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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.

Although most physical problems in fluid mechanics and heat transfer are governed by nonlinear differential equations, it is less common to be confronted with a “so – called” implicit differential equation, i.e. a differential equation where the highest order derivative cannot be isolated. The purpose of this paper is to derive and analyze an implicit differential equation that arises from a simple model for radiation dominated heat transfer based upon an unsteady lumped capacitance approach.

Here we discuss an implicit differential equation that arises from a simple model for radiation dominated heat transfer based upon an unsteady lumped capacitance approach. Due to the implicit nature of this problem, standard integration schemes, e.g. Runge‐Kutta, are not conveniently applied to this problem. Moreover, numerical solutions do not provide the insight afforded by an analytical solution.

A predictor predictor‐corrector scheme with secant iteration is presented which readily integrates differential equations where the derivative cannot be explicitly obtained. These solutions are compared to numerical integration of the equations and show good agreement.

The paper emphasizes that although large‐scale, multi‐dimensional time‐dependent heat transfer simulation tools are routinely available, there are instances where unsteady, engineering models such as the one discussed here are both adequate and appropriate.

A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate integro‐differential governing equations for a grey and non‐scattering medium with grey and diffuse walls are developed and solved for several model problems. We consider axisymmetric, cylindrical geometries with top and bottom boundaries of arbitrary convex shape. The method is accurate for media of any optical thickness and is capable of handling a wide array of axisymmetric geometries and boundary conditions. Several techniques are presented to reduce computational overhead, such as employing a Swartz‐Wendroff approximation and cut‐off criteria for evaluating radiation integrals. The method is successfully tested against several cases from the literature and is applied to some additional example problems to demonstrate its versatility. Solution of a free‐boundary, combined‐mode heat transfer problem representing the solidification of a semitransparent material, the Bridgman growth of an yttrium aluminium garnet (YAG) crystal, demonstrates the utility of this method for analysis of a complex materials processing system. The method is suitable for application to other research areas, such as the study of glass processing and the design of combustion furnace systems.

Our physical universe is 1.5×10¹⁰ years old. It began with the Big Bang. There is some debate about what happened in the first tenth of a second! The first 3×10⁵ years were radiation dominated. Since then it has been matter dominated. (This in accordance with the first law of thermodynamics which states that total mass-energy is conserved.) The universe has continuously expanded in space and in the future either this may continue, or expansion may stabilise at a fixed size or the universe may contract in the Big Crunch (depending on the spatial curvature). At a certain scale the universe is spatially isotropic and homogeneous. Its trajectory exhibits increasing entropy in accordance with the second law of thermodynamics. These statements are in accordance with certain models and empirical data: distant galaxies are receding from us at a velocity proportional to their distance; there is greater spatial uniformity at greater distances from us; there is uniform presence in space of radiation with a temperature of 2.7K; etc.

Personal life experience is not sufficient for an adequate environmental risk evaluation. People cannot understand environmental danger without having necessary information. Once established, however, environmental awareness has a direct influence on people's evaluations and, consequently, on their lifestyles (Sjoberg, 1996).

The paper aims to focus on modeling of combined mixed convection and volumetric radiation within a vertical channel using a hybrid thermal lattice Boltzmann method (LBM). The multiple relaxation time LBM (MRT-LBM) is used to compute the dynamical field. The thermal field is determined by a finite difference method (FDM), and the simple relaxation time-LBM (SRT-LBM) serves to calculate the radiative part. The geometry considered concerns a vertical channel defined by two diffuse and isothermal walls. The active fluid represents a gray gas participating in absorption, emission and isotropically scattering. The parametrical study conducted aims to highlight the effect of Richardson number (Ri), Planck number (Pl) and the optical thickness (τ) on dynamical and thermal fields. It is found that radiation affects greatly heat transfer.

MRT-LBM is used to compute the dynamical field. The thermal field is determined by FDM, and SRT-LBM serves to calculate the radiative part.

This study has shown the strong capability of this approach to simulate similar problems. The Planck number largely affects the streamlines and isotherms distribution. Also, it causes disappearance of reversal flow, undesirable in most industrial applications, for low Planck numbers. The optical thickness causes the disappearance of reversal flow, in the case in which it appears, for lower opacity. However, for higher opacity it leads to a recurrence of reversed flow.

The use of a new original method composed of MRT-LBM to solve the fluid velocity, FDM to handle the temperature equation and extended SRT-LBM to compute the radiative part of the energy equation.

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.

This paper seeks to review the literature on methods for solving the radiative transfer equation (RTE) and integrating the radiant energy quantities over the spectrum required to predict the flow, the flame and the thermal structures in chemically reacting and radiating combustion systems.

The focus is on methods that are fast and compatible with the numerical algorithms for solving the transport equations using the computational fluid dynamics techniques. In the methods discussed, the interaction of turbulence and radiation is ignored.

The overview is limited to four methods (differential approximation, discrete ordinates, discrete transfer, and finite volume) for predicting radiative transfer in multidimensional geometries that meet the desired requirements. Greater detail in the radiative transfer model is required to predict the local flame structure and transport quantities than the global (total) radiation heat transfer rate at the walls of the combustion chamber.

The RTE solution methods and integration of radiant energy quantities over the spectrum are assessed for combustion systems containing only the infra‐red radiating gases and gas particle mixtures. For strongly radiating (i.e. highly sooting) and turbulent flows the neglect of turbulence/radiation interaction may not be justified.

Methods of choice for solving the RTE and obtaining total radiant energy quantities for practical combustion devices are discussed.

The paper has identified relevant references that describe methods capable of accounting for radiative transfer to simulate processes arising in combustion systems.

This paper describes an approach for the automatic calculation of view factors between surfaces of arbitrary shape, when taking into account possible screening effects due to intermediate surfaces.

The specifically developed numerical code is based on the utilization of boundary elements to fit the surfaces of an algorithm solving the shadow effect and on a Monte Carlo method for the numerical integrations.

The code has been tested for a set of geometrical configurations. It was clearly shown that it obtains good results in terms of accuracy and computing time. Its accuracy increases when the mesh of radiative surfaces is finer.

The use of the code is limited to opaque surfaces separated by an isothermal semi‐transparent medium which can be absorbent but not diffusing of the thermal radiation.

The study of the radiative exchanges between opaque surfaces with shadow effects due to intermediate surfaces may have concrete practical applications by using this code. Indeed, the code has been used for an industrial application, in order to evaluate view factors inside an enclosure, in the framework of studies concerned with the thermal comfort inside cars.

The originality of this paper lies in taking into account the surfaces of complex geometries by using a boundary elements approximation, the algorithm solving the shadow effect, based on the convexity of the quadrilateral in 2D or the polyhedron in 3D.

This paper aims to present the analytical investigation on an unsteady magneto-convective rotation of an electrically conducting non-Newtonian Casson hybrid nanoliquid past a vertical porous plate. The effects of thermal radiation, heat source/sink and hydrodynamic slip phenomenon are also taken into account. Ethylene glycol (EG) is adopted as a base Casson fluid. The Casson fluid model is accounted for to describe the rheological characteristics of non-Newtonian fluid. EG with copper and alumina nanoparticles is envisaged as a non-Newtonian Casson hybrid nanoliquid. The copper-alumina-ethylene glycol hybrid nanoliquid is considered as the regenerative coolant.

The perturbation method is implemented to develop the analytical solution of the modeled equations. Acquired solutions are used to calculate the shear stresses and the rate of heat transfer in terms of amplitudes and phase angles. Numerical results are figured out and tabled to inspect the physical insights of various emerging parameters on the pertinent flow characteristics.

This exploration discloses that the velocity profiles are strongly diminished by the slip parameter. Centrifugal and Coriolis forces caused by the plate rotation are found to significantly change the entire flow regime. The supplementation of nanoparticles is to lessen the amplitude of the heat transfer rate. A comparative study is carried out to understand the improvement of heat transfer characteristics of Casson hybrid nanoliquid and Casson nanoliquid. However, the Casson hybrid nanoliquid exhibits a lower rate of heat transfer than the usual Casson nanoliquid.

This proposed model would be pertinent in oceanography, meteorology, atmospheric science, power engineering, power and propulsion generation, solar energy transformation, thermoelectric and sensing material processing, tumbler in polymer manufacturing, etc. Motivated by such practical implications, the proposed study has been unfolded.

The novelty of this paper is to examine the simultaneous effects of the magnetic field, Coriolis force, suction/injection, slip condition and thermal radiation on non-Newtonian Casson hybrid nanoliquid flow past an oscillating vertical plate subject to periodically heating in a rotating frame of reference. A numerical comparison is also made with the existing published results under some limiting cases and it is found that the results are in good agreement with them. An in-depth review of the literature and the author’s best understanding find that such aspects of the problem have so far remained unexplored.