Consider a similar 1-D heat conduction problem to Example 2.2 from the class not
ID: 1766587 • Letter: C
Question
Consider a similar 1-D heat conduction problem to Example 2.2 from the class notes. Two slabs of different width and materials are in contact with one another. Slab B is generating heat at a rate of q per unit volume. The temperature of the left boundary is T1 and the temperature of the right boundary is T2. Assume 1-D and steady state. The properties are listed as follows. Constant properties: T1-300 K, T2-350 K, k1 = 200 w/mK, K2 400 w/mK, q = 1000 w/m, L1 = L2 = 0.2 m Q1) Set up the problem. If you recall what was performed in class, we wrote down governing equations for material A and material B separately, in order to obtain the analytical solutions. Using the finite-difference approach introduced in the video lectures, we can treat materials A and B as one combined computational domain, and re-formulate the problem as: kA, XL k(x) = 0, xL1 (x) = The simplified governing equation in this case would be: 2 T=T,, x=0 T = T2, x = L1 + L2Explanation / Answer
Central Difference Scheme has been applied. The ees code to determine the answers in the question is written as follows:
dx=(L1+L2)/n
L1=0.2
L2=0.2
n=7
k[1]=200
k[2]=200
k[3]=200
k[4]=200
k[5]=400
k[6]=400
k[7]=400
k[8]=400
q[1]=0
q[2]=0
q[3]=0
q[4]=0
q[5]=1000
q[6]=1000
q[7]=1000
q[8]=1000
duplicate i=2,n
k[i-1]*((T[i+1]-2*T[i]+T[i-1])/dx^2)+q[i+1]=0
end
T[1]=300
T[8]=350