Serpe has reported on the development of

“smart windows,” where the gap between two glass panes is filled with an aqueous solution containing hydrogel particles made of poly(#1-

isopropylacrylamide) or pNIPAm, which are thermo-responsive. At low temperature (e.g., < 32°C), the particles are swollen and become transparent allowing light to pass through. However, at higher temperatures, the hydrogel particles shrink and scatter the sunlight, preventing radiant heat transfer into the room during a sunny day and reducing air conditioning costs. Suppose that the double pane window described in Problem 3.1 is filled with such a hydrogel-containing solution. By how much will the convective/conductive heat transfer rate change compared to the case where the gap is filled with air? The thermal conductivity of pNIPA hydrogel has been reported to be on the order of 0.40 W/m K.

Data From Problem 3.1:

Double-pane glass windows, designed to reduces heat losses, consist, as the name implies, of two glass panes separated by a thin gap filled with dry air and sealed. Let’s compare the efficiency of a single-pane window (just one pane without an air gap) with that of a double-pane window with the same overall thickness of glass. The single-pane window has a surface area of 1.5 m² and the glass thickness is 0.5 cm. The doublepane window has the same area but comprises two 0.25-cm-thick glass panes separated by a 2-mm air gap. The convective heat transfer coefficients inside and outside the room are 10 and 20 W/m² K and the inside and outside temperatures are 25°C and 4°C, respectively.