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H₂O, CO₂ and CO are three main species in combustion systems which have high volume fractions. In addition, soot has strong absorption in the infrared band. Thus, H₂O, CO₂, CO and soot may take important roles in radiative heat transfer. To provide calculations with high accuracy, all of the participating media should be considered non-gray media. Thus, the purpose of this paper is to study the effect of non-gray participating gases and soot on radiative heat transfer in an inhomogeneous and non-isothermal system.

To solve the radiative heat transfer, the fluid flow as well as the pressure, temperature and species distributions were first computed by FLUENT. The radiative properties of the participating media are calculated by the Statistical Narrow Band correlated K-distribution (SNBCK), which is based on the database of EM2C. The calculation of soot properties is based on the Mie scattering theory and Rayleigh theory. The radiative heat transfer is calculated by the discrete ordinate method (DOM).

Using SNBCK to calculate the radiative properties and DOM to calculate the radiative heat transfer, the influence of H₂O, CO₂, CO and soot on radiation heat flux to the wall in combustion system was studied. The results show that the global contribution of CO to the radiation heat flux on the wall in the kerosene furnace was about 2 per cent, but that it can reach up to 15 per cent in a solid fuel gasifier. The global contribution of soot to the radiation heat flux on the wall was 32 per cent. However, the scattering of soot has a tiny influence on radiation heat flux to the wall.

This is the first time H₂O, CO₂, CO and the scattering of soot were all considered simultaneously to study the radiation heat flux in combustion systems.

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.

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.

A detailed numerical study is conducted on the effect of surface radiation on laminar natural convection in a tall vertical cavity filled with air. The cavity is heated and cooled, through its two vertical walls, by a linear or uniform heat flux q(y) and by a constant cold temperature, respectively. The horizontal walls are considered adiabatic. The paper aims to discuss these issues.

The radiosity method is employed to calculate the net radiative heat exchanges between elementary surfaces, while the finite volume method is implemented to resolve the governing equations of the fluid flow.

For each heat flux q(y) (ascending, descending or uniform), the effect of the emissivity ε (0ε1) on the local, average and maximum temperatures of the heated wall is determined as a function of the average Rayleigh number Ra_m (103Ra_m 6×104) and the cavity aspect ratio A (10A80). The effect of the coupling on the flow structures, convective and radiative heat transfers is also presented and analyzed. Overall, it is shown that surface radiation significantly reduces the local and average temperatures of the heated wall and therefore reduces the convective heat transfer between the active walls.

The studied configuration is of practical interest in several areas where overheating must be avoided. For this purpose, a simple design tool is developed to estimate the mean and the maximum temperatures of the hot wall in different operating conditions (Ra_m, A et ε).

The originality lies in the study of the interaction between surface radiation and natural convection in tall cavities submitted to a non-uniform heat flux and a constant cold temperature on the active walls. Also, the development of an original simplified calculation procedure for the hot wall temperatures.

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.

The paper aims to present the advanced mathematical and numerical models of conjugated heat and mass transfer in a multi-layer protective clothing, human skin and muscle subjected to incident external radiative heat flux.

The garment was made of three layers of porous fabric separated by the air gaps, whereas in the tissue, four skin sublayers and muscle layer were distinguished. The mathematical model accounted for the coupled heat transfer by conduction and thermal radiation with the associated phase transition of the bound water in the fabric fibres and diffusion of the water vapour in the clothing layers and air gaps. The skin and muscle were modelled with two equation model which accounted for heat transfer in the tissue and arterial blood. Complex thermal and mass transfer conditions at the internal or external boundaries between the fabric layers, air gaps and skin were assumed. Special attention was paid to modelling of thermal radiation emitted by external heat source, for example, a fire, penetrating through the protective clothing and being absorbed by the skin and muscle.

Temporal and spatial variations of temperature in the protective garment, skin and muscle, as well as volume fractions of the water vapour and bound water in the clothing, were calculated for various intensity of incident radiative heat flux. The results of numerical simulation were used to estimate the risk of the first-, second- and third-degree burns.

Because of the small thickness of the considered system in comparison to its lateral dimensions, the presented model was limited to 1D heat and moisture transfer. The convective heat transfer through the clothing was neglected.

The model may be applied for design of the new protective clothing and for assessment of thermal performance of the various types of protective garments. Additionally, the proposed approach may be used in the medicine for estimation of degree of thermal destruction of the tissue during treatment of burns.

The novel advanced thermal model of the multi-layer protective garment, skin and muscle layer was developed. For the first time, non-grey optical properties and various optical phenomena at the internal or external boundaries between the fabric layers, air gaps and skin were accounted for during simulation of thermal interactions between the external heat source (e.g. a fire), protective clothing and human skin.

The effect of radiation on unsteady natural convection in a two‐dimensional participating medium between two horizontal concentric and vertically eccentric cylinders is investigated numerically. The equations of transfer are written by using a bicylindrical coordinates system, the stream function, and the vorticity. The finite volume radiation solution method and the control volume approach are used to discretize the coupled equations of radiative transfer, momentum, and energy. Original results are obtained for three eccentricities, Rayleigh number equal to 10⁴, 10⁵, and a wide range of radiation‐conduction parameter. The effects of optical thickness, wall emissivity, and scattering on flow intensity and heat transfer are discussed.

The purpose of this paper is to present and validate some improvements to the lattice Boltzmann method (LBM) for solving radiative heat transfer in a participating medium. Validation of the model is performed by investigating the effects of spatial and angular discretizations and extinction coefficient on the solution. The error analysis and the order of convergence of the scheme are also reported.

LB scheme is derived from the radiative transfer equation, where isotropic scattering and radiative equilibrium condition are assumed. Azimuthal angle is discretized according to the lattice velocities on the computational plane, while, concerning the polar angle, an additional component of the discrete velocity normal to the plane is introduced. Radiative LB scheme is used to solve a 2‐D square enclosure benchmark problem. In order to validate the model, results of LB scheme are compared with a reference solution obtained through a Richardson extrapolation of the results of a standard finite volume method.

The proposed improvements drastically increase the accuracy of the previous method. Radiative LB scheme is found to be (at most) first order accurate. Numerical results show that solution gets more accurate when spatial and azimuthal angle discretizations are improved, but a saturation threshold exists. With regard to polar angle, minimum error occurs when a particular subdivision is considered.

The paper provides simple but effective improvements to the recently proposed lattice Boltzmann method for solving radiative heat transfer in a participating medium.

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.

This paper aims to present the numerical models and experimental outcomes pertain to the performance of the parabolic dish concentrator system with a modified cavity-type receiver (hemispherical-shaped).

The numerical models were evolved based on two types of boundary conditions; isothermal receiver surface and non-isothermal receiver surface. For validation of the numerical models with experimental results, three statistical terms were used: mean of absolute deviation, R² and root mean square error.

The thermal efficiency of the receiver values obtained using the numerical model with a non-isothermal receiver surface found agreeing well with experimental results. The numerical model with non-isothermal surface boundary condition exhibited more accurate results as compared to that with isothermal surface boundary condition. The receiver heat loss analysis based on the experimental outcomes is also carried out to estimate the contributions of various modes of heat transfer. The losses by radiation, convection and conduction contribute about 27.47%, 70.89% and 1.83%, in the total receiver loss, respectively.

An empirical correlation based on experimental data is also presented to anticipate the effect of studied parameters on the receiver collection efficiency. The anticipations may help to adopt the technology for practical use.

The developed models would help to design and anticipating the performance of the dish concentrator system with a modified cavity receiver that may be used for applications e.g. power generation, water heating, air-conditioning, solar cooking, solar drying, energy storage, etc.

The originality of this manuscript comprising presenting a differential-mathematical analysis/modeling of hemispherical shaped modified cavity receiver with non-uniform surface temperature boundary condition. It can estimate the variation of temperature of heat transfer fluid (water) along with the receiver height, by taking into account the receiver cavity losses by means of radiation and convection modes. The model also considers the radiative heat exchange among the internal ring-surface elements of the cavity.