MATLAB PDE BC'S

clc;clear all;close all;
L = 1;
x = linspace(0,L,75);
t = linspace(0,1,75);
m = 1;
sol = pdepe(m,@heatpde,@heatic,@heatbc,x,t);

sol1=1-sol;
figure(1)
surf(x,t,sol1);
xlabel('y/b');
zlabel('(T-T_0)/(T_1-T_0)');
title('Fig 12.1-1'); grid on;

function [c,f,s] = heatpde(x,t,u,dudx)
c = 1;
f = dudx;
s = 0;
end
function u0 = heatic(x)
u0 = 1;
end

function [pl,ql,pr,qr] = heatbc(xl,ul,xr,ur,t)
% left Bc = ul 
pl = ul;
ql = 0;
% right BC= ur 
pr = ur;
qr = 0;
end

I am a pde code. I am having a problem using the BC's in image. can you please help me.

Answer 1

[Torsten]

function [pl,ql,pr,qr] = heatbc(xl,ul,xr,ur,t)
Nu = 1.0;
% left Bc = ul 
pl = 0;
ql = 1;
% right BC= ur 
pr = Nu*ur;
qr = 1;
end

[Mr.DDWW]

clc;clear all;close all;

L = 1;

x = linspace(0,L,75);

t = linspace(0,1,75);

m = 1;

sol = pdepe(m,@heatpde,@heatic,@heatbc,x,t);

sol1=1-sol;

figure(1)

surf(x,t,sol1);

mesh (x,t,sol1);

xlabel('y/b');

zlabel('(T-T_0)/(T_1-T_0)');

title('Fig 12.1-1'); grid on;

function [c,f,s] = heatpde(x,t,u,dudx)

c = 1;

f = dudx;

s = 0;

end

function u0 = heatic(x)

u0 = 1;

end

function [pl,ql,pr,qr] = heatbc(xl,ul,xr,ur,t)

Nu = 1.0;

% left Bc = ul

pl = 0;

ql = 1;

% right BC= ur

pr = Nu*ur;

qr = 1;

end

I want to to obatain the solution from the image by chaning the size of the mesh (space coordubate ) I am not sure if my solution is correct

[Torsten]

The boundary conditions from the image - transfered to pdepe language - should be implemented as

function [pl,ql,pr,qr] = heatbc(xl,ul,xr,ur,t)
Nu = 1.0;
% left Bc = ul 
pl = 0;
ql = 1;
% right BC= ur 
pr = Nu*ur;
qr = 1;
end

I don't understand what this has to do with the size of the mesh in spatial direction.

[Mr.DDWW]

Well, I am supposed to obtain the numerical solution from the image by changing the size of the mesh

[Torsten]

If it's the equation from the image you are trying to solve, you'll have to set m=0 instead of m=1 in your code.

If you want to solve the problem for different spatial meshes, change the "75" in

x = linspace(0,L,75);

to a different number.

Answer 2

[Mr.DDWW]

It is a slab. So the symmetry (m) = 1