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This study aims to perform a comprehensive investigation to model the thermal characteristics of a coupled conduction-radiation heat transfer in a two-dimensional irregular enclosure including a triangular-shaped heat source.

For this purpose, a promising hybrid technique based on the concepts of blocked-off method, FVM and DOM is developed. The enclosure consists of several horizontal, vertical and oblique walls, and thermal conductivity within the enclosure varies directly with temperature and indirectly with position. To simplify the complex geometry, a promising mathematical model is introduced using blocked-off method. Emitting, absorbing and non-isotropic scattering gray are assumed as the main radiative characteristics of the steady medium.

DOM and FVM are, respectively, applied for solving radiative transfer equation (RTE) and the energy equation, which includes conduction, radiation and heat source terms. The temperature and heat flux distributions are calculated inside the enclosure. For validation, results are compared with previous data reported in the literature under the same conditions. Results and comparisons show that this approach is highly efficient and reliable for complex geometries with coupled conduction-radiation heat transfer. Finally, the effects of thermo-radiative parameters including surface emissivity, extinction coefficient, scattering albedo, asymmetry factor and conduction-radiation parameter on temperature and heat flux distributions are studied.

In this paper, a hybrid numerical method is used to analyze coupled conduction-radiation heat transfer in an irregular geometry. Varying thermal conductivity is included in this analysis. By applying the method, results obtained for temperature and heat flux distributions are presented and also validated by the data provided by several previous papers.

The solution of radiative heat transfer problems in participating media is often obtained using the standard discrete ordinates method (SDOM). This method produces anomalies caused by ray effects if radiative boundary conditions have discontinuities or abrupt changes. Ray effects may be mitigated using the modified discrete ordinates method (MDOM), which is based on superposition of the solutions obtained by considering separately radiation from the walls and radiation from the medium. The purpose of this paper is to study the role of ray effects in combined conduction‐radiation problems and investigate the superiority of the MDOM over SDOM.

The MDOM has been used to calculate radiative heat transfer in irregular geometries using body‐fitted coordinates. Here, the blocked‐off region concept, originally developed in computational fluid dynamics, is used along with the finite volume method and SDOM or MDOM to solve combined conduction‐radiation heat transport problems in irregular geometries. Enclosures with an absorbing, emitting and isotropically or anisotropically scattering medium are analyzed.

The results confirm the capability of the MDOM to minimize the anomalies due to ray effects in combined heat transfer problems, and demonstrate that MDOM is more computationally efficient than SDOM.

The paper demonstrates the application of MDOM to combined conduction‐radiation heat transfer problems in irregular geometries using blocked‐off method.

This paper aims to develop a numerical model to investigate coupled conduction radiation heat transfer in a multilayer semi-transparent polymeric foam.

The model uses a multi-phase approach in which the radiative transfer is determined by solving the radiative transfer equation explicitly in the whole medium incorporating an interface condition valid in the geometric optics rgime. This is executed by using a combination of ray splitting and a discrete curved ray tracing technique. Both partial photon reflection and total internal reflection at the interface are considered in the present investigation.

The directional distribution of intensity within the whole medium can be determined, which is used to obtain the detailed temperature profile inside the domain. The performance of the proposed methodology has been tested by simulating the modelled foam at ambient conditions. The results obtained from the simulations are in good agreement with the published results and shows that there is a global non-linearity in the temperature profile in problems where conduction to radiation parameter is small.

Specular nature of radiative transfer at the interface is accounted for in the present analysis. Instead of working with direction integrated quantities (as in the case of P1 approximation), each bundle of rays is treated separately within the whole medium. This model serves as a starting point for a detailed spatially three dimensional study of heat transfer in foams and the mathematical nature of the formulation is such that it may result in an implementation to three-dimensions.

Present study aims to extend the lattice Boltzmann method (LBM) to simulate radiation in geometries with curved boundaries, as the first step to simulate radiation in complex porous media. In recent years, researchers have increasingly explored the use of porous media to improve the heat transfer processes. The lattice Boltzmann method (LBM) is one of the most effective techniques for simulating heat transfer in such media. However, the application of the LBM to study radiation in complex geometries that contain curved boundaries, as found in many porous media, has been limited.

The numerical evaluation of the effect of the radiation-conduction parameter and extinction coefficient on temperature and incident radiation distributions demonstrates that the proposed LBM algorithm provides highly accurate results across all cases, compared to those found in the literature or those obtained using the finite volume method (FVM) with the discrete ordinates method (DOM) for radiative information.

For the case with a conduction-radiation parameter equal to 0.01, the maximum relative error is 1.9% in predicting temperature along vertical central line. The accuracy improves with an increase in the conduction-radiation parameter. Furthermore, the comparison between computational performances of two approaches reveals that the LBM-LBM approach performs significantly faster than the FVM-DOM solver.

The difficulty of radiative modeling in combined problems involving irregular boundaries has led to alternative approaches that generally increase the computational expense to obtain necessary radiative details. To address the limitations of existing methods, this study presents a new approach involving a coupled lattice Boltzmann and first-order blocked-off technique to efficiently model conductive-radiative heat transfer in complex geometries with participating media. This algorithm has been developed using the parallel lattice Boltzmann solver.

The effects of anisotropy and radiation cannot be considered negligible while investigating the stability of the fluid in convection. Hence, the purpose of this paper is to analyze how these effects could affect the system while considering a couple-stress dielectric fluid. Therefore, the study establishes the effect of thermal radiation in a couple-stress dielectric fluid with an anisotropic porous medium using Goody's approach (Goody, 1956).

To analyze the effect of radiation on the onset of convection, the Milne–Eddington approximation is employed to convert radiative heat flux to thermal heat flux. The equations are further developed to approximate for transparent and opaque medium. Stability of the quiescent state within the framework of linear theory is performed. The principle of exchange of stabilities is shown to be valid by means of single-term Galerkin method. Large values of conduction–radiation and absorptivity parameters are avoided as fluid is considered as liquid rather than gas.

The radiative heat transfer effect on a couple-stress dielectric fluid saturated anisotropic porous medium is examined in terms of Milne–Eddington approximation. The effect of couple-stress, dielectric, anisotropy and radiation parameters are analyzed graphically for both transparent and opaque medium. It is observed that the conduction–radiation parameter stabilizes the system; in addition, the critical Darcy–Rayleigh number also shows a stabilizing effect in the absence of couple-stress, dielectric and anisotropy parameters, for both transparent and opaque medium. Furthermore, the absorptivity parameter stabilizes the system in the transparent medium, whereas it exhibits a dual effect in the case of an opaque medium. It was also found that an increase in thermal and mechanical anisotropy parameters shows an increase in the cell size, whereas the increase in Darcy–Roberts number and conduction–radiation parameter decreases the cell size. The validity of principle of exchange of stability is performed and concluded that marginal stability is the preferred mode than oscillatory.

The effects of anisotropy and radiation on Rayleigh–Bénard convection by considering a couple-stress dielectric fluid has been analyzed for the first time.

To provide a finite volume code, based on Cartesian coordinates, for studying combined conductive and radiative heat transfer in three‐dimensional irregular geometries.

In the present study, a three‐dimensional blocked‐off‐region procedure was presented and implemented in a numerical code based on the finite volume method to model combined conductive and radiative heat transfer in complex geometries. This formulation was developed and tested in three‐dimensional complex enclosures with diffuse reflective surfaces and containing gray absorbing‐emitting and isotropically scattering medium. This approach was applied to analyze the effect of the main of thermoradiative parameters on the temperature and flux values for three‐dimensional L‐shaped enclosure.

The proposed isotropic model leads to satisfactory solutions with comparison to reference data, which entitles us to extend it to anisotropic diffusion cases or to non‐gray media. The blocked‐off‐region procedure traits both straight and curvilinear boundaries. For curved or inclined boundaries, a fine or a non‐uniform grid is needed.

This paper offers a simple Cartesian practical technique to study the combined conductive and radiative heat transfer in three‐dimensional complex enclosures with both straight and curvilinear boundaries.

The purpose of this paper is to focus on thermal characteristics behavior of forced convection flow in a duct over forward facing step (FFS), in which all of the heat transfer mechanisms, including convection, conduction and radiation, take place simultaneously in the fluid flow.

The fluid is treated as a gray, absorbing, emitting and scattering medium. The Navier‐Stokes and energy equations are solved numerically by computational fluid dynamics (CFD) techniques to obtain the velocity and temperature fields. Discretized forms of these equations are obtained by the finite volume method and solved using the SIMPLE algorithm. Since the gas is considered as a radiating medium, all of the convection, conduction and radiation heat transfer take place simultaneously in the gas flow. For computation of the radiative term in the gas energy equation, the radiative transfer equation (RTE) is solved numerically by the discrete ordinate method (DOM) to find the radiative heat flux distribution inside the radiating medium. By this numerical approach, the velocity, pressure and temperature fields are calculated.

The effect of wall emissivity, optical thickness, albedo coefficient and the radiation‐conduction parameter on heat transfer behavior of the system are also investigated. The numerical results for two cases of convection‐conduction and conduction‐radiation problems are compared with the available data published in open literature and good agreement was obtained.

This is the first time in which flow over FFS in a duct, considering all heat transfer mechanisms including conduction, convection and radiation, is solved numerically.

In many industrial applications, convection radiation and conduction participate simultaneously to the heat transfers. A numerical approach able to cope with such problems has been developed. The code SYRTHES is tackling conduction and radiation (limited to non participating medium). Radiation is solved by a radiosity approach, and conduction by a finite element method. Accurate and efficient algorithms based on a mixing of analytical/numerical integration, and ray tracing techniques are used to compute the view factors. The fluid part is solved by CFD codes like ESTET (Finite volumes) or N3S (Finite elements). SYRTHES relies on an explicit numerical scheme to couple all the phenomena. No stability problems have been encountered. To provide further flexibility, the three phenomena are solved on three independent grids. All data transfers being automatically taken care of by SYRTHES. Illustrating applications are shown.

The purpose of this paper is to consider heat and mass transfer by natural convection from a vertical cylinder in porous media for a temperature‐dependent fluid viscosity in the presence of radiation and chemical reaction effects.

The governing equations are transformed into non‐similar differential equations and then solved numerically by an efficient finite‐difference method.

It is found that there are significant effects on the heat and mass transfer characteristics of the problem due to the variation of viscosity and radiation and chemical reaction effects.

The paper combines the effects of radiation, chemical reaction, non‐Darcy porous media effects along with the variation of viscosity with temperature.

The purpose of this paper is to present a computationally efficient model to solve combined conduction/radiation heat transfer problems in absorbing, emitting, non‐scattering, non‐gray materials.

The model is formulated for steady‐state condition and based on an iterative approach where the medium is discretized into finite strips and the extinction spectrum is divided into finite bands to consider the extinction coefficient variation with the wavelength.

Temperature fields and heat flux distributions are presented to demonstrate the capability of the formulation. It is shown that the model is quite accurate and efficient even for the cases of pure radiation. Differently from other models, the number of iterations required by the model for convergence is very low, even in the cases dominated by radiation.

The model has great potential to contribute with the evaluation and design of materials for thermal insulation, where radiation heat transfer can be the dominant mechanism, such as aerogel materials which are recognized as the solids with the lowest thermal conductivity and are intended to be used in building and construction, aerospace, transportation and other applications.