All Study Guides Heat and Mass Transport Unit 4
🌬️ Heat and Mass Transport Unit 4 – Radiation Heat TransferRadiation heat transfer involves energy transfer through electromagnetic waves without a medium. This unit covers key concepts like blackbodies, emissivity, and absorptivity, as well as fundamental laws like Stefan-Boltzmann and Planck's law. Understanding these principles is crucial for analyzing thermal systems.
The unit delves into various types of radiation, surface properties, and geometric considerations like view factors. It explores radiation exchange between surfaces, enclosure analysis, and practical applications in engineering. Problem-solving techniques and examples help apply these concepts to real-world scenarios.
Key Concepts and Definitions
Radiation heat transfer involves the transfer of energy through electromagnetic waves without requiring a medium
Electromagnetic spectrum encompasses a wide range of wavelengths, including visible light, infrared, and ultraviolet radiation
Blackbody an idealized surface that absorbs all incident radiation and emits the maximum amount of energy at a given temperature
Emissivity (ε \varepsilon ε ) a material property that quantifies the ability of a surface to emit radiation relative to a blackbody (ranges from 0 to 1)
Real surfaces have emissivities less than 1, while a blackbody has an emissivity of 1
Absorptivity (α \alpha α ) the fraction of incident radiation that a surface absorbs (ranges from 0 to 1)
A blackbody has an absorptivity of 1, absorbing all incident radiation
Reflectivity (ρ \rho ρ ) the fraction of incident radiation that a surface reflects (ranges from 0 to 1)
Transmissivity (τ \tau τ ) the fraction of incident radiation that a surface transmits (ranges from 0 to 1)
For opaque surfaces, transmissivity is zero
Fundamental Laws and Equations
Stefan-Boltzmann law quantifies the total radiant heat energy emitted by a blackbody per unit area and time: E b = σ T 4 E_b = \sigma T^4 E b = σ T 4
σ \sigma σ is the Stefan-Boltzmann constant (5.67 × 1 0 − 8 5.67 \times 10^{-8} 5.67 × 1 0 − 8 W/m²·K⁴)
T T T is the absolute temperature of the surface (in Kelvin)
Planck's law describes the spectral distribution of blackbody radiation as a function of wavelength and temperature
Wien's displacement law states that the wavelength of maximum emission from a blackbody is inversely proportional to its temperature: λ max = 2898 μ m ⋅ K T \lambda_{\max} = \frac{2898 \mu m \cdot K}{T} λ m a x = T 2898 μ m ⋅ K
Kirchhoff's law of thermal radiation relates the emissivity and absorptivity of a surface at a given temperature and wavelength: ε λ = α λ \varepsilon_{\lambda} = \alpha_{\lambda} ε λ = α λ
Net radiation heat transfer between two surfaces depends on their temperatures and radiative properties: Q n e t = ε σ A ( T 1 4 − T 2 4 ) Q_{net} = \varepsilon \sigma A (T_1^4 - T_2^4) Q n e t = ε σ A ( T 1 4 − T 2 4 )
ε \varepsilon ε is the emissivity of the surface
A A A is the surface area
T 1 T_1 T 1 and T 2 T_2 T 2 are the absolute temperatures of the surfaces
Types of Radiation Heat Transfer
Surface radiation occurs when electromagnetic waves are emitted, absorbed, or reflected by surfaces
Emission originates from the thermal energy of matter, with the rate depending on surface temperature and emissivity
Gas radiation involves the emission and absorption of radiation by gases, such as carbon dioxide and water vapor
Gases can be transparent to certain wavelengths while absorbing or emitting others
Participating media radiation considers the interaction of radiation with matter within a medium, such as in furnaces or combustion chambers
Scattering, absorption, and emission processes can occur within the medium
Solar radiation the energy emitted by the sun, which can be harnessed for various applications (solar thermal collectors, photovoltaic cells)
Earth's atmosphere absorbs and scatters a portion of the incoming solar radiation
Thermal radiation the electromagnetic radiation emitted by matter due to its temperature
All objects with a temperature above absolute zero emit thermal radiation
Properties of Radiating Surfaces
Emissivity depends on factors such as material composition, surface finish, temperature, and wavelength
Polished metals generally have low emissivities, while rough and oxidized surfaces have higher emissivities
Selective surfaces have emissivities that vary significantly with wavelength
Used in applications where specific wavelength ranges need to be absorbed or emitted (solar collectors, thermal insulation)
Diffuse surfaces reflect radiation equally in all directions, following Lambert's cosine law
Matte surfaces exhibit diffuse behavior
Specular surfaces reflect radiation in a mirror-like manner, with the angle of reflection equal to the angle of incidence
Polished surfaces and mirrors exhibit specular behavior
Gray surfaces have emissivities that are independent of wavelength
Simplifies radiation heat transfer calculations
Real surfaces often exhibit a combination of diffuse and specular characteristics and have emissivities that vary with wavelength and temperature
View Factors and Geometric Considerations
View factor (F i j F_{ij} F ij ) represents the fraction of radiation leaving surface i i i that is intercepted by surface j j j
Also known as shape factor or configuration factor
Reciprocity relation states that the product of the view factor and area for two surfaces is equal: A i F i j = A j F j i A_i F_{ij} = A_j F_{ji} A i F ij = A j F ji
Summation rule the sum of all view factors from a surface i i i to all other surfaces in an enclosure, including itself, is equal to unity: ∑ j = 1 n F i j = 1 \sum_{j=1}^{n} F_{ij} = 1 ∑ j = 1 n F ij = 1
View factors depend on the size, shape, and orientation of the surfaces involved
Analytical expressions exist for simple geometries (parallel plates, perpendicular plates, concentric cylinders)
Crossed-strings method a graphical technique for determining view factors between surfaces using crossed strings and uncrossed strings
Contour integral method an analytical approach for calculating view factors using double integrals over the surfaces
Hottel's crossed-string method an algebraic method for calculating view factors in enclosures with three or more surfaces
Radiation Heat Exchange Between Surfaces
Net radiation heat exchange between two surfaces depends on their temperatures, emissivities, and view factor
Q 1 → 2 = σ ( T 1 4 − T 2 4 ) 1 − ε 1 A 1 ε 1 + 1 A 1 F 12 + 1 − ε 2 A 2 ε 2 Q_{1\rightarrow2} = \frac{\sigma (T_1^4 - T_2^4)}{\frac{1-\varepsilon_1}{A_1 \varepsilon_1} + \frac{1}{A_1 F_{12}} + \frac{1-\varepsilon_2}{A_2 \varepsilon_2}} Q 1 → 2 = A 1 ε 1 1 − ε 1 + A 1 F 12 1 + A 2 ε 2 1 − ε 2 σ ( T 1 4 − T 2 4 )
Radiosity (J J J ) the total radiation energy leaving a surface per unit area and time, including emitted and reflected radiation
J i = ε i σ T i 4 + ( 1 − ε i ) ∑ j = 1 n F i j J j J_i = \varepsilon_i \sigma T_i^4 + (1-\varepsilon_i) \sum_{j=1}^{n} F_{ij} J_j J i = ε i σ T i 4 + ( 1 − ε i ) ∑ j = 1 n F ij J j
Irradiation (G G G ) the total radiation energy incident upon a surface per unit area and time
G i = ∑ j = 1 n F i j J j G_i = \sum_{j=1}^{n} F_{ij} J_j G i = ∑ j = 1 n F ij J j
Radiation network method models the radiation heat exchange between surfaces using a network of resistances and potentials
Surfaces are represented as nodes, and view factors and emissivities determine the resistances between nodes
Enclosure analysis involves solving a system of equations for the radiosities or heat transfer rates in an enclosure with multiple surfaces
Matrix inversion or iterative methods can be used to solve the system of equations
Applications in Engineering and Industry
Thermal insulation materials with low emissivities (reflective foils) can reduce radiation heat transfer and improve energy efficiency
Solar thermal collectors harness solar radiation to heat fluids for various applications (water heating, space heating, power generation)
Selective surfaces with high absorptivity in the solar spectrum and low emissivity in the infrared spectrum enhance collector efficiency
Radiative cooling systems exploit the emission of infrared radiation to the cold sky to achieve cooling without the need for external power
Used in passive cooling of buildings and electronic devices
Furnaces and combustion chambers involve radiation heat transfer between high-temperature gases, flames, and surfaces
Proper design and material selection can optimize heat transfer and energy efficiency
Spacecraft thermal control relies on radiation heat transfer to maintain acceptable temperature ranges in the harsh space environment
Radiators, insulation, and surface coatings are used to manage heat rejection and absorption
Greenhouse effect the trapping of infrared radiation by atmospheric gases, leading to increased surface temperatures on Earth
Relevant to climate change and global warming studies
Problem-Solving Techniques and Examples
Identify the mode(s) of radiation heat transfer involved (surface, gas, participating media)
Determine the relevant surface properties (emissivity, absorptivity, reflectivity) and geometric factors (view factors, surface areas)
Apply the appropriate equations or methods for the given scenario (Stefan-Boltzmann law, radiosity, radiation network)
Example: Calculate the net radiation heat transfer between two parallel plates with known temperatures and emissivities
Simplify the problem by making reasonable assumptions (gray surfaces, diffuse surfaces, nonparticipating media)
Example: Assume a gas mixture is nonparticipating to focus on surface radiation heat transfer
Use tabulated data, charts, or correlations to obtain view factors for common geometries
Example: Determine the view factor between two perpendicular rectangles using a chart or analytical expression
Solve systems of equations for enclosures using matrix inversion or iterative methods
Example: Set up and solve the radiosity matrix for a three-surface enclosure
Interpret the results and consider the implications for the specific application or system
Example: Evaluate the effectiveness of a radiative cooling system based on the calculated heat rejection rate