The R-factor for housing insulation gives the thermal resistance in units of ft2 °F h/BTU. A good wall for harsh climates, corresponding to about 10 in of fiberglass, has R = 39 ft2 °F h/BTU.
a) Determine the thermal resistance (in m2 K/W) in SI units.
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b) Find the heat flow per square meter through a wall that has insulation with an R-factor of 39, with an outside temperature of -18.9 °C and an inside temperature of 24.7°C.
a) To convert the thermal resistance from ft2 °F h/BTU to SI units (m2 K/W), we need to use the conversion factors:
1 ft = 0.3048 m
1 °F = 0.5556 °C
1 BTU = 1.055 kJ
First, let's convert the thermal resistance from ft2 °F h/BTU to ft2 °C h/W:
R(ft2 °C h/W) = R(ft2 °F h/BTU) * (0.5556 °C/°F)
R(ft2 °C h/W) = 39 ft2 °F h/BTU * (0.5556 °C/°F)
Now, let's convert from ft2 °C h/W to m2 K/W:
R(m2 K/W) = R(ft2 °C h/W) / (10.764 ft2/m2)
R(m2 K/W) = (39 ft2 °C h/W * 0.5556 °C/°F) / (10.764 ft2/m2)
R(m2 K/W) = 2.522 m2 K/W
Therefore, the thermal resistance in SI units is approximately 2.522 m2 K/W.
b) To find the heat flow per square meter through the wall, we can use the formula:
Heat flow = (Temperature difference) / (Thermal resistance)
First, let's convert the temperatures from °C to °K:
Outside temperature = -18.9 °C + 273.15 °K = 254.25 °K
Inside temperature = 24.7 °C + 273.15 °K = 297.85 °K
Now, let's calculate the temperature difference:
Temperature difference = Inside temperature - Outside temperature
Temperature difference = 297.85 °K - 254.25 °K
Temperature difference = 43.60 °K
Now, let's calculate the heat flow per square meter:
Heat flow = Temperature difference / Thermal resistance
Heat flow = 43.60 °K / 2.522 m2 K/W
Heat flow = 17.26 W/m2
Therefore, the heat flow per square meter through the wall is approximately 17.26 W/m2.