RADIANT HEAT TRANSFER CASE STUDY
Introduction
Radiant heat transfer involves the transfer of heat by electromagnetic radiation that arises due to the temperature of a body. Most energy of this type is in the infra-red region of the electromagnetic spectrum although some of it is in the visible region. The term thermal radiation is frequently used to distinguish this form of electromagnetic radiation from other forms, such as radio waves, x-rays, or gamma rays. The transfer of heat from a fireplace across a room in the line of sight is an example of radiant heat transfer.
Radiant heat transfer does not need a medium, such as air or metal, to take place. Any material that has a temperature above absolute zero gives off some radiant energy. When a cloud covers the sun, both its heat and light diminish. This is one of the most familiar examples of heat transfer by thermal radiation
Black Body Radiation
A body that emits the maximum amount of heat for its absolute temperature is called a black body. Radiant heat transfer rate from a black body to its surroundings can be expressed by the following equation.
where
Q = heat transfer (W) (Btu/hr)
𝜎 = Stefan-Boltzman constant 5.6703 10⁻⁸ (W/m².K⁴) (0.174 Btu/hr-ft²-°R⁴)
A = surface area (m²) (ft²)
T = temperature (K) (°R)
Two black bodies that radiate toward each other have a net heat flux between them. The net flow rate of heat between them is given by an adaptation of Equation
where
A = surface area of the first body (m²) (ft²)
T₁ = temperature of the first body (K) (°R)
T₂ = temperature of the second body (K) (°R)
All bodies above absolute zero temperature radiate some heat. The sun and earth both radiate heat toward each other. This seems to violate the Second Law of Thermodynamics, which states that heat cannot flow from a cold body to a hot body. The paradox is resolved by the fact that each body must be in direct line of sight of the other to receive radiation from it. Therefore, whenever the cool body is radiating heat to the hot body, the hot body must also be radiating heat to the cool body. Since the hot body radiates more heat (due to its higher temperature) than the cold body, the net flow of heat is from hot to cold, and the second law is still satisfied.
Emissivity Coefficient
Real objects do not radiate as much heat as a perfect black body. They radiate less heat than a black body and are called gray bodies. To take into account the fact that real objects are gray bodies
where:
𝓔 = emissivity of the gray body (dimensionless)
Emissivity is simply a factor by which we multiply the black body heat transfer to take into account that the black body is the ideal case. Emissivity is a dimensionless number and has a maximum value of 1.0.
NOTE : The emissivity lies in the range 0 < ε < 1 and depends on the type of material and the temperature of the surface. The emissivity of some common materials are:
Radiation Configuration Factor
Radiative heat transfer rate between two gray bodies can be calculated by the equation stated below.
where:
fa = is the shape factor, which depends on the spatial arrangement of the two objects (dimensionless)
fe = is the emissivity factor, which depends on the emissivities of both objects (dimensionless)
which takes into account the emissivity of both bodies and their relative geometry.
Radiation Constants of some common Building Materials
The radiation constant is the product between the Stefan-Boltzmann constant and the emissivity constant for the material
The radiation constant of some common materials can be found in the table below:
Introduction
Radiant heat transfer involves the transfer of heat by electromagnetic radiation that arises due to the temperature of a body. Most energy of this type is in the infra-red region of the electromagnetic spectrum although some of it is in the visible region. The term thermal radiation is frequently used to distinguish this form of electromagnetic radiation from other forms, such as radio waves, x-rays, or gamma rays. The transfer of heat from a fireplace across a room in the line of sight is an example of radiant heat transfer.
Radiant heat transfer does not need a medium, such as air or metal, to take place. Any material that has a temperature above absolute zero gives off some radiant energy. When a cloud covers the sun, both its heat and light diminish. This is one of the most familiar examples of heat transfer by thermal radiation
Black Body Radiation
A body that emits the maximum amount of heat for its absolute temperature is called a black body. Radiant heat transfer rate from a black body to its surroundings can be expressed by the following equation.
Q =𝜎AT⁴
where
Q = heat transfer (W) (Btu/hr)
𝜎 = Stefan-Boltzman constant 5.6703 10⁻⁸ (W/m².K⁴) (0.174 Btu/hr-ft²-°R⁴)
A = surface area (m²) (ft²)
T = temperature (K) (°R)
Q =𝜎A(T₁⁴-T₂⁴)
where
A = surface area of the first body (m²) (ft²)
T₁ = temperature of the first body (K) (°R)
T₂ = temperature of the second body (K) (°R)
All bodies above absolute zero temperature radiate some heat. The sun and earth both radiate heat toward each other. This seems to violate the Second Law of Thermodynamics, which states that heat cannot flow from a cold body to a hot body. The paradox is resolved by the fact that each body must be in direct line of sight of the other to receive radiation from it. Therefore, whenever the cool body is radiating heat to the hot body, the hot body must also be radiating heat to the cool body. Since the hot body radiates more heat (due to its higher temperature) than the cold body, the net flow of heat is from hot to cold, and the second law is still satisfied.
Emissivity Coefficient
Real objects do not radiate as much heat as a perfect black body. They radiate less heat than a black body and are called gray bodies. To take into account the fact that real objects are gray bodies
Q =𝓔𝜎AT⁴
where:
𝓔 = emissivity of the gray body (dimensionless)
Emissivity is simply a factor by which we multiply the black body heat transfer to take into account that the black body is the ideal case. Emissivity is a dimensionless number and has a maximum value of 1.0.
NOTE : The emissivity lies in the range 0 < ε < 1 and depends on the type of material and the temperature of the surface. The emissivity of some common materials are:
- oxidized Iron at 390 oF (199 oC) - ε = 0.64
- polished Copper at 100 oF (38 oC) - ε = 0.03
Radiative heat transfer rate between two gray bodies can be calculated by the equation stated below.
Q = fa fe 𝜎 A(T₁⁴- T₂⁴ )
fa = is the shape factor, which depends on the spatial arrangement of the two objects (dimensionless)
fe = is the emissivity factor, which depends on the emissivities of both objects (dimensionless)
The two separate terms fa and fe can be combined and given the symbol f. The heat flow between two gray bodies can now be determined by the following equation:
Q = f 𝜎 A(T₁⁴- T₂⁴ )
The symbol (f) is a dimensionless factor sometimes called the radiation configuration factor,which takes into account the emissivity of both bodies and their relative geometry.
Once the configuration factor is obtained, the overall net heat flux can be determined. Radiant heat flux should only be included in a problem when it is greater than 20% of the problem.
The radiation constant is the product between the Stefan-Boltzmann constant and the emissivity constant for the material
The radiation constant of some common materials can be found in the table below:
Radiant Heat Transfer Summary
- Black body radiation is the maximum amount of heat that can be transferred from an ideal object.
- Emissivity is a measure of the departure of a body from the ideal black body.
- Radiation configuration factor takes into account the emittance and relative geometry of two objects.
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