Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being T_{1, in} = 300 K and T_{2, in} = 350 K. The heat capacity rates of the two fluids are C₁ = 1000 W/K and C₂ = 400 W/K, and the effectiveness of the heat exchanger is 0.5. The actual heat transfer rate is _____ kW.

(Answer in integer)

A cylindrical rod of length ℎ and diameter 𝑑 is placed inside a cubic enclosure of side length 𝐿. 𝑆 denotes the inner surface of the cube.

The view-factor F_S-S is 

A very large metal plate of thickness 𝑑 and thermal conductivity 𝑘 is cooled by a stream of air at temperature 𝑇∞ = 300 K with a heat transfer coefficient ℎ, as shown in the figure. The centerline temperature of the plate is TP. In which of the following case(s) can the lumped parameter model be used to study the heat transfer in the metal plate?