Heat Transfer Engineering

Design equations and calculator example Heat Loss through Aluminum Framed Window.

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A fixed aluminum-framed window with glass glazing is being considered for an opening that is H = 4 ft high and W = 6 ft wide (Fig. 1) in the wall of a house that is maintained at 72°F. Determine the rate of heat loss through the window and the inner surface temperature of the window glass facing the room when the outdoor air temperature is 15°F if the window is selected to be (a) -in. single glazing, (b) double glazing with an air space of in., and (c) low-e-coated triple glazing with an air space of in.

Solution: The rate of heat loss through an aluminum framed window and the inner surface temperature are to be determined from the cases of single-pane, double-pane, and low-e triple-pane windows.

Assumptions 1 Steady operating conditions exist. 2 Heat transfer through the window is one-dimensional. 3 Thermal properties of the windows and the heat transfer coefficients are constant.

Properties The U-factors of the windows are given in the following webpage: Overall U-factors for various windows and skylights

Analysis The rate of heat transfer through the window can be determined from:

Analysis The rate of heat transfer through the window can be determined from

where T_i and T_o are the indoor and outdoor air temperatures, respectively; U_overall is the U-factor (the overall heat transfer coefficient) of the window; and A_window is the window area, which is determined to be:

The U-factors for the three cases can be determined directly from Overall U-factors (heat transfer coefficients) for various windows and skylights to be 6.63, 3.51, and 1.92 W / (m² · °C), respectively, to be multiplied by the factor 0.176 to convert them to Btu / (h · ft² · °F).

Also, the inner surface temperature of the window glass can be determined from Newton’s law:

Where h_i is the heat transfer coefficient on the inner surface of the window, which is determined from (heat transfer coefficients to be h_i = 8.3 W/m² · °C = 1.46 Btu / [h ft² · °F]. Then the rate of heat loss and the interior glass temperature for each case are determined as follows:

(a) Single glazing:

(b) Double glazing ( in. air space):

(c) Triple glazing ( in. air space, low-e coated):

Therefore, heat loss through the window will be reduced by 47 percent in the case of double glazing and by 71 percent in the case of triple glazing relative to the single-glazing case. Also, in the case of single glazing, the low inner-glass surface temperature will cause considerable discomfort in the occupants because of the excessive heat loss from the body by radiation. It is raised from 26.5°F, which is below freezing, to 47.9°F in the case of double glazing and to 58.8°F in the case of triple glazing.