).*y))))./((y.^3).*((((c.*sin(y))-(y.*cos(y))).^2)+((b.^2).*(y.^2).*(sin(y).^2))));
I(K,J)= vpaintegral(fun,y,[0,Inf]); %integration wrt y with other constants
end
end
I = (vpa(I,15))
I =

Dyuman Joshi on 24 Apr 2023
%Formatting your code properly is a good coding practice
K1=6; %(W/m.K)Thermal conductivity of Fe3O4 nanoparticle
K2=0.598; %Thermal conductivity of water-https://thermtest.se/thermal-conductivity-of-water
k1=1.82E-06; %(m^2/s) Diffusivity of Fe3O4 nanoparticle
k2=2.29e-9; %at 25C (m^2/s) diffusivity of water- https://en.wikipedia.org/wiki/Molecular_diffusion
Vol=(4/3)*3.14*a^3; %Volume of nanoparticle
A=8.68E-05; %(W)heatproduced/ unit volume
b=(K2/K1)*((k1/k2)^1/2);
r=linspace(15e-9,17e-9,10);
c=1-(K2/K1);
t=linspace(1e-12,100e-12,10);
gama1=(a^2)/k1;
sigma=((r/a)-1)*((k1/k2)^1/2);
%preallocation
I = zeros(numel(t),numel(r));
%Function to integrate
fun = @(y,t) ((exp(((-y.^2).*t)./gama1)).*(sin(y)-(y.*cos(y))).*((b.*y.*sin(y).*cos(sigma.*y))-((c.*sin(y)-y.*cos(y)).*sin(sigma.*y))))./((y.^3).*((((c.*sin(y))-(y.*cos(y))).^2)+((b.^2).*(y.^2).*(sin(y).^2))));
for k = 1:numel(t)
%Pass the value of t(k)
I(k,:)=integral(@(y) fun(y,t(k)),0,inf,'ArrayValued',true); %integration wrt y with other constants
end
format long
I
I = 10×10
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