Question

76.
Figure shows a thermal network of five metal rods
of the same cross-section area, if the heat current
from the ends A and B is 180 W. Find the heat
current through curved (lower) part.
-45cm-
45cm
*30cm
А
(100°C)
30cm-
B
(0°C)
90 cm
(1) 70 W
(2) 80 W
(3) 90 W
(4) 100 W​

Answer 1

Answer:

80w

Explanation:

is the thermal network

Answer 2

The heat curreent flow through curved part is 72 W.

Step 1: Find the heat current through curved path.

Total heat current = $H_1+H_2$                                            ...(i)

180 =  $H_1+H_2$  

​$H_1 = \frac{K_1A_1\triangle T_1}{l}$

Where,

K = Thermal conductivity

A = Area of cross section

l = Distance traveled by heat

ΔT = temperature difference between curved path

$H_1 = \frac{K_1A_1\triangle T_1}{45}$                                                                      ...(ii)

$H_1 = \frac{K_1A_1\triangle T_1}{30}$                                                                       ...(iii)

$\frac{H_1}{H_2} = \frac{30}{45}$  [$K_1=K_2 , A_1=A_2 , \triangle T_1 = \triangle Y_2$]

$3H_1=2H_2$

$H_2=\frac{3}{2} H_1$

Putting the value of $H_2$ in equation (i)

$180=H_1+\frac{3}{2} H_1$

$180=\frac{5}{2} H_1$

$H_1= \frac{360}{5}$

$H_1 = 72$ W