Plot a graph showing the trend of the insulation thickness

Question

Air at T_∞2 (^oC) is flowing over the roof surface of a corridor with uniform velocity of V_air (km/hr). The length and width of the room are respectively, 8m and 3m. The roof consists of 5-cm concrete brick (k_brick= 38 W/m.K). It is demanded to decrease the rate of heat transfer by more than 50% via using an insulation layer of (k_ins= 0.03 W/m.K).

Determine

(a) The adequate thickness (x) of the insulation required when the reduction in heat transfer is 55%, 60%, 65%, 70%, 75%, 80%, 85%, 90%,95%, and 99%.

(b) Plot a graph showing the trend of the insulation thickness (x) vs. the reduction percent.

(c) Select the insulation thickness that you believe is realistic to use.

Properties of Air: k = 0.03095 W/m K; v = 2.306 x 10-5 m²/s; Pr = 0.7111