Heat Transfer - GATE practice papers - Mechanical

1)   Two layers of different metals are made composite connecting parallel. The heat flow takes place as shown in figure. Thermal resistances of the two layers are R1 = 0.036 K/W and R2 = 0.05 K/W What is the thermal resistance of the system? (Marks: 02)

Heat transfer through parallel composite metal wall

- Published on 19 Oct 15

a. 0.086 K/W
b. 47.778 K/W
c. 0.0209 K/W
d. none of the above
Answer  Explanation 

ANSWER: 0.0209 K/W

Explanation:
In a composite wall when layers are connected in parallel, the thermal resistance of the system is given by,

(1 / R) = (1 / R2) + (1 / R2)

R = (R1 × R2) / (R1 + R2)

R = (0.036 × 0.05) + (0.036 + 0.05)

R = 0.0209 K/W


2)   A copper plat has dimensions 1m × 2m × 0.08m. The one of the largest surfaces is kept at 100 °C and other one is at 0 °C. Thermal conductivity of the copper plate k is 400 W/mK. What is the rate at which energy flows through the plate and the thermal resistance of the plate? (Marks: 02)
- Published on 19 Oct 15

a. 800 kW, 1 × 10– 3 K/W
b. 800 kW, 1 × 10– 4 K/W
c. 80000 W, 1 × 10– 3 K/W
d. 80000 W, 1 × 10– 4 K/W
Answer  Explanation 

ANSWER: 800 kW, 1 × 10– 4 K/W

Explanation:
According to the Fourier's law of heat conduction,
Rate of heat flow is given by,

qk = ( k A ΔT ) / l

= (400 × 1 × 2 × (80 – 0)) / 0.08
=800 kW

And thermal resistance is given by,

Rt = l / kA

= 0.08 / (400 × 1 × 2)
=1 × 10– 4 K/W


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