Heat transfer by radiation is a crucial mode of energy transfer, especially at high temperatures. This section explores the fundamentals of thermal radiation, including , , and . Understanding these concepts is key to grasping how energy moves without a medium.
calculations are essential for engineering applications. We'll dive into the and how to calculate heat exchange between surfaces. These tools help engineers design everything from to systems.
Thermal Radiation Fundamentals
Blackbody Radiation and Planck's Law
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Thermal radiation is electromagnetic radiation emitted by matter due to its temperature and is a mode of heat transfer that does not require a medium (vacuum)
Blackbody radiation is the theoretical maximum amount of thermal radiation that can be emitted by an object at a given temperature (ideal radiator)
The spectral distribution of blackbody radiation varies with temperature according to Planck's law
Planck's law describes the spectral emissive power of a blackbody as a function of wavelength and temperature
Emissivity and Surface Properties
Emissivity is a surface property that represents the ratio of the actual thermal radiation emitted by a surface to the theoretical maximum (blackbody radiation) at the same temperature
Emissivity values range from 0 to 1, with a perfect blackbody having an emissivity of 1 (ideal absorber and emitter)
The emissivity of a surface depends on factors such as material (metal, ceramic, polymer), surface finish (polished, rough), and wavelength of the emitted radiation (visible, infrared)
Real surfaces have emissivity values less than 1, and their emissivity can vary with temperature and wavelength
Emissivity is an important factor in determining the effectiveness of a surface in emitting or absorbing thermal radiation
Radiative Heat Transfer Calculations
Stefan-Boltzmann Law
The Stefan-Boltzmann law relates the total energy emitted by a blackbody to its absolute temperature: E=σT4, where E is the total emissive power, σ is the Stefan-Boltzmann constant (5.67×10−8 W/m²·K⁴), and T is the absolute temperature (K)
The net radiative heat transfer rate between two surfaces can be calculated using the Stefan-Boltzmann law and the surface properties (emissivity, area, and temperature)
The radiative heat transfer rate between two surfaces is proportional to the difference in the fourth power of their absolute temperatures (Q∝(T14−T24))
The Stefan-Boltzmann law is used to calculate the radiative heat transfer rate in applications such as solar collectors, thermal insulation, and heat exchangers
Radiative Heat Exchange Between Surfaces
The net radiative heat transfer rate between two surfaces depends on their temperatures, emissivities, areas, and
The radiative heat exchange between two blackbody surfaces is given by: Q=σA1F12(T14−T24), where A1 is the area of surface 1, F12 is the view factor from surface 1 to surface 2, and T1 and T2 are the absolute temperatures of the surfaces
For gray surfaces (constant emissivity over all wavelengths), the radiative heat exchange is modified by the emissivities of the surfaces: Q=σA1F12(ε1T14−ε2T24), where ε1 and ε2 are the emissivities of surfaces 1 and 2, respectively
Radiative heat exchange calculations are essential for designing and analyzing systems involving high-temperature processes, such as furnaces, boilers, and combustion chambers
View Factors in Radiative Heat Transfer
Definition and Reciprocity Relation
View factors (also known as shape factors or configuration factors) represent the fraction of radiation leaving one surface that directly reaches another surface
View factors depend on the geometry and orientation of the surfaces involved in the radiative heat transfer (parallel plates, perpendicular plates, concentric cylinders)
The states that the product of the area and view factor for two surfaces is equal: A1F12=A2F21, where A1 and A2 are the areas of surfaces 1 and 2, and F12 and F21 are the view factors from surface 1 to 2 and from surface 2 to 1, respectively
The reciprocity relation is useful for determining view factors when one of them is known or can be easily calculated
Calculating View Factors
View factors for common geometries, such as parallel plates, perpendicular plates, and concentric cylinders, can be found in standard heat transfer references or calculated using integral expressions
For example, the view factor between two parallel plates of equal size separated by a distance L is given by: F12=π1[1+(LW)2−LW], where W is the width of the plates
View factors for complex geometries can be determined using numerical methods, such as the double area integration method or the Monte Carlo method
Accurate view factor calculations are crucial for predicting the radiative heat transfer between surfaces in various applications, such as thermal insulation, solar energy systems, and spacecraft thermal control
Surface Properties and Radiative Exchange
Kirchhoff's Law and Surface Properties
Surface properties, such as emissivity, , and , significantly influence radiative heat exchange between surfaces
states that, for a given surface at a given temperature and wavelength, the emissivity is equal to the absorptivity: ε=α
Surfaces with high emissivity and absorptivity (close to 1) are good radiators and absorbers (black surfaces), while surfaces with low emissivity and absorptivity (close to 0) are poor radiators and absorbers (white or reflective surfaces)
Reflectivity is the fraction of incident radiation that is reflected by a surface, and it is related to emissivity and absorptivity by: ρ=1−ε−α
The sum of emissivity, absorptivity, and reflectivity for a given surface is equal to 1: ε+α+ρ=1
Selective Surfaces and Applications
, which have high emissivity or absorptivity in specific wavelength ranges, can be used to control radiative heat exchange in applications such as solar collectors and thermal insulation
Solar selective surfaces have high absorptivity in the visible and near-infrared wavelengths (solar spectrum) and low emissivity in the mid- and far-infrared wavelengths (thermal radiation spectrum), maximizing solar energy absorption while minimizing thermal losses
Thermal insulation materials, such as low-emissivity coatings and reflective foils, have low emissivity in the infrared wavelengths, reducing radiative heat transfer and improving insulation effectiveness
Selective surfaces are also used in thermophotovoltaic systems, where a high-temperature emitter with a selective emission spectrum is used to generate electricity via photovoltaic cells
Understanding and manipulating surface properties is essential for optimizing radiative heat transfer in various engineering applications, from energy conservation to aerospace thermal management