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Figure shows a metal rod of uniform cros...

Figure shows a metal rod of uniform cross section `A`, with variable thermal conductivity given by `k(x)=k_(0) sec((pi)/(6L)x)`. If the end `A` is maintained at temperature `T_(0)`, the rod carries a thermal current `I_(0)` (from `B` to `A`) in steady state and `(I_(0)L)/(k_(0)AT_(0))=(pi)/3`, find the temperature of the end `B` of the rod. Let's say this temperature is `k T_(0)`, find integer value `k`.

Text Solution

Verified by Experts

The correct Answer is:
2
`I_(0)=(k_(0)A)/(cos((pi)/(6L)x)dx)`
`impliesT=T_(0)+(6I_(0)L)/(pik_(0)A)sin((pi)/(6Lx))`
`impliesT=2T_(0)` at `x=L`
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