## The ends A and B of a rod of length 10cm long have their temperature distribution kept at 20 deg C and 70 deg C. Find the steady state tempe

Question

The ends A and B of a rod of length 10cm long have their temperature distribution kept at 20 deg C and 70 deg C. Find the steady state temperature distribution of the rod. *

1 point

u(x)=5x+20

u(X)=2X+50

u(x)=5x+2

u(X)=2X+5​

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1 month 2021-08-13T16:19:49+00:00 1 Answer 0 views 0

1. ### SOLUTION

GIVEN

The ends A and B of a rod of length 10cm long have their temperature distribution kept at 20° C and 70° C.

TO DETERMINE

The steady state temperature distribution of the rod.

• u(x)=5x+20
• u(X)=2X+50
• u(x)=5x+2
• u(X)=2X+5

### EVALUATION

The equation for heat flow is given by

In steady state temperature the above equation reduces to

The solution is given by

where a and b constants

Now it is given that

At x = 0, u = 20 and at x = 10, x = 70

Using x = 0, u = 20 we get from (1)

Again Using x = 10, u = 70 we get from (1)

From Equation (1) we get by putting the value of a and b

In steady state temperature distribution of the rod

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