Chapter 18, Problem 057 (a) What is the rate of energy loss in watts per square

Question

Chapter 18, Problem 057 (a) What is the rate of energy loss in watts per square meter through a glass window 3.1 mm thick if the outside temperature is-19°F and the inside temperature is +77°F? (b) A storm window having the same thickness of glass is installed parallel to the first window, with an air gap of 5.3 cm between the two windows. What now is the rate of energy loss if conduction is the only important energy-loss mechanism? (The thermal conductivity of window glass is 1.0 W/m.K, and of air is 0.026 W/m-K.) (a) Number Units (b) Number Units

Explanation / Answer

a. given

t = 3.1 mm

A = 1 m^2

Tc = -19 F = -28.3333 C

Th = 77 F = 25 C

hence

rate of heat conduction = r

r = 0.96(Th - Tc)/t

r = 16516.02580645 W/m^2 = 16.516 kW/m^2

b. gap, d = 5.3 cm

let temperaute on the cooler side of air inside the glasses be tc, on the hot side = th

then

r = 1(Th - th)/t = 0.026(th - tc)/d = 1(tc - Tc)/t

hence

tc + th = Tc + Th = 53.333 C

(25 - th)/t = 0.026(th - 53.333 + th)/d

0.0030415*th - 0.0811064 = 25 - th

th = 25.00505 C

hence

r = 1.6301745083 kW/m^2

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