Consider a 400 mm x 400 mm window in an aircraft For a tempe

Consider a 400 mm x 400 mm window in an aircraft. For a temperature difference of 90°C from the inner to the outer surface of the window, calculate the heat loss glass, and aerogel windows, respectively. The thermal conductivities of the aerogel and polycarbonate are 0.014 W/m K and k 0.21 m K, respec tively. Evaluate the thermal conductivity of the soda lime glass at 300 K. If the aircraft has 130 windows and the cost to heat the cabin air is $11kW. h, compare the costs associated with the heat loss through the windows for an 8-hour intercontinental flight. Answeu Glass Slf 50

Solution

The thermal conductivity of glass at 300 K is Kg = 1.4 W/m-K

Qg = Kg *A *T/L.............Eq.(1)

Now A = 0.4 x 0.4 = 0.16 m2

L = 12 mm = 0.012 meter.

T = 90 deg C

Putting the values in equation 1 we get.

Qg = 1680 watt = 1.68 kW. ; for 130 windows Qg = 1.68 * 130 = 218.4 kW

Cost associated with glass windows Cg = 1.68 kW x 8 Hr x 1 / kW-Hr = 13.44 dollar

Cost for 130 nos windows Cg = 13.44 * 130 = 1747.2 dollar approx 1750 dollar

Similarly

for Poly carbonate Qp = Kp *A *T/L.............Eq.(2)

Kp = 0.21 W/m-k

Hence Qp = 252 Watts = 0.252 kW ; for 130 windows Qp = 0.252 * 130 = 32.76 kW

Cost Cp = 0.252 x 8 = 2.016 dollar

Cost for 130 nos windows Cg = 2.016 * 130 = 262.08 dollar

And,

Qag = Kag *A *T/L.............Eq.(3)

Kag = 0.014 w/m-K

So, Qag = 16.8 watt = 0.0168 kW; for 130 windows Qag = 0.0168 * 130 = 2.184 kW

Cag = 0.0168 x 8 = 0.1344 dollar.

Cost for 130 nos windows Cag = 0.1344 * 130 = 17.472 dollar

Total cost = N x (Cg+Cp+Cag) = 130 x (13.44 + 2.016 +  0.1344 ) = 2026.752 dollar.

If you have any doubt please ask.