Consider a house whose windows are made of 0.375-in-thick glass (k = 0.48 Btu/h·ft·°F and α = 4.2 × 10^-6 ft²/s). Initially, the entire house, including the walls and the windows, is at the outdoor temperature of T_o = 35°F. It is observed that the windows are fogged because the indoor temperature is below the dew-point temperature of 54°F. Now the heater is turned on and the air temperature in the house is raised to T_i = 72°F at a rate of 2°F rise per minute. The heat transfer coefficients at the inner and outer surfaces of the wall can be taken to be h_i = 1.2 and h_o = 2.6 Btu/h·ft²·°F, respectively, and the outdoor temperature can be assumed to remain constant. Using the explicit finite difference method with a mesh size of Δx = 0.125 in, determine how long it will take for the fog on the windows to clear up (i.e., for the inner surface temperature of the window glass to reach 54°F).

Transcribed Image Text:

T₁ h₁ House Fog Window glass Ax 12 34 0.375 in To ho Outdoors