A pipe carrying hot fluid is to be insulated by two layers of ins

A pipe carrying hot fluid is to be insulated by two layers of ins
| A pipe carrying hot fluid is to be insulated by two layers of insulators, A and B, having thermal conductivities k and 2k respectively and of equal radial thickness. If the heat transfer coefficient from the outer surface to the air remains constant, how the two insulators must be placed to minimise the heat transfer? 

A. Material A must be outside

B. Material B must be outside

C. The heat transfer will be the same regardless of their relative placement. 

D. The order of placement will depend upon the outside heat transfer coefficient.

Please scroll down to see the correct answer and solution guide.

Right Answer is: B

SOLUTION

Concept:

The thermal resistance of pipe is given as \({{R}_{th}}=\frac{\ln \frac{{{R}_{2}}}{{{R}_{1}}}}{2\pi KL}\)

\({{R}_{th}}\propto \frac{1}{K}\)

Therefore, thermal resistance is inversely proportional to conductivity K.

As K is the thermal conductivity of inner pipe A and 2K is the thermal conductivity of pipe B.

KB > KA ⇒ RA > RB

therefore, a material having higher thermal resistance i.e. lower thermal conductivity should be used for the inner surface to minimize the heat transfer.

So material A will be inside, and B will be the outside material.

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