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The temperatures on the two sides of a plane wall are t1 and t2 and thermal conductivity of the wall material is prescribed by the relation K = k0 e (-x/δ) Where, k0 is constant and δ is the wall thickness. Find the relation for temperature distribution in the wall?

The temperatures on the two sides of a plane wall are t1 and t2 and thermal conductivity of the wall material is prescribed by the relation K = k0 e (-x/δ) Where, k0 is constant and δ is the wall thickness. Find the relation for temperature distribution in the wall? Correct Answer t 1 – t x / t 1 – t 2 = x/δ

Q = -k A d t/d x = -k0 e (-x/δ) d t/d x. Separating the variables and upon integration, we get Q/k0 A = (t 1 – t 2)/ δ (e – 1). Therefore heat transfer through the wall, Q = k0 A (t 1 – t 2)/ δ (e – 1). At x = x and t = t x we get the answer.

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