Question

******ONLY MATLAB CODE NO OTHER WAY OF SOLUTION******

Consider a one-dimensional slab with conductivity 1 W/m-K. The slab width is 20 cm. The left face of the slab is at 100oC and the heat flux at the right face is 1 kW/m2. The slab experiences a volumetric heat generation rate given by S = 1000 - 5T W/m3. Determine the steady-state temperature distribution in the slab, for two grid spacings with the requirement that there should be at least 20 CVs in each case.

Answer 1

clc;

clear;

n=input("No of interior points");

T(1)=input("Enter Left side temperature");

l=input("Length of the plate");

k=input("Thermal conductivity of plate");

Sc=input("Heat source constant in W");

Sp=input("Heat source variable in W");

q=input("enter heat flux at right side");

dx=l/n;

d(1)=1;

b(1)=0;

a(1)=0;

c(1)=T(1);

d(n+2)=-(k/dx);

b(n+2)=k/dx;

a(n+2)=0;

c(n+2)=q;

for i=2

    b(i)=2*k/dx;

    a(i)=k/dx;

    c(i)=-Sc*dx;

  d(i)=-((a(i)+b(i))-(Sp*dx));

end

for i=3:n

    b(i)=k/dx;

    a(i)=k/dx;

    c(i)=-(Sc*dx);

    d(i)=-((a(i)+b(i))-(Sp*dx));

end

for i=n+1

    b(i)=k/dx;

    a(i)=2*k/dx;

    c(i)=-(Sc*1000)*dx;

    d(i)=-((a(i)+b(i))-(Sp*1000*dx));

end

D(1)=d(1);

C(1)=c(1);

for i=2:n+2

    D(i)=d(i)-((b(i)*a(i-1))/D(i-1));

    C(i)=c(i)-((b(i)*C(i-1))/D(i-1));

end

T(n+2)=(C(n+2)/D(n+2));

for i=n+1:-1:1

    T(i)=(C(i)-(a(i)*T(i+1)))/D(i);

end

len(1)=0;

len(2)=dx/2;

for i=3:n

    len(i)=len(i-1)+dx;

end

len(n+1)=l-(dx/2);

len(n+2)=l

disp(T)

plot2d(len,T)