Generalized Wien’s Displacement Law in Determining the True Temperature of $$\text{ ZrB }_{2}$$ ZrB 2 –SiC-Based Ultrahigh-Temperature Ceramic: Thermodynamics of Thermal Radiation

Fisenko, Anatoliy I.; Lemberg, Vladimir F.

doi:10.1007/s10765-013-1429-8

Cited by 9 publications

(5 citation statements)

References 13 publications

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“…Fisenko and Lemberg 88 investigated the temperature dependence of the generalized Wien displacement law and the normal total emittance. Summarizing most of the experimental results, they estimated that the total normal emittance of ZrB 2 ‐SiC would be the following function of the temperature ( T in Kelvin unit),

\begin{eqnarray} {\epsilon }^ \bot \ \left( T \right) &=& \ 22.92464 - \left( {3.88345\ \times {{10}}^{ - 2}} \right)T \nonumber\\&+& \left( {2.25517\ \times \ {{10}}^{ - 5}} \right){T}^2 - \left( {4.34928 \times {{10}}^{ - 9}} \right){T}^3\nonumber\\&&{\rm{\ for\ wavelength\ }} = \ 4.03{\rm{\ \mu m\ to\ }}18{\rm{\ \mu m}}\end{eqnarray}

…”

Section: Radiative Properties Of Uhtcmentioning

confidence: 99%

Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra‐high temperature ceramics

Saad

Martínez

Trice

2023

Int J Ceramic Engine & Sci

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Emissivity as a function of wavelength, direction, and temperature correlates to a material's efficiency in radiating thermal energy. Knowledge of emissivity is essential for designing and developing radiation-cooled thermal protective systems for hypersonic applications. It is desirable to achieve a high emissivity (with a value close to 1) to maximize heat radiation from a hot surface of a hypersonic vehicle's leading edge during atmospheric re-entry. With the goal of providing the hypersonic materials community with this necessary knowledge, this article offers a basic understanding of thermal radiation, methods for measuring emissivity at high temperatures, and a comprehensive overview of the emissivity of ultra-high temperature ceramics.

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\begin{eqnarray} {\epsilon }^ \bot \ \left( T \right) &=& \ 22.92464 - \left( {3.88345\ \times {{10}}^{ - 2}} \right)T \nonumber\\&+& \left( {2.25517\ \times \ {{10}}^{ - 5}} \right){T}^2 - \left( {4.34928 \times {{10}}^{ - 9}} \right){T}^3\nonumber\\&&{\rm{\ for\ wavelength\ }} = \ 4.03{\rm{\ \mu m\ to\ }}18{\rm{\ \mu m}}\end{eqnarray}

…”

Section: Radiative Properties Of Uhtcmentioning

confidence: 99%

Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra‐high temperature ceramics

Saad

Martínez

Trice

2023

Int J Ceramic Engine & Sci

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“…The true temperature is determined by the position of the maximum of the Planck function. The performance of this method was demonstrated on the thermal radiation of tungsten, molybdenum, luminous flames, and zirconium, hafnium, and titanium carbides, and ZrB2-SiC-based ultra-high temperature ceramics [22][23][24][25][26][27].…”

Section: Planck Function and Wien's Displacement Law In A Finite Freq...mentioning

confidence: 99%

Polylogarithmic Representation of Radiative and Thermodynamic Properties of Thermal Radiation in a Given Spectral Range: I. Blackbody Radiation

Fisenko¹,

Lemberg²

2015

Int J Thermophys

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Using polylogarithm functions the exact analytical expressions for the radiative and thermodynamic properties of blackbody radiation, such as the Wien displacement law, Stefan-Boltzmann law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, and pressure in the finite range of frequencies are constructed. The obtained expressions allow us to tabulate these functions in various finite frequency bands at different temperatures for practical applications. As an example, the radiative and thermodynamic functions using experimental data for the monopole spectrum of the Cosmic Microwave Background (CMB) radiation measured by the COBE FIRAS instrument in the 60 -600 GHz frequency interval at the temperature T = 2.725 K are calculated. The expressions obtained for the radiative and thermodynamic functions can be easily presented in wavelength and wavenumber domains.

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“…It is important to note that a knowledge of the frequency dependence of the spectral emissivity also allows to determine the thermal radiative and thermodynamic properties of a real-body within a finite range of frequencies. In [36][37][38], the thermal radiative and thermodynamic properties of some materials have been studied using spectral emissivity data presented in tabular form. These materials are: a) the hafnium, zirconium, and titanium carbides; b) ZrB2-SiC-based ultra-high temperature ceramics; and c) molybdenum.…”

Section: Introductionmentioning

confidence: 99%

Polylogarithmic Representation of Radiative and Thermodynamic Properties of Thermal Radiation in a Given Spectral Range: II. Real-Body Radiation

Fisenko¹,

Lemberg²

2015

Int J Thermophys

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The general analytical expressions for the thermal radiative and thermodynamic properties of a realbody are obtained in a finite range of frequencies at different temperatures. The frequency dependence of the spectral emissivity is represented as a power series. Stefan-Boltzmann's law, total energy density, number density of photons, Helmholtz free energy density, internal energy density, enthalpy density, entropy density, heat capacity at constant volume, pressure, and total emissivity are expressed in terms of the polylogarithm functions. The general expressions for the thermal radiative and thermodynamic functions are applied for the study of thermal radiation of liquid and solid zirconium carbide. These functions are calculated using experimental data for the frequency dependence of the normal spectral emissivity in the visible-near infrared range at the melting (freezing) point. The gaps between the thermal radiative and thermodynamic functions of liquid and solid zirconium carbide are observed. The general analytical expressions obtained can easily be presented in wavenumber domain.

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Generalized Wien’s Displacement Law in Determining the True Temperature of $$\text{ ZrB }_{2}$$ ZrB 2 –SiC-Based Ultrahigh-Temperature Ceramic: Thermodynamics of Thermal Radiation

Cited by 9 publications

References 13 publications

Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra‐high temperature ceramics

Radiation heat transfer during hypersonic flight: A review of emissivity measurement and enhancement approaches of ultra‐high temperature ceramics

Polylogarithmic Representation of Radiative and Thermodynamic Properties of Thermal Radiation in a Given Spectral Range: I. Blackbody Radiation

Polylogarithmic Representation of Radiative and Thermodynamic Properties of Thermal Radiation in a Given Spectral Range: II. Real-Body Radiation

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