Heat Transfer Calculations Research Articles

Asymmetric Heat Transfer in Aircraft Electrothermal Anti-Icing

Aircraft icing is an important cause of air disasters, and electrothermal anti-icing is a common protection method. In this work, the influence of icing meteorological conditions on the anti-icing was studied through an icing wind tunnel experiment on the fairing. Based on the finite volume method, a transient heat transfer calculation method for electrothermal anti-icing was proposed. The calculated results were compared with the experimental results, and the influence of heating mode and structure layout on the anti-icing effect was analyzed. The results show that the calculated results are in good agreement with the experimental results, and the heat transfer of the anti-icing structure shows obvious asymmetry. First, during heating, the temperature gradient of the structural profile is large, the high temperature is concentrated in the heating layer, and the temperature distribution of the heating layer is relatively uniform. During cooling, the temperature distribution of the structural profile is more uniform, the high temperature is mainly concentrated in the back conduction layer, and the temperature of the outer wall increases first and then decreases from the center to the surroundings. Second, when the spray is turned on, the temperature of the outer wall is significantly reduced, but the temperature of the heating layer hardly changes. Third, the uniform heating mode can simultaneously raise the temperature of the outer wall and reduce the temperature of heating layer. Fourth, while the front conduction layer can significantly affect the temperature of the heating layer and the outer wall, the effect of the back conduction layer is small. However, the back one can be used to control the structural temperature more finely.

A Novel Optimization Strategy for Reducing the Initial Error of a Quasi-Steady Algorithm for Conjugate Heat Transfer

The present study proposes a novel optimization strategy (NOS) for quasi-steady algorithms to optimize the initial error in the fast calculation of conjugate heat transfer (CHT) simulations. In this approach, the change in Nusselt number at the fluid–solid coupling interface is dynamically monitored, and the update of the flow field is turned off according to a given Nusselt variation standard to speed up the solution of the transient temperature field. The NOS has been applied to problems of convective heat transfer in solid parts with internal heat sources. The feasibility of NOS is first verified by using an undisturbed boundary example, and the results show that the optimization strategy reduces the initial error by 92.3% compared with the quasi-steady algorithm, and the calculation time is reduced by 50% compared with the traditional coupling algorithm. The NOS is then combined with the quasi-steady algorithm, and boundary transient disturbances are added to the case. The results indicate that the computational time for NOS and the quasi-steady algorithm is 2.6 and 2.9 times greater than that of traditional algorithms. Nevertheless, NOS significantly optimizes the relative error of the quasi-steady algorithm by 97.3% during the initial computation phase.

Mismatch problem of the model and topology of oil pumping facilities

The mismatch of the model and the topology of real objects is important in modeling technological processes, which is the purpose of this paper. The problem is considered when modeling hot oil pumping in the "Kasymov–Bolshoy Chagan" oil pipeline. In this problem, the topology of objects consists of the linear part of the pipeline and technological equipment (pumps and heating furnaces) of the stations. The accuracy of the simulation results is determined by the calculations of pressure and temperature in the oil pipeline. The pressure in the pipeline is created by pumps at the stations and is determined by the dependence of the pressure and efficiency of the pump on the oil flow rate. These characteristics change depending on the service life of the pump. The identification of the actual dependences of the pressure and efficiency of the pump on the oil flow rate was carried out by the regression analysis of experimental data. The pressure in the linear part is determined by the hydraulic resistance of the pipeline. The actual dependence of the hydraulic resistance coefficient on the Reynolds number and wall roughness was obtained by regression analysis of experimental data. The temperature in the oil pipeline is created at the stations by heating furnaces. The identification of the actual characteristics of the heating furnace was also found by regression analysis of the experimental data. The temperature distribution in the linear part is determined by the heat transfer of oil with the surrounding environment. An undefined parameter for calculating heat transfer is the soil thermal conductivity, which depends on the type of rock and the degree of soil moisture. The soil thermal conductivity is determined in such a way that at a given oil flow rate, oil temperatures at the beginning of the section and soil at the section, the calculated oil temperature at the end of the section has the smallest discrepancy with the actual one. Thus, the determination of the actual dependencies of the objects makes it possible to increase the accuracy of the results of hot pumping modeling and eliminates the mismatches of the model and the topology of the objects.

Energy saving analysis and thermal performance evaluation of a hydrogen-enriched natural gas-fired condensing boiler

Hydrogen-enriched natural gas (HENG) has attracted widespread attention due to its lower pollutant emissions and industrial decarbonization in the past decades. HENG combustion boosts the water content in the flue gas, which is highly favorable for condensing boilers to recover additional latent heat. The energy saving and thermal performance of a condensing boiler burning HENG were evaluated at a constant heat load of 2.8 MW in this study. The variations in combustion products and boiler efficiency were investigated based on the material balance and energy conservation. The heat transfer calculations were employed to evaluate the thermal performance of boiler heating surfaces. The energy recovery performance of the condenser was assessed via a thermal design method. Results show that H2 enrichment enhances the radiation intensity of the flame due to the incremental triatomic gases with higher emissivity in the furnace. The heat absorption ratio increases with H2 enrichment in the radiative heating surface, while it shows a reverse tendency in the convective heating surface. The condensing boiler efficiency based on lower heating value increases from 101.83% to 110.60%, the total heat transfer rate of the condenser increases from 2.77 × 105 W to 4.61 × 105 W, and the total area required decreases from 46.45 m2 to 42.16 m2, as the H2 enriches from 0 to 100% under the exhaust flue gas temperature of 318 K. Although the amount of recoverable heat in the exhaust flue gas increases considerably after H2 blending, the original condenser with natural gas as the designed fuel could meet the requirements of the heat recovery for HENG without increasing the extra heating surface. When the H2 fraction is enriched from 0 to 100%, CO2 emission intensity drops from 6.05 × 10−8 kg J−1 to 0. This work may offer some theoretical references for the application and generalization of HENG condensing boilers.

Development of bubble dynamic parameter models in subcooled flow boiling of saline solution

Concentrated saline solutions are inevitably used as coolants in the industry heat exchangers. From the aspect of simulation prediction, the closure models for RPI model, including the models of bubble departure diameter (Dw), departure frequency (f) and active nucleation site density (Nw), are of great importance for the overall success of heat transfer calculation. However, the applicability of the existing closure models for the nucleate flow boiling of saline solutions is yet to be answered. In this paper, the experiments of subcooled flow boiling of the NaCl solutions with concentration range of 0%–6% were conducted. The experimental data of the three bubble parameters, Dw, f and Nw, were obtained under different operating conditions, making up for the shortage of the bubble parameter data of saline solution in literature. The impacts of key influencing parameters for each of the three bubble parameters were discussed. For model development, the prediction performance of several existing representative Dw, f and Nw models on saline solution were studied. The results indicate that the available models for Dw, f and Nw show rather large deviations for saline solutions. Therefore, new models for Dw, f and Nw were developed according to the correlation method and the influencing parameter analyses. The parameters and dimensionless groups, which can be used to characterize the variations of Nw, Dw and f, were determined. The dimensionless parameters including Boiling number (Bo), density ratio (ρ⁎), dimensionless surface tension, Prandtl number and a suggested dimensionless temperature (ΛT), can be used to characterize the variation of Dw. And the dimensionless groups of Bo, ρ⁎, ΛT, and the non-dimensional bubble departure diameter, can be used to correlating with the non-dimensional departure frequency. As for Nw, the wall superheat and solution concentration are the most critical factors for model correlating. The new correlations for predicting the Dw, f and Nw during subcooled flow boiling in both the pure water and saline solutions were built and validated.

Heat Transfer Correlations for Smooth and Rough Airfoils

Low-fidelity methods such as the Blade Element Momentum Theory frequently provide rotor aerodynamic performances. However, these methods must be coupled to databases or correlations to compute heat transfer. The literature lacks correlations to compute the average heat transfer around airfoil. The present study develops correlations for an average heat transfer over smooth and rough airfoil. The correlation coefficients were obtained from a CFD database using RANS equations and the Spalart–Allmaras turbulent model. This work studies the NACA 0009, NACA 0012, and NACA 0015 with and without the leading roughness representative of a small ice accretion. The numerical results are validated against lift and drag coefficients from the literature. The heat transfer at the stagnation point compares well with the experimental results. The database indicates a negligible dependency on airfoil thickness. The work presents two correlations from the database analysis: one for the smooth airfoils and one for the rough airfoils. For the zero lift coefficient, the average Nusselt number is maximum. This increases with Re0.636 for the smooth surface and with Re0.85 for the rough surface. As the lift increases, the average Nusselt is reduced by values proportional to the square of the lift coefficient for the smooth surface, while it is reduced by values proportional to Re and the square of the lift coefficient for the rough surface.

Design of Solar dish concentration by using MATLAB program and Calculation of geometrical concentration parameters and heat transfer

Renewable energy sources plays an important role in electricity generation. Various renewable energy sources like wind, solar, geothermal, ocean thermal, and biomass can be used for generation of electricity and for meeting our daily energy needs. Energy from the sun is the best option for electricity generation as it is available everywhere and is free to harness. The goal of research is to calculate the energy, engineering characteristics of solar concentrators by writing their own equations MATLAB program and compare the theoretical results with the results of the researchers was compatible.

Selected Papers from the 8th International Symposium on Advances in Computational Heat Transfer (CHT-21)

"Selected Papers from the 8th International Symposium on Advances in Computational Heat Transfer (CHT-21)." Heat Transfer Engineering, ahead-of-print(ahead-of-print), pp. 1–2

Numerical study on conjugate heat transfer in a liquid-metal-cooled pipe based on a four-equation turbulent heat transfer model

Conjugate heat transfer between liquid metal and solid is a common phenomenon in a liquid-metal-cooled fast reactor's fuel assembly and heat exchanger, dramatically affecting the reactor’s safety and economy. Therefore, comprehensively studying the sophisticated conjugate heat transfer in a liquid-metal-cooled fast reactor is profound. However, it has been evidenced that the traditional Simple Gradient Diffusion Hypothesis (SGDH), assuming a constant turbulent Prandtl number (Prt, usually 0.85 - 1.0), is inappropriate in the Computational Fluid Dynamics (CFD) simulations of liquid metal. In recent decades, numerous studies have been performed on the four-equation model, which is expected to improve the precision of liquid metal’s CFD simulations but has not been introduced into the conjugate heat transfer calculation between liquid metal and solid. Consequently, a four-equation model, consisting of the Abe k−ε turbulence model and the Manservisi kθ−εθ heat transfer model, is applied to study the conjugate heat transfer concerning liquid metal in the present work. To verify the numerical validity of the four-equation model used in the conjugate heat transfer simulations, we reproduce Johnson’s experiments of the liquid lead-bismuth-cooled turbulent pipe flow using the four-equation model and the traditional SGDH model. The simulation results obtained with different models are compared with the available experimental data, revealing that the relative errors of the local Nusselt number and mean heat transfer coefficient obtained with the four-equation model are considerably reduced compared with the SGDH model. Then, the thermal-hydraulic characteristics of liquid metal turbulent pipe flow obtained with the four-equation model are analyzed. Moreover, the impact of the turbulence model used in the four-equation model on overall simulation performance is investigated. At last, the effectiveness of the four-equation model in the CFD simulations of liquid sodium conjugate heat transfer is assessed. This paper mainly proves that it is feasible to use the four-equation model in the study of liquid metal conjugate heat transfer and provides a reference for the research of conjugate heat transfer in a liquid-metal-cooled fast reactor.

Development of a Novel Strand Reduction Technology for the Continuous Casting of Homogeneous High‐Carbon Steel Billet

Internal quality issues concerning center segregation, porosity, and internal crack are the major problems with respect to the production of high‐carbon steels billet with a continuous casting process. Herein, a heat transfer calculation model is developed, verified, and applied to calculate the appropriate casting speed and secondary cooling intensity of the continuous casting billet with a section size of 160 mm square during mechanical reduction processes. The mechanical reduction on the homogeneity of the billet is investigated by several field trails to improve the internal quality of the high‐carbon 82 A steel billet. Consequently, a superoptimum crack‐free high‐carbon steel billet with high homogeneity both in segregation and in compactness is successfully achieved through a novel strand reduction pattern, combined with consecutive multiroll soft reduction and single‐roll heavy reduction.

Building thermal environment solution model and radiation heat transfer calculation model based on Gebhart absorption coefficient

The building walls temperatures are different, and there are radiation heat transfers between the walls, which have the characteristics of multiple reflections and multiple absorptions. The Gebhart absorption coefficient considers the radiation energy both directly absorbed by the wall and indirectly absorbed by other walls multiple times reflections. The absorption coefficient Gij is used to represent the proportion of radiation energy absorbed by surface j from the radiation energy of surface i. Through employing Gebhart absorption coefficient, the Gebhart absorption coefficient matrix is constructed based on the wall angle factors and the wall radiation emissivity. The building thermal environment solution model is established, which can calculate the indoor air temperature and wall temperature. The wall radiation heat transfer calculation model is built to calculate the net radiation heat transfer of the walls. An experimental bench was carried out to verify the above theoretical calculation results. The research results showed that the theoretical calculated values of the air temperatures of the building thermal environment solution model were basically consistent with the measured values, and the deviation was within 0.25°C. The deviation between the calculated values of the wall temperatures and the measured values was basically within 1.0°C. The error between the calculated values of the wall radiation heat transfer calculation model and the measured values varied within a small range. The Gebhart absorption coefficient is more appropriate in characterizing radiation heat transfer mechanism of the walls, and it provides a new way and thought for the analysis of radiation heat transfer on building wall.

Автоматизация теплового расчета реактора для производства серосодержащего сорбента при разогреве реакционной смеси

The article highlights the problem of automation the thermal design of a reactor for the synthesis of a sulfur-containing sorbent obtained from the use of waste products of epichlorohydrin, chlorinated lignin and sodium polysulfides is considered. Automated design helps to reduce the intensity of the process, improve the quality of design decisions, significantly reduce production costs, which has a positive effect on the cost of finished products. It has been found that due to the incompatibility of the similarity criteria of chemical and mass transfer processes there is little possibility to carry out a large-scale transition in a reactor based on physical similarity. In the course of a large-scale transition from a laboratory unit to a small production unit there were used the computational methods based on engineering experience that allow increasing the reliability of the results obtained. There have been determined the initial values, which will be used in the design for a reactor with a propeller agitator to mix a working mass having a dynamic viscosity coefficient of 6.01 sP and a solid phase content of 31.8%. The agitator type was determined by calculating the physical properties of the ingredients and selecting the mixer designs. A flowchart and a formal description of the algorithm for calculating heat transfer during a reaction mixture heating are given; the program interface is written in C# displaying the results of thermal design of the working mixture heating. As a result of the calculation, there has been calculated the amount of heat and time required to heat the working mixture, coefficient of heat transfer from the working mass to the reactor wall, mass flow rate of water and its costs, velocity of water in the thermal jacket, mode of water flow in the jacket and other similarity criteria.

Optimization of double-layer shaped phase change wallboard in buildings in two typical climate areas in China

Phase change material (PCM) applied in buildings can significantly improve thermal comfort and realize building energy conservation. In recent years, double-layer shaped phase change wallboards (DLSPCWs) that depends on the latent heat absorption and release of two kinds of PCMs can effective control the indoor temperature fluctuation, and have been play an important role in improving the indoor thermal environment. The related researches show that, it is rare but necessary to optimize the DLSPCWs in different typical climate areas in order to further promote the application development of PCMs in buildings for energy conservation. Aimed this, fifty-four different DLSPCWs were constructed in this study by selecting different phase change thermal storage layer from four kinds of form-stable PCMs and changing the thickness of the layer to optimize the structure of DLSPCW in two typical climate areas, including severe cold area (Xining city, China) and hot summer and warm winter area (Haikou city, China) respectively. Comsol Multiphysics was used for heat transfer simulation and calculation of the DLSPCW in order to determine its best structure combination pattern for the two areas, and DesignBuilder for comparing and analyzing the building energy conservation effect when using the optimal DLSPCW in buildings. Compared with the ordinary wall, the optimized DLSPCW saved 14,198.96 kW·h electric energy during the heating period in Xining, while 18,816.62 kW·h electric energy in Haikou during the cooling period. The results proved that the optimum structure of the DLSPCW not only reduced the heating load and the cooling load but realized the maximum utilization of the PCMs.

Heat Transfer Calculations during Flow in Mini-Channels with Estimation of Temperature Uncertainty Measurements

The main aim of this work was to provide heat transfer calculations of flow boiling in mini-channels with an application for the Trefftz functions. The test section comprised five parallel mini-channels with a depth of 1 mm, with a common heated wall. For the estimation of the temperature uncertainty, during the experiment the temperature measurement was performed with the use of K-type thermoelements and an infrared camera in two mini-channels simultaneously. According to the Guide to the Expression of Uncertainty in Measurement, the Monte Carlo method is a practical alternative to the GUM uncertainty framework. Since the uncertainty components are not approximately the same magnitude, the Monte Carlo method was indicated to estimate the uncertainty of the surface temperature measurement. The results obtained from this simulation method were compared with the results of the computation related to the uncertainty propagation method. The results of both methods of temperature measurement were found to be consistent. The results of the statistical analysis were used to describe heat transfer calculations. The heat transfer investigations concerning the subcooled boiling region were performed during the other experiment. The local heat transfer coefficients on the contact surface between the working fluid and the heated wall were calculated from the Robin boundary condition. The mathematical model described by the heat equation in the mini-channel wall and by the Fourier-Kirchhoff equation in a flowing fluid leads to an inverse heat transfer problem. This problem was solved using the FEM with the Trefftz-type basis functions. The estimation of temperature uncertainty measurements due to the Monte Carlo method was included in the final results of the heat transfer coefficient.

Experimental and numerical study of heat transfer under laminarization condition in a small size supersonic nozzle

The present paper compares measured and calculated heat transfer parameters for a small-size slot supersonic nozzle. Heat transfer coefficient and temperature recovery factor were examined under conditions of partial laminarization of boundary layer caused by moderate flow acceleration and low Reynolds numbers. The transient heat transfer method was implemented for estimation of these values for the nozzle subsonic and supersonic parts. Maximum values of flow acceleration parameter K lied in the range 1.3 … 2.75∙10−6. Experimentally measured value was normalized to the developed turbulent boundary layer heat transfer coefficient and reached St/StRex = 0.5–0.7 and indicated partial laminarization phenomenon. It was shown that the temperature recovery factor hasn't been affected by the flow acceleration. The results are compared to numerical heat transfer predictions using sst, γ-sst and γ-Reθ-sst turbulence models. Numerical calculations and experimental data were found to be in reasonably good agreement for low acceleration level with K less than 0.75∙10−6. Nevertheless, γ-sst turbulence model made slightly conservative estimation whereas in contrast γ-Reθ-sst model overestimates quantities for the moderate flow acceleration conditions.

Improved Monte Carlo method for radiative heat transfer in semitransparent media with BRDF surface

This paper proposes an improved Monte Carlo method (IMCM) for the radiative heat transfer solution in semitransparent media with BRDF surface for the first time. This method not only keeps the strong points of high precision and excellent applicability to the calculation of radiative heat transfer in complex shape scattering media with BRDF surface, but also overcomes the shortcomings of time-consuming for huge amounts of energy beams tracing in the Monte Carlo method. In the IMCM we developed, the energy beams of reflection or scattering can be worked out by proportional iteration accumulation. The scattering and reflection process only need to be sampled twice rather than lots of scattering and reflection energy beams tracing. This improvement not only retains the high accuracy of the MCM, but also greatly improves the calculation efficiency. A number of radiative heat transfer problems in semitransparent media enclosure with BRDF surface are studied. The effects of absorption coefficient, wall emissivity and scattering characteristics on radiative heat transfer are analyzed. Results indicate that the IMCM is a very efficient method with high precision for solving radiative heat transfer.

Расчет теплопередачи через ограждающую конструкцию с полупрозрачным экраном

Расчет теплопоступлений через ограждения является важной частью задачи прогнозирования летнего теплового режима здания под прозрачным куполом, интерес к строительству которых в северных регионах возрос в последнее время. В работе рассмотрена относительно простая, пригодная для инженерных расчетов модель теплопередачи через ограждающую конструкцию с полупрозрачным экраном, позволяющую учесть парниковый эффект. Для верификации модели было проведено сравнение расчетных и экспериментальных данных и получено их хорошее согласие, что подтверждает работоспособность предложенной модели. Показано, что наличие полупрозрачного экрана из-за парникового эффекта значительно изменяет температуру стены здания под куполом и величину теплового потока, откуда следует важность учета таких факторов, как оптические свойства экрана, температура небесного свода и других климатических факторов при расчете теплового режима купольных систем. The evaluation of heat input through fences is an important part of the task of predicting the summer thermal regime of a building under a transparent dome, the interest in the construction of which in the northern regions has increased recently. In this work, a relatively simple model for engineering calculations of heat transfer through a building envelope with a translucent screen, which allows to take into account the greenhouse effect, is considered. The model has been verified by comparing the calculated and experimental data and their good agreement has been obtained, which confirms the performance of the proposed model. It is shown that the presence of a translucent screen due to the greenhouse effect significantly changes the temperature of the building wall under the dome and the value of heat flux, which implies the importance of taking into account such factors as the optical properties of the screen, the temperature of the sky, and other climatic factors when calculating the thermal regime of dome systems.

Computational flow and heat transfer study on impingement cooling in a turbine blade leading edge using an innovative convergent nozzles

The present paper discusses a detailed numerical study performed to investigate flow and heat transfer characteristics of impingement cooling of the leading edge of a HP gas turbine blade model. An array of innovative converging shape nozzles are used as jets which strike the surface to be cooled. A comprehensive study is presented investigating various parameters which effect impingement cooling. These parameters include varying Mach number of the flow as 0.2 to 0.8, converging ratio of the nozzle varied as 2 to 8 at two different minor diameters of 0.25–0.5 mm of the jet, pitch distance is changed from 3 to 5 mm, and inter-jet distance changed from 3 mm to 6 mm. Each parameter is independently scrutinized keeping other parameters constant. The results indicate the formation of primary stagnation region where Nusselt number augmentation is maximum compared to secondary stagnation region. Cross-flow effect plays a significant role in reducing peak values in the Nusselt number in the downstream region. Enhancement in peak Nusselt number value is greater for high values of Mach number of the flow, lower jet-to-target distances and the higher converging ratio at a lower value of jet diameter. Average Nusselt number is found to be higher for lower values of pitch distance.

Study on Calculation Method of Heat Exchange Capacity and Thermal Properties of Buried Pipes in the Fractured Rock Mass-Taking a Project in Carbonate Rock Area as an Example

Fractures are developed in carbonate rock areas, and the fracture water flow significantly influences the heat exchange between buried pipes and the rock mass by induing heat convection, providing the carbonate rock area a strong heat exchange capacity and preferable conditions for shallow geothermal development and utilization. In this paper, the calculation method of heat exchange capacity of buried pipes based on fracture distribution characteristics is proposed and deduced, featuring such advantages as quick speed and low cost. Taking an actual project in carbonate rock area as an example, the heat exchange capacity of buried pipes was obtained by the following two methods: in-situ thermal response test and calculation based on fracture distribution characteristics. In the thermal response test, the initial ground temperatures of the two test holes were 15.18 °C and 12.72 °C. By fitting the linear equation of time and average temperature with a linear thermal source model, the heat exchange capacities were 57.21 W/m and 58.22 W/m, the thermal conductivities were 3.56 W/(m·K) and 2.32 W/(m·K), the thermal diffusivities were 1.71 × 10−6 m2/s and 1.12 × 10−6 m2/s, and the volume specific heat capacity was 2.08 × 106 J (m3·K). The test results indicated that the thermal property parameters of rock and soil mass were higher than those of other areas, with obvious wide-range distribution characteristics. Through the statistical analysis of outcrop fracture characteristics, combined with the cube law to calculate the fracture water flow and convective heat transfer, an alternative method for the calculation and optimization of buried pipe heat transfer in fractured rock mass area is also proposed in this paper. According to the measured fracture distribution characteristics of the field outcrop, the heat exchange capacities of the two holes were 57.26 W/m and 58.56 W/m, which were basically consistent with the thermal response test values and verified the reliability of the calculation method of heat exchange capacity of buried pipes based on fracture distribution characteristics.

Generalized lattice Boltzmann method for radiative transfer problem in slab and irregular graded-index media.

The lattice Boltzmann method (LBM) has been developed as a powerful solution method in computational fluid dynamics and heat transfer. However, the development of the LBM for solving radiative transfer problems has been far from perfect. This paper proposes a generalized form of the lattice Boltzmann model for the multidimensional radiative transfer equation (RTE) in irregular geometry with a graded index based on body-fitted coordinates. The macroscopic RTE is recovered from Chapman-Enskog analysis, which provides two possible procedures to formulate the Boltzmann equation in graded-index media and irregular geometries. These proposed models have been tested by considering one-and two-dimensional problems of the RTE, and the benchmark solutions reported in the literature were used for comparisons. Afterwards, the LBM is used to analyze the radiation transport in graded-index media for various forms of scattering law, refractive index, boundary reflection, laser and optical properties, and temperatures. The graded-index function and the geometry type have a significant effect on radiative transport in cases in which the refractive index matches or mismatches the boundary. It is also apparent that the developed LBM is an efficient, powerful, robust, and accurate solver for radiative transport in inhomogeneous media with a graded-index function and irregular geometries.