Radiative Transfer Coefficients Research Articles

Prediction on effects of absorptivity and emissivity for surface temperature distribution using an improved thermal network model

AbstractThe conventional thermal network model for satellite surface temperature distribution is directly solved by a new solution method on the basis of the Monte Carlo Ray Tracing (MCRT) method. The solar direct incidence area, the solar radiation transfer coefficient, the infrared radiation transfer coefficient, and the network conduction and radiation coefficients are calculated by Monte Carlo statistical analysis rather than the Gebhart approach. The advantage of the MCRT method is that the surface material characteristics are taken into account in the solving process. The effect of absorptivity and emissivity for temperature distributions is analyzed in detail. Numerical simulation is carried out for the temperature distribution of the satellite surface with different solar incidences of round angle and zenith angle. In the steady stage, the maximum temperature difference reaches up to 200 K and increasing the absorptivity‐emissivity ratio will lead to a rapid temperature rise. In the unsteady stage, the cooling velocity of the main body surface is always smaller than that of the solar array surface and the maximum temperature of the main body is larger than the solar arrays. Under the same absorptivity‐emissivity ratio, the solar incidence angle has a great effect on the uniform character of temperature distribution. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res, 39(7): 539–553, 2010; Published online 16 July 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/htj.20316

A new improved solution to thermal network problem in heat-transfer analysis of spacecraft

A new improved solution, Detached Variables-Parameters Coefficient (DVPC) method and Monte Carlo Ray Tracing (MCRT) method, is proposed to solve a thermal network problem in heat-transfer analysis of spacecraft. DVPC method emphasized directly on correcting the key Solar Absorption Coefficient (SAC) material parameter rather than the network conduction and radiation coefficients generally. MCRT method is contributed to reducing computation assumption and clarifying physical concepts and used to solve solar direct incidence area and network radiation transfer coefficient with different round circular angles and zenith angles of solar incidence radiation. Numerical simulation is carried out for temperature distribution of satellite. In steady stage, maximum temperature difference reaches up to 200 K and increasing the radio of absorptivity to emissivity will lead to temperature rise rapidly. In unsteady stage, maximum temperature value of satellite main body is lager than that of solar array. To begin with, cooling velocity increased rapidly and got to maximum value, then descended slowly and reached up to steady stage with 17 K discrepancy. Meanwhile, increasing SAC is better than that of decreasing to true value.

Conduction and radiation in a rectangular isotropic scattering medium with black surfaces by the RTNAM

The ray tracing-node analyzing method (RTNAM) has been successfully developed to solve 1-D coupled heat transfer in isotropic and anisotropic scattering media in the past, and in this paper it is further extended to solving the 2-D coupled heat transfer in a rectangular isotropic scattering medium. Using the control-volume method, the partial transient energy equation is discretized in implicit scheme. The effect of radiation on heat transfer is considered as a radiative source term (RST) in the discretized energy equation, and in combination with spectral band model, the RST is calculated using the radiative transfer coefficients (RTCs), which are deduced by the ray tracing method. The Patankar’s linearization method is used to linearize the RST and the opaque boundary condition, and the linearized equations are solved by the ADI method. Before solving the RTCs for isotropic scattering media, the RTCs without considering scattering must be solved at first. And then, the RTCs without considering scattering are normalized according to their integrality relationships. In addition, the correctness of the results obtained by the RTNAM is validated, and effects of scattering albedo and refractive index on transient temperature distribution are investigated.

Transient radiation and conduction heat transfer inside a plane-parallel participating gray medium with boundaries having different reflecting characteristics

A hybrid ray-tracing method is developed for the solution to the radiative transfer in a plane-parallel participating medium having one specular surface and another diffuse surface. By this method, radiative transfer coefficients (RTCs) for specular–diffuse (S–D) surfaces are deduced. The medium surfaces are considered to be semitransparent. The effects of convection–radiation parameter, conduction–radiation parameter and refractive index on transient coupled heat transfer are investigated. Results show that the temperature curves of the medium having S–D surfaces is higher than those of the medium having S–S surfaces (two specular surfaces); the total heat flux at steady state for the S–D surfaces is lower than that for the S–S surfaces.

Radiative heat transfer in a participating medium with specular–diffuse surfaces

The results obtained by ray-tracing method can be regarded as benchmarks for its good accuracy. However, up to now, this method can be only used to solve radiative transfer within medium confined between two specular surfaces or two diffuse surfaces. This article proposes a hybrid ray-tracing method to solve the radiative transfer inside a plane-parallel absorbing–emitting–scattering medium with one specular surface and another diffuse surface (S–D surfaces). By the hybrid ray-tracing method, radiative transfer coefficients (RTCs) for S–D surfaces are deduced. Both surfaces of the medium under consideration are considered to be semitransparent or opaque. This paper examines the effects of scattering albedo, opaque surface emissivity and anisotropically scattering on steady-state heat flux and transient temperature fields. From the results it is found that the effects of anisotropic scattering is more for a bigger optical thickness medium; and keeping other optical parameters unchanged, anisotropic scattering affects transient temperature distributions so much in a small refractive index medium.

Numerical simulation on antenna temperature field of complex structure satellite in solar simulator

A thermal network model is developed for studying the temperature variation of complicated structure satellite surfaces. The solar incident areas, the infrared and solar radiation transfer coefficients among surfaces are numerically simulated by means of Monte Carlo ray tracing (MCRT) method in model. The non-uniformity and the instability of solar radiation, which plays the important roles in simulating outer-space heat flux designation parameters by solar simulator, are studied for analysis variation of antenna temperature fields in detail. Results showed non-uniformity irradiation effects are greater than those of instability for this kind of geometry sheltering structure.

Numerical Method of the Ray Tracing-Node Analyzing Method for Solving 2-D Transient Coupled Heat Transfer in a Rectangular Semitransparent Medium

For the ray tracing-node analyzing method for solving 2-D transient coupled heat transfer, the transient differential energy equation is discretized using the fully implicit finite-difference method and the radiative source term is expressed by the radiative transfer coefficients (RTCs). The Patankar linearization method is used to linearize the radiative source term and the opaque boundary conditions, and then the opaque boundary conditions are dealt with the additional source term method (ASTM). The ADI method is applied to solve the nominal linearizing equations. This study shows that using ASTM to handle the opaque boundary conditions is necessary; otherwise, the solution diverges.

Transient coupled heat transfer in a rectangular medium with black surfaces

The main objective of this paper is to extend to two-dimensional (2-D) medium the ray tracing-node analyzing method, which has already been successfully used to solve one-dimensional (1-D) problem of coupled heat transfer in a semitransparent medium. For simplicity, an infinitely long rectangular semitransparent medium with four black opaque surfaces is chosen as our studying object. A control volume method in the implicit scheme is adopted for discretizing the partial transient energy equation. In combination with spectral band model, the radiative heat source term is calculated using the radiative transfer coefficients (RTCs), which are deduced by the ray tracing method. The Partankar's linearization method is used to linearize the radiative source term and the opaque boundary condition, and the linearized equations are solved by the ADI method. Effects of absorption coefficient, refractive index and conductivity on transient cooling process in the 2-D gray rectangular medium are investigated under the condition that the radiation and convection processes cool one side of the rectangular medium while heat the remaining three sides.

Relationship between the Kubelka-Munk scattering and radiative transfer coefficients

The relationship between the Kubelka-Munk (K-M) and the transport scattering coefficient is obtained through a semi-empirical approach. This approach gives the same result as that given by Gate [Appl. Opt.13, 236 (1974)] when the incident beam is diffuse. This result and those given by Star et al. [Phys. Med. Biol.33, 437 (1988)] and Brinkworth [Appl. Opt.11, 1434 (1972)] are compared with the exact solution of the radiative transfer equation over a large range of optical properties. It is found that the latter expressions, which include an absorption component, do not give accurate results over the range considered. Using the semi-empirical approach, the relationship between the K-M and the transport scattering coefficient is derived for the case where the incident light is collimated. It is shown that although the K-M equation is derived based on diffuse incident light, it can also represent very well the reflectance from a slab of infinite thickness when the incident light is collimated. However, in this case the relationship between the coefficients has to include a function that is dependent on the anisotropy factor. Analysis indicates that the K-M transform achieves the objective of obtaining a measure that gives the ratio of absorption to scattering effects for both diffuse and collimated incident beams over a large range of optical properties.

Ray-Tracing/Nodal-Analyzing Model for Transient Thermal Behavior of a Scattering Medium with a Variable Refractive Index

ABSTRACT Transient combined radiation-conduction inside a semitransparent scattering gray medium with a graded index is examined. By nodal analysis, the radiative source term of the energy equation is deduced through radiative transfer coefficients (RTCs), which are deduced through a multilayer model of radiative transfer, established by employing a ray-tracing method based on the zonal method. The basic idea is that a medium with a continually variable refractive index is discretized into certain number of isothermal sublayers with constant refractive index in each sublayer and the radiative transfer in a curve inside the graded index medium is regarded as that in a straight line within each sublayer. The present results accord very well with previous results. The results show that the multilayer model for radiative transfer to simulate the radiative transfer in a graded refractive index medium is reliable and correct. In addition, effects of convection boundary conditions, scattering albedo, opaque surface emission, and refractive index distribution on transient thermal behavior are also investigated for the graded index medium.

Effect of reflecting modes on combined heat transfer within an anisotropic scattering slab

Under various interface reflecting modes, different transient thermal responses will occur in the media. Combined radiative–conductive heat transfer is investigated within a participating, anisotropic scattering gray planar slab. The two interfaces of the slab are considered to be diffuse and semitransparent. Using the ray tracing method, an anisotropic scattering radiative transfer model for diffuse reflection at boundaries is set up, and with the help of direct radiative transfer coefficients, corresponding radiative transfer coefficients (RTCs) are deduced. RTCs are used to calculate the radiative source term in energy equation. Transient energy equation is solved by the full implicit control-volume method under the external radiative–convective boundary conditions. The influences of two reflecting modes including both specular reflection and diffuse reflection on transient temperature fields and steady heat flux are examined. According to numerical results obtained in this paper, it is found that there exits great difference in thermal behavior between slabs with diffuse interfaces and that with specular interfaces for slabs with big refractive index.

Ray tracing method for transient coupled heat transfer in an anisotropic scattering layer

A radiative transfer model for a linearly or nonlinearly anisotropic scattering medium is developed by the ray tracing method. Under specular reflection, the radiative transfer coefficients of absorbing and anisotropic scattering layer with opaque boundaries are deduced. Coupled radiative and conductive heat transfer is solved. The advantage of the method is that it only needs to disperse spatial position, but not solid angle. A comparison of the present results with the previous results shows that the radiative transfer coefficients of an anisotropic scattering slab are correct. The influence of optical thickness, surface emissivity, spectrum characteristics, albedo, and boundary conditions on the transient temperature and the heat flux distribution are analyzed. According to analyzed results of linear scattering and nonlinear scattering, it is found that the ratio of two-dimensionless heat fluxes with two different scattering phase functions is a monotone function of optical thickness. It can be used as a benchmark to verify the results.

Monte Carlo ray-tracing simulation for radiative heat transfer in turbulent fluctuating media under the optically thin fluctuation approximation

The Monte Carlo ray-tracing method (MCRT) based on the concept of radiation distribution factor is extended to solve radiative heat transfer problem in turbulent fluctuating media under the optically thin fluctuation approximation. A one-dimensional non-scattering turbulent fluctuating media is considered, in which the mean temperature and absorption coefficient distribution are assumed and the shape of probability density function is given. The distribution of the time-averaged volume radiation heat source is solved by MCRT and direct integration method. It is shown that the results of MCRT based on the concept of radiation distribution factor agree with these of integration solution very well, but results of MCRT based on the concept of radiative transfer coefficient do not agree with these of integration solution. The solution of time-averaged radiative transfer equation by the concept of radiative transfer coefficient should be treated with caution.

Refractive Index Effects on Heat Transfer in Multilayer Scattering Composite

By the use of the ray tracing method, in combination with Hottel and Sarofim's zonal method and spectral model, transient coupled radiative and conductive heat transfer in a multilayer absorbing, isotropically scattering composite with semitransparent and specular surfaces and interfaces is investigated. The specular reflectivities of all of the surfaces and interfaces are determined by Fresnel's reflective law and Snell's refractive law. For the ray tracing method, the complex total reflection problem of the multilayer composite is properly solved, and the radiative transfer coefficients (RTCs) of the multilayer composite are derived. The RTCs are used to calculate a radiative source term, and the transient energy equation is solved by the fully universal implicit discrete control volume method. Combined with extinction coefficient, conduction-radiation parameter, scattering albedo, layer thickness, and number of layers, the effects of refractive index on pure radiative and coupled radiative and conductive heat transfer are investigated

Sçattering characteristics effect on combined heat transfer through an anisotropic nongray media

Transient combined heat transfer by radiation and conduction is investigated within a participating nongray planar slab with one surface coated. Anisotropic scattering is included. By the modified ray tracing method, a radiative transfer model is developed and radiative transfer coefficients (RTCs) under specular reflection are deduced. Five spectral bands are used to simulate radiative spectral properties of translucent material. Radiative source term is calculated by RTCs. Transient energy equation is solved by the full implicit control-volume method under the external radiative and convective boundary conditions. The influences of scattering characteristics such as various scattering phase functions and scattering albedo values on the transient thermal behavior are examined. According to numerical results obtained in this paper, it is found that fully backward scattering, fully forward scattering and forward mixed scattering make a great difference in transient temperature distributions and steady-state total heat flux with isotropic scattering case as a reference.

Coupled radiation–conduction heat transfer in an anisotropically scattering slab with mixed boundaries

Ray tracing method combined with Hottel's zonal method is used to establish radiation transfer model in anisotropic scattering media. The transmission progress of radiation intensity in the absorbing, emitting and anisotropically scattering medium is divided into two sub-progresses: emitting–attenuating–reflecting progress and absorbing–scattering progress. For the medium with both surfaces being semitransparent and mirror-like, radiative transfer coefficients are developed. Energy equation of transient coupled radiation and conduction heat transfer is solved by the fully implicit control-volume method. In this paper, it needs only to disperse spatial location while spatial solid angle is integrated directly. On this basis, effects of conduction–radiation parameter, spectral refractive index and scattering phase functions etc., on the temperature field and radiative heat flux field within an anisotropic scattering medium are examined. The results show that: the linear part in linear or nonlinear scattering phase function can produce great difference of the temperature field and radiative heat flux field between anisotropic scattering medium and isotropic scattering medium.

Transient coupled heat transfer in a multi-layer composite with opaque specular surfaces and semitransparent specular interfaces

In this paper, one-dimensional transient coupled radiative and conductive heat transfer in a multi-layer absorbing and isotropic scattering composite is investigated. The composite is considered to be of opaque specular boundaries and semitransparent specular interfaces. In combination with ray tracing method, spectral band model and the Hottel and Sarofim's zonal method, the radiative transfer coefficients (RTCs) of the multi-layer composite are deduced. The RTCs are used to calculate the radiative heat source term in the transient energy control equation, which is solved by the fully implicit discrete control-volume method. The effects of refractive index and vacuum space on transient coupled heat transfer are analyzed. Except for refractive index, all the other parameters of each layer have been kept the same, and the total thickness also has been kept unchanged, then along the thickness of the composite when the decrement or the increment of refractive index decreases as layer number increases, the temperature profile becomes smoother and the steady heat flux increases.

Transient coupled heat transfer in multilayer composite with one specular boundary coated

By the ray tracing⧹node method, the transient coupled radiative and conductive heat transfer in absorbing, scattering multilayer composite is investigated with one surface of the composite being opaque and specular, and the others being semitransparent and specular. The effect of Fresnel’s reflective law and Snell’s refractive law on coupled heat transfer are analyzed. By using ray tracing method in combination with Hottel and Sarofim’s zonal method and spectral band model, the radiative intensity transfer model have been put forward. The difficulty for integration to solve radiative transfer coefficients (RTCs) is overcame by arranging critical angles according to their magnitudes. The RTCs are used to calculated radiative heat source term, and the transient energy equation is discretized by control volume method. The study shows that, for intensive scattering medium, if the refractive indexes are arranged decreasingly from the inner part of the composite to both side directions respectively, then, the total reflection phenomenon in the composite is advantageous for the scattered energy to be absorbed by the layer with the biggest refractive index, so at transient beginning a maximum temperature peak may appear in the layer with the biggest refractive index.

Emissive power of semitransparent spherical particle with nonuniform temperature

The ray tracing method and the zonal method is extended to study the emissive power of semitransparent spherical particle with nonuniform temperature. The particle emissive power is calculated by the radiative transfer coefficients. The effects of the related parameters on the particle emissive power and the errors resulted from omitting the nonuniformity of particle temperature are analyzed and discussed. The results show that omitting the nonuniformity of particle temperature will result in large errors of particle emissive power, and the errors increase with the nonuniformity of particle temperature. The particle emissive power based on the average temperature may deviate from its real value, and the size parameter and absorption index strongly affects the ratio of particle emissive power based on the average temperature and its real value.

Transient Coupled Heat Transfer in Three-Layer Composite with Opaque Specular Surfaces

A ray tracing/node analyzing method is applied to investigate one-dimensional transient coupled radiative and conductive heat transfer in a three-layer absorbing and isotropically scattering composite with opaque specular surfaces and semitransparent specular interfaces. The reflectivities of the semitransparent interfaces are angularly dependent and determined by Fresnel's reflective law and Snell's refractive law. The radiative transfer coefficients for calculating the radiative heat source term are deduced by the ray tracing method in combination with the zonal method. The transient energy equation is solved by the fully implicit control-volume method in combination with the spectral band model. The effects of surface emissivity, scattering albedo, refractive index and extinction coefficient on transient coupled heat transfer are investigated in detail under radiative and convective boundary conditions