Radiative Heat Transfer Equation Research Articles

Simulation of Effect a Variable Height of Porous Absorber on Ventilation Solar Chimney Performance

The improvement in solar chimneys' thermal performance and thermal behavior that can be achieved by adding metal foam has been tested in computational work. The flow and heat transfer governing equations for solar chimney models were solved using computational fluid dynamics (CFD). It was solved using the control volume numerical method in ANSYS FLUENT 14.5. It is used to construct a finite volume modeling technique for solving the governing equations and the radiation heat transfer equations. With standard flat absorber plates, the results showed that heat transmission was increased by the inclusion of metal foam (10 PPI), leading to an increase in air velocity at the solar chimney of around 13.3%. The highest average air velocity with 10 PPI drops by 54.4% as the height of the absorber plate changes from 5 cm to 25 cm respectively.

NUMERICAL AND EXPERIMENTAL INVESTIGATION OF SEMICIRCULAR SOLAR UPDRAFT TOWER SYSTEM EMPLOYING POROUS COPPER METAL FOAM

The numerical and experimental study was carried out under Iraqi weather conditions to verify the improvement of the performance of the solar updraft tower system SUTS by introducing porous metal foam as a heat-absorbent plate. a semicircular basin of the solar collector was divided into two equal identical quarters. A porous foam material was fixed on one of the basins while the other basin was fixed on a traditional copper plate. The positions of the metal foam absorber plate are changed with two inclination angles (0֯ and 18֯) and the optimum position is achieved when it gives the highest thermal performance. A finite volume modeling technique is used to solve the governing equations and radiation heat transfer equations by using ANSYS Fluent. The experimental part was conducted in Baghdad / Iraq at latitude 33.3°. The presence of the metal foam absorber plate caused a significant decrease in the average temperatures of the heat-absorbent plate. The maximum airflow temperature was recorded with an inclined angle of 18◦. The metal foam as a heat-absorbent plate enhanced the efficiency and the output power of the SUTS to about 51.9% and 47.2% respectively compared to the traditional plate.

Affect of the Scattering Asymmetry by Structural Element of Thermal- or Environmental-Barrier Ceramics on Subsurface Radiant Overheating

The problem of the formation and estimation of a thermoradiant and temperature field in ceramics Thermal- Environmental-Barrier Coatings (TBC/EBC) has been considered with complex heat transfer but under the influence of the penetrating intense radiant component. The authors proposed to analyze not only TBC but also EBC from the point of view of the optics of semitransparent scattering and absorbing media in the range of ~0.4–4 μm of external radiant action. This paradigm allows us to continue the study of ceramic fibers embedded in ceramic matrix CMCs (C/C, C/SiC, SiC/SiC) as a traditional class of opaque materials. However, at the same time, mullites, Al2O3/Al2O3 have been reviewed as a class of semitransparent elements for designing CMCs. The relevance of studying the effect of oriented fibers on the formation of thermoradiation and temperature fields in a semitransparent material was noted. Modeling the scattering asymmetry coefficient influence (scattering phase function) on the generation of the subsurface thermal radiation source was carried out. The methodology for calculating the thermoradiative field in a semitransparent medium (with relative absorption, scattering indexes, and scattering asymmetry coefficient) was used under a one-dimensional two-flux model as the first approximation for solving the radiative heat transfer equation. Calculations of temperature profiles in opaque and semitransparent ceramics were presented under heat load typical for the combustion chambers operating regime of diesel and gas turbine engines.

Czochralski (CZ) process modification with cooling tube in the response to market Global silicon shortage

Recently, the silicon wafer producers, affected by Covid-19 and USA-China competition, looks for new production processes to increase the production. On the other hand, the common parts of CZ puller such as heater, crucible and thermal shield are optimized over time and now the common CZ process is reached to limitation for further improvement. Here, we propose a modified CZ method by adding a cooling tube into the growth zone. The new proposed Cz method is applied to the 8″ crystal growth process. A fully 3D transition model including energy equation, Navier–Stokes equation, surface-to-surface radiation heat transfer, moving mesh and thermal stress equations is implemented. The simulation is performed for both original and new CZ method. It was proved that the new CZ method increases the pulling speed up to 25 %. To ensure about the crystal quality, the thermal stress is compared between original and new proposed CZ method. Although it was found that the thermal stress increases about twice but still the maximum von Mises stress never exceeds the critical value 25 MPa. Additionally, the power consumption is also found to enhance maximum 2 kW under new conditions. To evaluate the model the interface and heater power for the original CZ puller is compared with industrial CZ process and it shows acceptable accuracy.

Comparison of Hybrid DDAD/St and DDAD-TVDR-Schemes for Solving the 2D Radiative Heat Transfer Equation

Comparison of Hybrid DDAD/St and DDAD-TVDR-Schemes for Solving the 2D Radiative Heat Transfer Equation

Analysis of radiative heat transfer in two-dimensional irregular geometries by developed immersed boundary–lattice Boltzmann method

The Immersed Boundary–lattice Boltzmann method (IB-LBM) is developed to analyze radiative heat transfer in two-dimensional (2D) irregular geometries. Lattice Boltzmann method (LBM) has been adopted to discretize the radiative heat transfer equation in an absorbing and emitting media, and the immersed boundary method (IBM) is used to model the boundaries of irregular geometries. Due to the mismatch between boundary and computational nodes in the Immersed Boundary method, a radiative density term based on the difference of radiation intensity is added to the lattice Boltzmann equation to satisfy the boundary condition. Radiative heat flux distribution is obtained for several irregular geometries which are maintained at an isothermal media or radiative equilibrium condition in the enclosure. The results are successfully validated by comparing the results obtained from other methods of irregular geometries analysis, such as the blocked-off domain, embedded boundary, and body-fitted grid method. According to the obtained results, their accuracy, and numerical cost, the combined IB-LBM benefits from the unique and worthy advantages of both IBM and LBM in solving the complicated analysis of 2D radiative heat transfer problems. Compared to the traditional methods used for the radiative analysis of irregular geometries, the immersed boundary method can solve the complexities of modeling curved boundaries effortlessly. It should be pointed that for optically thin media, the proposed model shows poor performance.

Numerical Study of Combined Surface Radiation and Natural Convection in Vertical Conical Annular Enclosure

The present study investigates the combined free convection and surface radiation in a conical annular cylinder filled with air (Pr=0.71). The steady-state continuity, Navier–Stokes and energy equations were carried out by the finite volume method, and the Discrete Ordinates Method (DOM) was used to solve the radiative heat transfer equation (RTE). The boundary conditions are such that the inner and the outer radius of cone are maintained at hot (Th) and cold (Tc) isothermal temperature. The horizontal upper and lower walls are assumed to be isolated. Concerning the radiation exchange, we consider that the fluid (air) is transparent, so only the solid surfaces contribute to the radiation exchange and assumed to be diffuse-gray. The computations are performed for Rayleigh number (Ra) in the range 103≤Ra≤106 , the surface emissivity (ε) 0≤ε≤1 and the cone angle () 63o, 76o, 80o and 84o. The key parameters for this analysis are considered as Rayleigh number (Ra), surface emissivity (ε) and the cone angle (). Results are presented in terms of isotherms, streamlines and the average Nusselt numbers.

The Role and Effects of Thermal Radiation on the Non-equilibrium Heat Transfer in a Porous Filled Enclosure

In this paper, the temperature differential between the solid and liquid phases in considering of combined conduction-convection-radiation heat transfer in porous media is investigated. Simultaneous solution of the solid and fluid energy equations encompasses local thermal nonequilibrium, with volumetric radiative heat flux needed in the solid-phase energy equation. The two energy equations together with the radiative heat transfer equation are simultaneously solved using the Chebyshev spectral method. The influences of the Planck numbers, the optical thicknesses, the scattering albedos, and the emissivities of the bounding walls on the thermal behavior are investigated. The results show that: (1) When Pl increases above 20, the effect of radiation on the flow and thermal field can be ignored. (2) Changing ⌖L has a significant effect on the solid phase temperature while, the effect is little on the fluid phase temperature. (3) For ω = 1.0, the distribution of θS − θf seems to be centrally symmetric. (4) θS − θf are always positive except for εW = 1.0.

Computing Method for Designing a Thermostat for Laboratory Tests of Infrared Optoelectronic Systems

A model of a thermal vacuum system (thermostat) for regulation and stabilization of temperature of the primary mirror of a cooled optical collimator for carrying out tests of optoelectronic equipment operating in the infrared region is designed. An original method for solving the system of nonlinear equations of radiative heat transfer in a thermostat is developed, and the uniformity of the temperature distribution over the primary mirror surface is analyzed.

Inverse design of an irregular-shaped radiant furnace using neural network and a modified hybrid optimization algorithm

In this study, the inverse solution technique is applied to design a three-dimensional heating furnace where radiation is the dominant part of heat transfer. The heat transfer mechanism is fully radiative and the furnace medium is non-gray with a mixture of 71.2% N2, 17.7% CO2, and 11.1% H2O. The design parameters include the temperature and location of the two heaters as well as the location of the design body. For the purpose of estimation of the design parameters to achieve a desired uniform heat flux at the design body, the inverse problem is considered as an optimization problem. The discrete ordinate method (DOM) is used to solve the radiation heat transfer equation (RTE) and non-gray calculations are performed by the spectral line based on the weighted-sum-of-gray-gases (WSGG) model. Additionally, the updated coefficients of the high-temperature spectral databases (HITEMP2010) are applied for non-gray gases. This study employs a modified hybrid method based on the artificial neural network (ANN) and genetic algorithm (GA) coupled with sequential quadratic programming (SQP) to optimize design parameters. In the present work, the results of three optimization algorithms including GA alone, ordinary GA-SQP and a modified form of GA-SQP are compared to find the best method to optimize the furnace problem. The final optimization results demonstrate a negligible difference between the optimized and the desired heat flux which is less than one percent. The consequences prove that the modified form of the GA-SQP algorithm (present work) is faster than others.

Неоднородная краевая задача радиационного теплообмена для многокомпонентной среды

An analysis of the solvability of an inhomogeneous boundary value problem for the equations of radiative heat transfer with the Fresnel conjugation conditions is presented. The nonlocal unique solvability of the boundary value problem is proved.

Numerical Solution of the 2D Radiative Heat Transfer Equation Using SPH Method

Numerical Solution of the 2D Radiative Heat Transfer Equation Using SPH Method

Full-scale 3D-modelling of the radiative heat transfer in rotary kilns with a present bed material

This work discusses the development and use of a detailed 3D radiative heat transfer model of a rotary kiln with a present bed material, used for iron ore pelletizing. A discrete ordinates method is used to solve the radiative heat transfer equation with radiative properties calculated using a weighted-sum-of-grey-gases (WSGG) model for gases and Mie and Rayleigh theory for particles including fuel, ash and soot. Measurement data gathered from a pilot-scale test furnace, comprising temperature, gas composition and particle concentration, is used in combination with temperature data and operation parameters gathered from a conventional rotary kiln to model a full-scale rotary kiln with a present bed material. The modelled cases have a thermal input of about 37 MWth and in addition to radiative heat transfer, conductive heat transfer within, as well as between, the bed and wall material are included in the model along with convective heat transfer from the gas and heat release from exothermic reactions in the bed. The model also considers the rotational wall and includes a simplified mixing model of the bed material as well as heat losses from the outside wall of the rotary kiln due to radiation and convection. For two different flames, one coal and one oil flame, surface temperatures are calculated on the inside and outside of the rotary kiln and compared to measurements. The model appears to predict the inner wall and bed surface temperatures well with errors less than 11%. The total heat transfer to the present bed material was also studied revealing that more than 80% originated from the radiative heat transfer within the furnace.

Analysis and evaluations of four models of thermal radiation for densely packed granular systems

Thermal radiation is an important part of heat transfer in granular systems, such as the packed pebble bed of high-temperature gas-cooled reactor (HTGR), bubbling fluidized bed, and other packed granular beds. In this paper, four models of multiple-body radiation within the packed granular bed were proposed and discussed in full integral scales, i.e. black radiation model, uniform radiation model, local radiation model and particle scale radiation model. For particle radiation with black surfaces, the black radiation model was proven to be valid strictly and it agreed with existing correlations and models. The radiative flux in the packed bed increased significantly with the particle emissivity. However, the existed Asakuma radiation model, two-flux model and the newly proposed local radiation model were almost independent of the particle emissivity since the uniform assumption was inappropriate for the gray radiation in the packed bed. The effect of emissivity was handled correctly in the local radiation model without the uniform assumption. Since the computation cost of local radiation model in large-scale granular systems was huge and not applicable in the CFD-DEM simulation, the particle scale radiation model was developed in this study to predict the radiation flux in discrete element method (DEM). It was shown that the effect of particle emissivity was a separable term in the radiative heat transfer equation. The particle scale radiation model provided a good approximation of the local radiation model and enabled efficient prediction of radiative heat transfer in a densely packed bed.

On Radiative Transfer and Gray Body Parameter for Partially Transparent Media

We obtained a solution to radiative heat transfer equations, which describes a multi-layer gray semi-transparent medium in terms of an opaque body. It is shown that the thermal disturbance between the layers of a medium qualitatively changes its optical properties. We introduced a gray body parameter, which allowed us to describe multilayer gray semi-transparent media with low thermal conductivity. We propose a method for calculating heat transfer by thermal radiation in a gray semi-transparent medium and present the results of radiative heat transfer calculations for screen-vacuum and powder insulation materials as examples of such media.

Effect of Surface Radiation on Free Convection in Vertical Cylinders Partially Annular

The coupled of free convection with surface radiation in an annular region of two concentric vertical cylinders filled with air has been numerically investigated. The steady-state continuity, Navier–Stokes and energy equations were carried out by the finite volume method, and the Discrete Ordinates Method (DOM) was used to solve the radiative heat transfer equation (RTE). The computations have been performed for 103 ≤Ra≤ 106, with the emissivity coefficient of all the walls varying between 0 and 1. The influence of the both, Rayleigh numbers and emissivity coefficient of the wall for fixed height ratio X=0.5 on natural convection and radiation heat transfer in enclosure have been solved. The result shows that surface radiation significantly altered the temperature distribution and the flow patterns, especially at higher Rayleigh numbers. The average Nusselt number has also been discussed for different emissivity through the enclosure.

Three-dimensional combined radiation-magnetoconvection of low electrically conductive dielectric oxide melt

PurposeThe purpose of this paper is to investigate the coupled effect of magnetic field and radiation on convective heat transfer of low electrically conductive dielectric oxide melt.Design/methodology/approachThe 3D Navier–Stokes equations are formulated using the vector potential-vorticity formulation and solved using the finite volume method (FVM). The radiative heat transfer equation is discretized using the FTnFVM method. A code was written using FORTRAN language.FindingsThe obtained numerical results are focused on the effect of the different parameters on the heat transfer and the flow structure with a special interest on the 3D transvers flow. It is found that the flow is developing in inner spirals and the magnetic field intensifies this 3D character. The radiation acts mainly at the core of the enclosure and causes the apparition of the merging phenomenon near the front and back walls.Originality/valueThe effect of magnetic field on convective heat transfer of highly electrically conductive fluids has been intensively studied. Reciprocally, the case of a fluid with low electrical conductivity is not so much investigated, especially when it is coupled with the effect of radiation. These two effects are studied in this paper for the case of a low-conductive LiNbO3 oxide melt.

Stability of Stationary Solutions of the Radiative Heat Transfer Equations

A model of complex heat transfer, including the $${{P}_{1}}$$ -approximation for the radiative transfer equation, is considered. The asymptotic stability of the steady states without requiring the smallness of the initial perturbations is proven.

Stability of stationary solutions of radiative heat transfer equations

Stability of stationary solutions of radiative heat transfer equations

Investigation of transient conduction–radiation heat transfer in a square cavity using combination of LBM and FVM

In this paper, the effect of surface radiation in a square cavity containing an absorbing, emitting and scattering medium with four heated boundaries is investigated, numerically. Lattice Boltzmann method (LBM) is used to solve the energy equation of a transient conduction–radiation heat transfer problem and the radiative heat transfer equation is solved using finite-volume method (FVM). In this work, two different heat flux boundary conditions are considered for the east wall: a uniform and a sinusoidally varying heat flux profile. The results show that as the value of conduction–radiation decreases, the dimensionless temperature in the medium increases. Also, it is clarified that, for an arbitrary value of the conduction–radiation parameter, the temperature decreases with decreasing scattering albedo. It is observed that when the boundaries reflect more, a higher temperature is achieved in the medium and on boundaries.