To reduce the home heating requirements, modern building codes in many parts of the country require the use of double-glazed or double-pane windows, i.e., windows with two panes of glass. Some of these so called thermopane windows have an evacuated space between the two glass panes while others trap stagnant air in the space. (a) Consider a double-pane window with the dimensions shown in the sketch given below. If this window has stagnant air trapped between the two panes and the convective heat transfer coefficients on the inside and outside surfaces are 4 W/(m2 K) and 15 W/(m2 K), respectively, calculate the overall heat transfer coefficient for the system. (b) If the inside air temperature is 22°C and the outside air temperature is –5°C, compare the heat loss through a 4 m2

Question

double-pane window with the heat loss through a single-pane window. Comment on the effect of the window frame on this result. (c) If the total window area of a home heated by electric resistance heaters at a cost of $.10/kWh is 80 m2 how much more cost can you justify for the double-pane windows if the average temperature difference during the six winter months when heating is required is about 15°C?



GIVEN

- Double-pane window with stagnant air in gap

- Convective heat transfer coefficients



- Air temperatures



FIND

(a) The overall heat transfer coefficient

(b) Compare heat loss of double- and single-pane window

(c) Cost to justify for the use of double-pane window.

ASSUMPTIONS

- Steady state conditions prevail

- Radiative heat transfer is negligible

SKETCH

Answer 1

The thermal circuit for the system is shown below



The individual resistances are



The total resistance for the double-pane window is



Therefore the overall heat transfer coefficient is



(b) The rate of heat loss through the double-pane window is



The thermal circuit for the single-pane window is



The total thermal resistance for the single-pane window is



The overall heat transfer coefficient for the single-pane window is



Therefore, the rate of heat loss through the single-pane window is



The heat loss through the double-pane window is only 28% of that through the single-pane

window.

(c) The average heat loss through double-pane windows during the winter months





The yearly savings of the double-pane windows is $1157. Therefore if we would like to have a

payback period of two years, we would be willing to invest $2314 in double panes.