Numerical simulation of radiative heat transfer from non-gray gases in three-dimensional enclosures

The discrete ordinates and the discrete transfer methods are applied to the numerical simulation of radiative heat transfer from non-gray gases in three-dimensional enclosures. Several gas radiative property models are used, namely the correlated k-distribution (CK), the spectral line-based weighted-sum-of-gray-gases (SLW) and the weighted-sum-of-gray-gases (WSGG) methods. The results are compared with recently published accurate calculations based on the statistical narrow band model. The WSGG model is computationally efficient, but often yields relatively large errors. It should be used only if moderate accuracy is sufficient. The SLW model is the best alternative regarding the compromise between accuracy and numerical efficiency. However, an optimization of the coefficients of the model is essential to reduce the computational requirements, especially in the case of gas mixtures. The CK model is the most accurate of the methods evaluated here, but too time consuming for engineering applications, although recent developments may partly overcome this shortcoming.     

An improved model to calculate radiative heat transfer in hot combustion gases

Radiative heat transfer plays an important role in the chemical reactions in the combustor. The widely used WSGG model proposed by Smith is established for normal pressure, which shows inevitable computational errors when dealing with radiative heat transfer problems at reduced or elevated pressures. In this paper, an improved global model is established to calculate the radiant energy exchanges between combustion gases and combustor chamber walls. Compared with the Smith model, the new model shows better performance in a wide range of pressure regions. The model accuracy is examined by computing the emissivity, radiative heat flux as well as the radiative source of H₂O–CO₂ gas mixtures at different pressure values. Finally, the radiative heat transfer inside a 3D TBCC(turbine-based combined cycle) engine exhaust system where strong gradients of pressure and temperature exist, is also addressed. The computational results show that the developed model provides approximate results at much less computational costs than the high-precision MSMGFSK-c8 model, which makes it competitive in complicated combustion systems.     

Effect of band or line shape on radiative transfer in a nongray two-dimensional medium

An exact formulation is presented for a nongray two-dimensional, finite, planar, absorbing-emitting medium in radiative equilibrium. The absorption coefficient consists of an array of equal intensity, nonoverlapping bands or lines. Rectangular, triangular, exponential, Doppler and Lorentz shapes are specifically considered. Exact expressions are obtained for a medium subjected to collimated and diffuse radiation. The integral equations are linearized by the narrow-band approximation. The solution for the cosine-varying, collimated, monochromatic radiation model is used to construct the solutions for other boundary conditions. The two-dimensional equations are reduced to one-dimensional equations by the method of separation of variables. Results for the diffuse case are presented for several spatial variations.     

Combined radiant and convective heat transfer to laminar steam flow between gray parallel plates with uniform heat flux

The non-linear integro-differential equations descrining combined radiation and convection heat transfer to non-gray non-isothermal steam in laminar flow between gray parallel plates are developed and solved numerically. The results are discussed and compared with a gray, linear, analytical solution and with available experimental data.     

A concept of equivalent absorption and emission coefficients for gray analysis of radiative heat transfer

Due to the non-gray of gas radiation, the total emissivity differs from the total absorptivity. Therefore, in gray analysis, the equivalent absorption coefficient is not equal to the equivalent emission coefficient. Based on this idea, in this paper, a concept of equivalent absorption coefficient and equivalent emission coefficients is presented for gray analysis of gas radiative heat transfer. The equivalent emission coefficients are calculated by Leckner's formula and the equivalent absorption coefficients are estimated by inverse analysis. A one-dimensional gas radiation is taken as an example to show the efficiency of this concept. The results show that the concept of equivalent absorption and emission coefficients is feasible. It is necessary to use both the equivalent absorption coefficient and the equivalent emission coefficient for gray analysis.     

Coupling heat conduction and radiative transfer

A method to compute combined heat conduction and radiative transfer in a semitransparent medium is proposed. The heat equation is solved by an implicit finite-difference scheme and the radiation is simulated using a ray-tracing method. Stability and convergence for the coupling of both methods is shown. The crucial point for ray-tracing as well as for discrete-ordinate methods is the selection of the transfer directions and their associated weights. Using a model problem different direction sets proposed in the literature are compared with respect to their accuracy and the computational effort.     

Many-body radiative heat transfer theory

In this Letter, an N-body theory for the radiative heat exchange in thermally nonequilibrated discrete systems of finite size objects is presented. We report strong exaltation effects of heat flux which can be explained only by taking into account the presence of many-body interactions. Our theory extends the standard Polder and van Hove stochastic formalism used to evaluate heat exchanges between two objects isolated from their environment to a collection of objects in mutual interaction. It gives a natural theoretical framework to investigate the photon heat transport properties of complex systems at the mesoscopic scale.     

Theoretical study of combined radiative conductive and convective heat transfer in semi-transparent porous medium in a spherical enclosure

A new method for the solution of the radiative transfer equation in spherical media based on a modified discrete ordinates method is extended to study radiative, conductive and convective heat transfer in a semi-transparent scattering porous medium. The set of differential equations is solved using the fourth-order Runge-Kutta method. Various results are obtained for the case of combined radiative and conductive heat transfer, as well as for the interaction of those modes with convection. The effects of some radiative properties of the medium on the heat transfer rate are examined.     

Assembly of full-spectrum k-distributions from a narrow-band database; effects of mixing gases, gases and nongray absorbing particles, and mixtures with nongray scatterers in nongray enclosures

Full-spectrum k-distributions provide great accuracy combined with outstanding numerical efficiency for the evaluation of radiative transfer in absorbing-emitting molecular gases, but they do have several shortcomings: (1) It is difficult to assemble k-distributions for gas mixtures from precalculated full-spectrum k-distributions of individual gas species (i.e., without calculating the mixture k-distribution directly from the HITRAN/HITEMP database), (2) it is impossible to assemble k-distributions for a gas mixed with nongray absorbing particles (such as soot) from gas-only full-spectrum k-distributions, and (3) like all global models, full-spectrum k-distributions cannot accommodate nongray scattering behavior and/or nongray wall reflectances. In the present paper we show how these restrictions can be relaxed by (1) assembling full-spectrum k-distributions for a gas mixture from a narrow-band k-distribution database created for individual gas species, (2) by assembling gas and nongray absorbing particle mixture full-spectrum k-distributions from the same narrow-band database, and finally (3) by showing how a group of part-spectrum k-distributions can be generated from the same database to accommodate nongray scattering and nongray walls.     

Impact of non-uniform heat sink/source and convective condition in radiative heat transfer to Oldroyd-B nanofluid: A revised proposed relation

Nanofluids are embryonic as auspicious thermo liquids for application of heat transfer which have been scrutinized precisely, in current eons. Thermo-physical properties of these liquids have noteworthy stimulus on their heat transfer features. The manifestation of dense nanoparticles in the base liquid ominously intensifies the effective liquid thermal conductivity and therefore heightens the features of heat transfer. The highest attention of this exertion is to investigate the features of nanoparticles mass flux conditions and non-uniform heat sink/source on magnetite Oldroyd-B nanofluid. Additionally, heat convective and thermal radiation mechanisms are considered. Homotopic approach has been established for the solution of non-linear structures. The upshots elucidate that the Brownian and thermophrosis nanoparticles exaggerate the temperature field, however analogous tendency is being noted for thermal radiation and non-uniform heat sink/source parameters. This exertion also investigated that the concentration of Oldroyd-B nanofluid decline for curvature parameter and augment for thermophrosis parameter. In addition, for the endorsement of up-to-date derived clarifications a comparison table of skin friction coefficient is organized in limiting circumstances.     

Near-field radiative heat transfer in mesoporous alumina

The thermal conductivity of mesoporous material has aroused the great interest of scholars due to its wide applications such as insulation,catalyst,etc.Mesoporous alumina substrate consists of uniformly distributed,unconnected cylindrical pores.Near-field radiative heat transfer cannot be ignored,when the diameters of the pores are less than the characteristic wavelength of thermal radiation.In this paper,near-field radiation across a cylindrical pore is simulated by employing the fluctuation dissipation theorem and Green function.Such factors as the diameter of the pore,and the temperature of the material are further analyzed.The research results show that the radiative heat transfer on a mesoscale is 2～4 orders higher than on a macroscale.The heat flux and equivalent thermal conductivity of radiation across a cylindrical pore decrease exponentially with pore diameter increasing,while increase with temperature increasing.The calculated equivalent thermal conductivity of radiation is further developed to modify the thermal conductivity of the mesoporous alumina.The combined thermal conductivity of the mesoporous alumina is obtained by using porosity weighted dilute medium and compared with the measurement.The combined thermal conductivity of mesoporous silica decreases gradually with pore diameter increasing,while increases smoothly with temperature increasing,which is in good agreement with the experimental data.The larger the porosity,the more significant the near-field effect is,which cannot be ignored.     

Simultaneous radiative and conductive heat transfer in non-gray media

Steady-state energy transfer through non-gray radiating and conducting media enclosed by black walls of unequal temperature is studied. A rectangular Milne-Eddington type relation is used to describe the frequency dependence of the absorption coefficient. Temperature distributions and total heat transfer results are presented for materials which absorb radiation (a) of low frequency, (b) of high frequency, (c) within a finite band width, and (d) of all frequencies (gray). The influence of optical thickness (τ₀) and conduction to a radiation interaction parameter (N) are examined and the results for non-gray materials are compared with those for a gray analysis. Exact results are compared with those determined by using the optically-thin and the optically-thick approximations, as well as with those evaluated for purely conductive and purely radiative transfer.     

Non-grey radiative heat transfer in the picket-fence approximation

The radiative heat transfer between parallel plates separated by an absorbing gas with a “picket-fence” absorption coefficient is treated by a variational technique. For the heat transfer, a simple rational algebraic expression is obtained and the variational results are found in excellent agreement with the numerically “exact” results reported recently by Reithet al.(⁸) An expression for the extrapolation distance is also deduced and the results are compared with the values reported earlier by Bond and Siewert.(⁵)     

Radiative properties of model gases for applications in radiative energy transfer

An approximate analysis of the radiative properties of gases is presented for use in problems of fluid mechanics involving radiative transfer of energy. The analytical expressions obtained are presented in a non-dimensional form which clarifies their meaning and gives insight into the numerical magnitudes of significant radiative properties.Results are presented for line and continuum spectral absorption coefficients as functions of frequency and temperature. The corresponding emission coefficients are integrated to obtain Planck mean absorption co-efficients. It is found, for example, that for monatomic gases in the temperature range considered, T < 30 000°K, the Planck mean for atomic lines always exceeds that for the continuum. Although the absorption coefficients for continuum radiation in this temperature range are greatest for frequencies above the ground state ionization frequency, the major contribution to the Planck mean absorption coefficient comes from frequencies below the ionization frequency.Comparison of the photon mean free paths with the particle mean free paths, shows that the Planck photon mfp is much longer than the particle mfp but that the photon mfp corresponding to the peak line absorption coefficient is much shorter than the particle mfp.     

Calculation of radiative heat transfer in argon arc plasmas

Radiation emission and absorption in arc plasmas are important energy transfer processes. Exact calculations, though possible in principle, are usually impossible in practice because of the need to treat a large number of spectral lines and also the continuum radiation in the whole spectrum range. Recently, we have used an approximate method of partial characteristics to evaluate the radiation intensities, radiation fluxes and the divergence of radiation fluxes for SF₆ arc plasma with cylindrical symmetry. In this paper, we have extended our calculations toargon arc plasmas for the plasma pressures of 0.1, 0.5 and 1.0 MPa. We have calculated the coefficients of absorption for Ar plasmas at temperatures from 300 to 35 000 K, and have used these coefficients to calculate the partial characteristics. Both the continuum and the line spectra have been included in calculations. We have taken into account the radiative photo-recombination and bremsstrahlung for the continuous spectrum, and over 500 spectral lines for the discrete spectra.The method of partial characteristics has been applied to three-dimensional calculations of radiative heat transfer — i.e. radiation intensity, radiation flux and its divergence — in simplified temperature profiles. Conclusions have been made concerning validity and utilization of the method of partial characteristics in general gas dynamics problems.     

Role of fluctuational electrodynamics in near-field radiative heat transfer

The objective of this paper is to discuss the role of fluctuational electrodynamics in the context of a generalized radiative heat transfer problem. Near-field effects, including the interference phenomenon and radiation tunneling, are important for applications to nanostructures. The classical theory of radiative transfer cannot be readily applied as the feature size approaches the dominant wavelength of radiative emission. At all length scales, however, propagation of radiative energy is properly represented by the electromagnetic wave approach, which requires the solution of the Maxwell equations. Fluctuational electrodynamics provides a model for thermal emission when solving a near-field radiation heat transfer problem, and the fluctuation-dissipation theorem provides the bridge between the strength of the fluctuations of the charges inside a body and its local temperature. This paper provides a complete and systematic derivation of the near-field radiative heat flux starting from the Maxwell equations. An illustrative example of near-field versus far-field radiation heat transfer is presented, and the length scale for transition from near- to far-field regime is discussed; the results show that this length scale can be as large as three times than predicted from Wien's law.     

Near-field radiative heat transfer between macroscopic planar surfaces

Near-field radiation allows heat to propagate across a small vacuum gap at rates several orders of magnitude above that of far-field, blackbody radiation. Although heat transfer via near-field effects has been discussed for many years, experimental verification of this theory has been very limited. We have measured the heat transfer between two macroscopic sapphire plates, finding an increase in agreement with expectations from theory. These experiments, conducted near 300?K, have measured the heat transfer as a function of separation over mm to μm and as a function of temperature differences between 2.5 and 30?K. The experiments demonstrate that evanescence can be put to work to transfer heat from an object without actually touching it.     

Adsorbate vibrational mode enhancement of radiative heat transfer

We show that radiative heat transfer between two solid surfaces at short separation may increase by many orders of magnitude when the surfaces are covered by adsorbates. In this case, the heat transfer is determined by resonant photon tunneling between adsorbate vibrational modes. We propose an experiment to check the theory.     

Evaluation method for radiative heat transfer in polydisperse water droplets

Simplifications of the model for nongray radiative heat transfer analysis in participating media comprised of polydisperse water droplets are presented. Databases of the radiative properties for a water droplet over a wide range of wavelengths and diameters are constructed using rigorous Mie theory. The accuracy of the radiative properties obtained from the database interpolation is validated by comparing them with those obtained from the Mie calculations. The radiative properties of polydisperse water droplets are compared with those of monodisperse water droplets with equivalent mean diameters. Nongray radiative heat transfer in the anisotropic scattering fog layer, including direct and diffuse solar irradiations and infrared sky flux, is analyzed using REM². The radiative heat fluxes within the fog layer containing polydisperse water droplets are compared with those in the layer containing monodisperse water droplets. Through numerical simulation of the radiative heat transfer, polydisperse water droplets can be approximated by using the Sauter diameter, a technique that can be useful in several research fields, such as engineering and atmospheric science. Although this approximation is valid in the case of pure radiative transfer problems, the Sauter diameter is reconfirmed to be the appropriate diameter for approximating problems in radiative heat transfer, although volume-length mean diameter shows better accordance in some cases. The CPU time for nongray radiative heat transfer analysis with a fog model is evaluated. It is proved that the CPU time is decreased by using the databases and the approximation method for polydisperse particulate media.