What is the Laplace Transformation and Solution for C(X) = AX + B C_0 at x=0 and CL at x=L with concentration initially at C_0 between x=0 and L.

Tolnaio 2021-01-02 Answered
What is the Laplace Transformation and Solution for C(X)=AX+B
C0 at x=0 and CL at x=L with concentration initially at C0 between x=0 and L.
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Expert Answer

timbalemX
Answered 2021-01-03 Author has 108 answers
Step 1
Given:
C(X)=AX+B(i)
We know that
L(f(x))=F(s),L(xn)=(n!)sn+1,L(1)=1s
Taking Laplace transform in (i) using the above identities and the fact that it is linear.
L(C(X))=AL(X)+BL(1)
L(C(s))=As2+Bs(ii)
Step 2
Also, when x=0, from (i) we get
C0=B when x=L, from (i)
C(L)=AL+B
CL=AL+C0
A=CLC0L Putting value of A, B in (ii), we get
L(C(s))=CLC0Ls2+C0s(iii)
On taking inverse Laplace Transform in (iii), we get
C(X)=CLC0LX+C0
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