During a warm summer night, the air inside a house is maintained at a fixed temperature via an air conditioning system. Separating the inside air from the outside air is a plane wall. The inner surface of the wall exchanges energy with the air inside the house via convection; the outer surface of the wall exchanges energy with the surrounding air via convection and the night sky via radiation. Known system parameters are listed below. Inner air temperature Surrounding air temperature Night sky temperature Wall thermal conductivity Wall-air convection coefficient Wall emissivity Wall thickness T₁ = 26°C Too = 33°C T₂ = 4°C k h = 30 W/m²-K € = 0.85 L a) Set up the equations that you allow you to calculate the heat flux through the wall. Keep everything symbolic and be careful with your heat transfer directions. Hint: If the AC is on, what does that tell you about the net direction of heat transfer? b) Write a computer script that calculates the heat flux through the wall for 20 values of the ratio of the wall thickness to the thermal conductivity, 0.1 0.8. This ratio is known as the thermal conduction resistance of the wall, per unit area of wall, Rond This resistance is analogous to electrical resistance, but instead of voltage and electrical current we have temperature and heat flux.
During a warm summer night, the air inside a house is maintained at a fixed temperature via an air conditioning system. Separating the inside air from the outside air is a plane wall. The inner surface of the wall exchanges energy with the air inside the house via convection; the outer surface of the wall exchanges energy with the surrounding air via convection and the night sky via radiation. Known system parameters are listed below. Inner air temperature Surrounding air temperature Night sky temperature Wall thermal conductivity Wall-air convection coefficient Wall emissivity Wall thickness T₁ = 26°C Too = 33°C T₂ = 4°C k h = 30 W/m²-K € = 0.85 L a) Set up the equations that you allow you to calculate the heat flux through the wall. Keep everything symbolic and be careful with your heat transfer directions. Hint: If the AC is on, what does that tell you about the net direction of heat transfer? b) Write a computer script that calculates the heat flux through the wall for 20 values of the ratio of the wall thickness to the thermal conductivity, 0.1 0.8. This ratio is known as the thermal conduction resistance of the wall, per unit area of wall, Rond This resistance is analogous to electrical resistance, but instead of voltage and electrical current we have temperature and heat flux.
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
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Chapter1: Basic Modes Of Heat Transfer
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During a warm summer night, the air inside a house is maintained at a fixed temperature
via an air conditioning system. Separating the inside air from the outside air is a plane wall.
The inner surface of the wall exchanges energy with the air inside the house via convection;
the outer surface of the wall exchanges energy with the surrounding air via convection and
the night sky via radiation. Known system parameters are listed below.
Inner air temperature ?? = 26°C
Surrounding air temperature ?∞ = 33°C
Night sky temperature ?? = 4°C
Wall thermal conductivity ?
Wall-air convection coefficient ℎ = 30 W/m2-K
Wall emissivity ? = 0.85
Wall thickness ?
a) Set up the equations that you allow you to calculate the heat flux through the wall.
Keep everything symbolic and be careful with your heat transfer directions.
Hint: If the AC is on, what does that tell you about the net direction of heat transfer?
b) Write a computer script that calculates the heat flux through the wall for 20 values of
the ratio of the wall thickness to the thermal conductivity, 0.1 ≤ ?
? ≤ 0.8. This ratio is
known as the thermal conduction resistance of the wall, per unit area of wall, ?cond
′′ .
This resistance is analogous to electrical resistance, but instead of voltage and
electrical current we have temperature and heat flux.
via an air conditioning system. Separating the inside air from the outside air is a plane wall.
The inner surface of the wall exchanges energy with the air inside the house via convection;
the outer surface of the wall exchanges energy with the surrounding air via convection and
the night sky via radiation. Known system parameters are listed below.
Inner air temperature ?? = 26°C
Surrounding air temperature ?∞ = 33°C
Night sky temperature ?? = 4°C
Wall thermal conductivity ?
Wall-air convection coefficient ℎ = 30 W/m2-K
Wall emissivity ? = 0.85
Wall thickness ?
a) Set up the equations that you allow you to calculate the heat flux through the wall.
Keep everything symbolic and be careful with your heat transfer directions.
Hint: If the AC is on, what does that tell you about the net direction of heat transfer?
b) Write a computer script that calculates the heat flux through the wall for 20 values of
the ratio of the wall thickness to the thermal conductivity, 0.1 ≤ ?
? ≤ 0.8. This ratio is
known as the thermal conduction resistance of the wall, per unit area of wall, ?cond
′′ .
This resistance is analogous to electrical resistance, but instead of voltage and
electrical current we have temperature and heat flux.
Transcribed Image Text:During a warm summer night, the air inside a house is maintained at a fixed temperature
via an air conditioning system. Separating the inside air from the outside air is a plane wall.
The inner surface of the wall exchanges energy with the air inside the house via convection;
the outer surface of the wall exchanges energy with the surrounding air via convection and
the night sky via radiation. Known system parameters are listed below.
Inner air temperature
Surrounding air temperature
Night sky temperature
Wall thermal conductivity
Wall-air convection coefficient
Wall emissivity
Wall thickness
T₂ = 26°C
Too = 33°C
T₂ = 4°C
k
h, Ta
h = 30 W/m²-K
ε = 0.85
L
a) Set up the equations that you allow you to calculate the heat flux through the wall.
Keep everything symbolic and be careful with your heat transfer directions.
Hint: If the AC is on, what does that tell you about the net direction of heat transfer?
b) Write a computer script that calculates the heat flux through the wall for 20 values of
the ratio of the wall thickness to the thermal conductivity, 0.1 ≤ ≤0.8. This ratio is
known as the thermal conduction resistance of the wall, per unit area of wall, Rond
This resistance is analogous to electrical resistance, but instead of voltage and
electrical current we have temperature and heat flux.
HĽA
h, Too
ε T
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