A composite rod made of three rods of equal length and cross-section as shown in the fig. The thermal conductivities of the materials of the rods are K/2, 5K and K respectively. The end A and end B ar

Question

A composite rod made of three rods of equal length and cross-section as shown in the fig. The thermal conductivities of the materials of the rods are K/2, 5K and K respectively. The end A and end B are at constant temperatures. All heat entering the face A goes out of the end B there being no loss of heat from the sides of the bar. The effective thermal conductivity of the bar is

TestHub · Accepted Answer

Rods in series: thermal resistances add.

$R = \frac{L}{( K /2 ) A} + \frac{L}{5 K A} + \frac{L}{K A} = \frac{L}{K A} (2 + \frac{1}{5} + 1) = \frac{16 L}{5 K A}$

Effective conductivity for total length 3L:

$K_{eff} = \frac{3 L}{R A} = \frac{3 L}{A} \cdot \frac{5 K A}{16 L} = \frac{15 K}{16}$

. Answer A.

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