Heat and Mass Transport

🌬️Heat and Mass Transport Unit 4 – Radiation Heat Transfer

Radiation 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) 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) 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) the fraction of incident radiation that a surface reflects (ranges from 0 to 1)
  • Transmissivity (τ\tau) 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: Eb=σT4E_b = \sigma T^4
    • σ\sigma is the Stefan-Boltzmann constant (5.67×1085.67 \times 10^{-8} W/m²·K⁴)
    • TT 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: λmax=2898μmKT\lambda_{\max} = \frac{2898 \mu m \cdot K}{T}
  • Kirchhoff's law of thermal radiation relates the emissivity and absorptivity of a surface at a given temperature and wavelength: ελ=αλ\varepsilon_{\lambda} = \alpha_{\lambda}
  • Net radiation heat transfer between two surfaces depends on their temperatures and radiative properties: Qnet=εσA(T14T24)Q_{net} = \varepsilon \sigma A (T_1^4 - T_2^4)
    • ε\varepsilon is the emissivity of the surface
    • AA is the surface area
    • T1T_1 and T2T_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 (FijF_{ij}) represents the fraction of radiation leaving surface ii that is intercepted by surface jj
    • 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: AiFij=AjFjiA_i F_{ij} = A_j F_{ji}
  • Summation rule the sum of all view factors from a surface ii to all other surfaces in an enclosure, including itself, is equal to unity: j=1nFij=1\sum_{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
    • Q12=σ(T14T24)1ε1A1ε1+1A1F12+1ε2A2ε2Q_{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}}
  • Radiosity (JJ) the total radiation energy leaving a surface per unit area and time, including emitted and reflected radiation
    • Ji=εiσTi4+(1εi)j=1nFijJjJ_i = \varepsilon_i \sigma T_i^4 + (1-\varepsilon_i) \sum_{j=1}^{n} F_{ij} J_j
  • Irradiation (GG) the total radiation energy incident upon a surface per unit area and time
    • Gi=j=1nFijJjG_i = \sum_{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


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© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.