Question #295988

An insulated rod of length has its ends A and B maintained at O^ C and 100 degrees * C respectively until steady state conditions prevailFind the steady -state temperature of the rod


1
Expert's answer
2022-02-15T13:21:32-0500

Let us remind the heat transfer equation :

tT=axxT\partial_t T = a \partial_{xx}T as the problem has only one spatial dimension.

The steady state corresponds to the condition tT=0;  T(t,x)=T(x)\partial_t T = 0; \; T(t,x)=T(x). Using this gives us

d2dx2T=0\frac{d^2}{dx^2} T = 0

And the general solution of such equation is given by

T=C1x+C2T = C_1x + C_2

Let us place the origin at the point AA and let us denote the rod's length by LL. Then we have :

C2=0CC_2 = 0^\circ C

C1L+0=100C1=100/LC_1L+0 = 100 \rightarrow C_1 = 100/L

Therefore, the temperature is given by T(x)=xL100T(x) = \frac{x}{L}\cdot 100


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS