#### Question

Three rods of lengths 20 cm each and area of cross section 1 cm^{2} are joined to form a triangle ABC. The conductivities of the rods are K_{AB}_{ }= 50 J s^{−1} m^{−1}°C^{−1}, K_{BC} = 200 J s^{−1}m^{−1}°C^{−1} and K_{AC} = 400 J s^{−1} m^{−1}°C^{−1}. The junctions A, B and C are maintained at 40°C, 80°C and 80°C respectively. Find the rate of heat flowing through the rods AB, AC and BC.

#### Solution

Thermal conductivity of rod AB, *K*_{AB} = 50 J/m-s-°C

Temperature of junction at A, *T*_{A} = 40°C

Thermal conductivity of rod BC*, K*_{BC} = 200 J/m-s-°C

Temperature of junction at B*, T*_{B}_{ }= 80°C

Thermal conductivity of rod BC*, **K*_{CA} = 400 J/m-s-°C

temperature of junction at C*, **T*_{C} = 80°C

*l* = 20 cm = 20 × 10^{−2} m

A = 1 cm^{2} = 10^{−4} m^{2}

^{(a) `(DeltaQ)_{AB}/(Deltat) = (K_{AB^A}(T_B - T_A))/l`}

`=( 50 xx1xx10^-4 (40))/(20xx10^-2)`

= 1 W

(b) `(DeltaQ_{AC})/(Deltat) =( K_{AC^-A}(T_C - T_A))

/(20xx10^2)`

= 8 w

( c ) `(DeltaQ)_{BC)/ (Deltat) = ((K_{BC})^6A(T_B - t_c))/l`

= 0