Current Attempt in ProgressDuring a winter day, the window of a patio door with a height of $1\mathrm{.}8$ m and width of $1\mathrm{.}0$ m shows a frost line near its base, hence the temperature of the window is T$,=0\backslash$deg C$.$ The room wall and air temperatures are $15\backslash$deg C$.$ Determined to reduce the $$7$ per week cost associated with heat loss through their patio window by convection and radiation, the tenants cover the inside of the window with a$50-$mm$-$thick sheet of extruded insulation. Because they are not very handy around the house, the insulation is installed poorly,resulting in an S $=5\mathrm{.}25-$mm gap between the extruded insulation and the window pane, allowing the room air to infiltrate into thespace between the pane and the insulation.