Question

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Answer 1

Question:

Two walls of thickness d1 and d2 and thermal condutivities k1 and k2 are in contact. in the steady state, if the temperatures at the outer surface are T1 and T2. The temperature at the common wall  will be?

Answer:

The temperature at comman wall is ( k1T1d2 + k2d2T1) / ( k1d2 + k2d1)

Explanation:

Given,

Thickness of walls = d1 and d2

Thermal conductivity of walls = k1 and k2

Temperature of walls = T1 and T2

To find: The temperature at the common wall  will be?

Solution:

Let the temperature at comman wall be Tw.

While connecting the walls, we will obtain series combination.

In series combination, dQ / dt = constant

or, k1.A(T1 - Tw) /d1 = k2.A(Tw - T2) /d2

or, Tw = ( k1T1d2 + k2d2T1) / ( k1d2 + k2d1)

Therefore,

The temperature at comman wall is ( k1T1d2 + k2d2T1) / ( k1d2 + k2d1)