GATE Mechanical Engineering Practice Quiz

Question 1

A plane wall 0.2 m thick with a thermal conductivity of 0.5 W/m·K has its inner face at 200 °C. Its outer face loses heat by convection to air at 30 °C with a coefficient of 10 W/m²·K. What is the steady heat flux through the wall?

Accepted Answer

340 W/m²

Question 2

A steel sphere of 50 mm diameter with k = 50 W/m·K is cooled with a convection coefficient of 100 W/m²·K. Using the characteristic length V/A, what is the Biot number?

Accepted Answer

0.017

Question 3

The steel sphere of the previous conditions has ρ = 7800 kg/m³ and c = 470 J/kg·K, with Lc = 0.00833 m and h = 100 W/m²·K. What is its lumped capacitance time constant?

Accepted Answer

306 s

Question 4

In a counterflow heat exchanger a hot stream cools from 100 °C to 60 °C while a cold stream is heated from 20 °C to 50 °C. What is the logarithmic mean temperature difference?

Accepted Answer

44.8 °C

Question 5

A black surface of 1 m² at 500 K exchanges radiation with large black surroundings at 300 K. What is the net rate of radiant heat loss?

Accepted Answer

3.08 kW

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