Heat and Mass Transfer

❤️‍🔥Heat and Mass Transfer Unit 4 – Radiation Heat Transfer

Radiation heat transfer is a crucial mode of energy transfer through electromagnetic waves. It occurs between surfaces at different temperatures without needing a medium. The Stefan-Boltzmann law governs this process, relating radiant heat power to absolute temperature. Understanding radiation heat transfer is essential for various applications, from solar energy systems to spacecraft thermal control. Key concepts include blackbody radiation, emissivity, view factors, and radiation exchange between surfaces. Radiation shields and participating media also play important roles in this field.

Fundamentals of Radiation Heat Transfer

  • Radiation heat transfer involves the transfer of energy through electromagnetic waves
  • Occurs between surfaces at different temperatures without requiring a medium for transmission
  • Governed by the Stefan-Boltzmann law, which relates the total radiant heat power emitted by a surface to its absolute temperature
    • Expressed as Q=σAT4Q = \sigma A T^4, where σ\sigma is the Stefan-Boltzmann constant (5.67×1085.67 \times 10^{-8} W/m²·K⁴)
  • Radiation heat transfer is proportional to the fourth power of the absolute temperature difference between surfaces
  • Depends on surface properties such as emissivity, absorptivity, and reflectivity
    • Emissivity (ε\varepsilon) is the ratio of the radiation emitted by a surface to that emitted by a blackbody at the same temperature
  • Radiation can be absorbed, reflected, or transmitted by a surface
  • Plays a significant role in high-temperature applications (furnaces, solar energy systems)

Blackbody Radiation and Emissivity

  • A blackbody is an ideal surface that absorbs all incident radiation and emits the maximum amount of energy at a given temperature
  • Blackbody radiation follows Planck's law, which describes the spectral distribution of emitted radiation as a function of wavelength and temperature
  • The total emissive power of a blackbody is given by the Stefan-Boltzmann law, Eb=σT4E_b = \sigma T^4
  • Real surfaces emit less radiation than a blackbody at the same temperature, characterized by their emissivity (ε\varepsilon)
    • Emissivity values range from 0 to 1, with 1 representing a perfect blackbody
  • Kirchhoff's law states that, at thermal equilibrium, the emissivity of a surface equals its absorptivity (α\alpha) at a given wavelength and temperature
  • The spectral emissivity of a surface varies with wavelength, while the total hemispherical emissivity is an average value over all wavelengths
  • Emissivity depends on factors such as material composition, surface finish, and temperature
    • Polished metals generally have low emissivities, while rough and oxidized surfaces have higher emissivities

View Factors and Geometric Effects

  • View factors (also known as shape factors or configuration factors) quantify the geometric relationship between surfaces exchanging radiation
  • The view factor F12F_{1-2} represents the fraction of radiation leaving surface 1 that is intercepted by surface 2
    • Calculated using the integral F12=1A1A1A2cosθ1cosθ2πr2dA2dA1F_{1-2} = \frac{1}{A_1} \int_{A_1} \int_{A_2} \frac{\cos \theta_1 \cos \theta_2}{\pi r^2} dA_2 dA_1
  • View factors depend on the size, shape, and orientation of the surfaces involved
  • The reciprocity relation states that A1F12=A2F21A_1 F_{1-2} = A_2 F_{2-1}, where A1A_1 and A2A_2 are the areas of surfaces 1 and 2, respectively
  • The summation rule requires that the sum of all view factors from a surface to its surroundings equals 1
  • Tabulated view factors are available for common geometric configurations (parallel plates, perpendicular plates, concentric cylinders)
  • The crossed-strings method and the unit-sphere method are techniques for determining view factors in more complex geometries
  • Radiation shields and baffles can be used to modify view factors and control radiation exchange between surfaces

Radiation Exchange Between Surfaces

  • Radiation exchange between surfaces involves the net transfer of energy due to emission, absorption, and reflection
  • The net radiation heat transfer between two surfaces is given by Q12=A1F12σ(T14T24)Q_{1-2} = A_1 F_{1-2} \sigma (T_1^4 - T_2^4), assuming diffuse, gray surfaces
  • For multiple surfaces, the radiosity method is used to determine the net radiation exchange
    • Radiosity (JJ) is the total radiation leaving a surface, including emitted and reflected radiation
    • The radiosity method involves solving a system of equations relating the radiosities, emissivities, and temperatures of the surfaces
  • The net radiation method is an alternative approach that directly considers the net radiation heat transfer between pairs of surfaces
  • Radiation exchange in enclosures can be analyzed using the enclosure theory, which accounts for multiple reflections and the conservation of energy
  • The presence of participating media (gases, particles) can affect radiation exchange by absorbing, emitting, and scattering radiation
  • Kirchhoff's law and the reciprocity relation are used to simplify radiation exchange calculations in certain cases

Radiation Shields and Insulation

  • Radiation shields are thin, reflective surfaces used to reduce radiation heat transfer between two surfaces
  • Shields work by reflecting a portion of the incident radiation back to the source, reducing the net radiation exchange
  • The effectiveness of a radiation shield depends on its emissivity, reflectivity, and the number of shields used
    • Low-emissivity materials (polished metals) make effective radiation shields
  • Multiple radiation shields can be used to further reduce heat transfer, with each additional shield providing diminishing returns
  • Evacuated spaces between shields minimize conduction and convection losses, enhancing the shield's performance
  • Radiation shields are commonly used in cryogenic storage tanks, spacecraft insulation, and high-temperature furnaces
  • Insulation materials with low thermal conductivity and high reflectivity can also be used to reduce radiation heat transfer
    • Examples include multilayer insulation (MLI) and aerogel blankets
  • The effectiveness of insulation depends on its thickness, thermal conductivity, and the temperature gradient across it
  • Proper installation and maintenance of radiation shields and insulation are crucial for optimal performance

Radiation in Participating Media

  • Participating media, such as gases and particles, can absorb, emit, and scatter radiation as it passes through them
  • Absorption occurs when radiation is converted into internal energy of the medium, while emission is the release of energy as radiation
  • Scattering involves the redirection of radiation by particles or molecules in the medium
    • Scattering can be classified as forward scattering (in the direction of the incident radiation) or backward scattering (in the opposite direction)
  • The radiative transfer equation (RTE) describes the change in radiation intensity as it travels through a participating medium
    • The RTE accounts for absorption, emission, and scattering effects
  • The absorption and scattering coefficients quantify the extent to which a medium absorbs or scatters radiation per unit path length
  • The optical thickness (τ\tau) is a dimensionless parameter that characterizes the attenuation of radiation in a participating medium
    • Optically thin media (τ1\tau \ll 1) have little effect on radiation, while optically thick media (τ1\tau \gg 1) significantly attenuate radiation
  • Participating media can have a significant impact on radiation heat transfer in applications such as combustion chambers, atmospheric modeling, and solar receivers
  • Numerical methods, such as the discrete ordinates method (DOM) and the Monte Carlo method, are used to solve the RTE and analyze radiation in participating media

Applications and Real-World Examples

  • Solar energy systems: Radiation is the primary mode of heat transfer in solar collectors, concentrators, and photovoltaic panels
    • Selective surfaces with high absorptivity in the solar spectrum and low emissivity in the infrared are used to maximize solar energy absorption
  • Thermal insulation: Radiation shields and insulation materials are used to minimize heat loss in buildings, refrigeration systems, and industrial processes
    • Examples include reflective foils, ceramic coatings, and aerogel blankets
  • Furnaces and high-temperature processes: Radiation is the dominant mode of heat transfer at high temperatures, such as in glass melting furnaces and steel production
    • Refractory materials with high emissivity are used to enhance radiative heat transfer and improve efficiency
  • Spacecraft thermal control: Radiation is the only means of heat transfer in the vacuum of space
    • Spacecraft use reflective coatings, multilayer insulation, and heat pipes to manage temperature and protect sensitive components
  • Greenhouse effect: Atmospheric gases (water vapor, carbon dioxide) absorb and emit infrared radiation, trapping heat near the Earth's surface
    • Understanding radiative transfer in the atmosphere is crucial for climate modeling and predicting global temperature changes
  • Radiative cooling: Surfaces can be designed to emit radiation in the atmospheric window (8-13 μm) to achieve cooling below ambient temperature
    • Applications include passive cooling of buildings and electronic devices
  • Thermal radiation in manufacturing: Radiation heat transfer is used in processes such as drying, curing, and heat treatment of materials
    • Infrared lamps and radiant heaters provide targeted heating without the need for convection or conduction

Problem-Solving Techniques

  • Identify the mode of radiation heat transfer (surface-to-surface, surface-to-medium, or medium-to-medium) and the relevant properties (emissivity, absorptivity, reflectivity)
  • Determine the geometry and configuration of the surfaces involved, and calculate view factors using tabulated values, the reciprocity relation, or numerical methods
  • Apply the appropriate radiation heat transfer equations, such as the Stefan-Boltzmann law, the net radiation exchange equation, or the radiosity method
    • For surface-to-surface problems, use Q12=A1F12σ(T14T24)Q_{1-2} = A_1 F_{1-2} \sigma (T_1^4 - T_2^4) for diffuse, gray surfaces
    • For enclosures, set up a system of equations relating the radiosities, emissivities, and temperatures of the surfaces, and solve for the unknown quantities
  • Consider the effect of participating media, if present, and use the radiative transfer equation (RTE) to account for absorption, emission, and scattering
    • Determine the absorption and scattering coefficients, and calculate the optical thickness of the medium
  • Simplify the problem by making appropriate assumptions, such as diffuse and gray surfaces, non-participating media, or one-dimensional radiation transfer
  • Use numerical methods, such as the finite difference method or the Monte Carlo method, to solve complex radiation problems involving participating media or irregular geometries
  • Verify the results by checking the units, performing energy balance calculations, and comparing with known solutions or experimental data
  • Iterate and refine the solution, if necessary, by adjusting the assumptions, using more accurate property values, or increasing the resolution of numerical methods


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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.