Calculation Of Thermal Conductivity Research Articles

TTEP: A code for efficient calculation of the thermal transport from constant electron-phonon coupling approximation

A Fortran code named TTEP (Thermal Transport from constant Electron-Phonon coupling approximation) is presented in this work. Within the framework of first-principles calculation, this code utilizes the deformation potential approximation to replace the electron–phonon (EP) coupling matrix element in the phonon scattering due to EP interaction. By adopting this approximation, our method achieves a balance between computational efficiency and accuracy, enabling the exploration of the thermal transport from EP interaction with much reduced computational consumption. One of the key features of TTEP is its versatility in handling a broad range of carrier concentration, including both hole and electron doping. We also extend the applicability of TTEP to actual doping case and capture EP effect over a wide temperature range. Other scattering mechanisms, such as grain boundary scattering and phonon–phonon interaction, have been included in the calculation of lattice thermal conductivity through the Matthiessen’s rule. Several test cases are presented in this work to demonstrate the above features.

Ab Initio-Based Bond Order Potential for Arsenene Polymorphs Developed via Hierarchical Reinforcement Learning.

Arsenene, a less-explored two-dimensional material, holds the potential for applications in wearable electronics, memory devices, and quantum systems. This study introduces a bond-order potential model with Tersoff formalism, the ML-Tersoff, which leverages multireward hierarchical reinforcement learning (RL), trained on an ab initio data set. This data set covers a spectrum of properties for arsenene polymorphs, enhancing our understanding of its mechanical and thermal behaviors without the complexities of traditional models requiring multiple parameter sets. Our RL strategy utilizes decision trees coupled with a hierarchical reward strategy to accelerate convergence in high-dimensional continuous search spaces. Unlike the Stillinger-Weber approach, which demands separate formalisms for buckled and puckered forms, the ML-Tersoff model concurrently captures multiple properties of the two polymorphs by effectively representing the local environment, thereby avoiding the need for different atomic types. We apply the ML model to understand the mechanical and thermal properties of the arsenene polymorphs and nanostructures. We observe an inverse relationship between the critical strain and temperature in arsenene. Thermal conductivity calculations in nanosheets show good agreement with ab initio data, reflecting a decrease in thermal conductivity attributable to increased anharmonic effects at higher temperatures. We also apply the model to predict the thermal behavior of arsenene nanotubes.

Probing the opto-electronic, phonon spectrum, and thermoelectric properties of lead-free fluoride perovskites A2GeSnF6 (A = K, Rb, Cs) for energy harvesting devices

The present work employs density functional theory to explore the structural, optoelectronic, and thermoelectric attributes of the halide-based double perovskite A2GeSnF6 (A = K, Rb, and Cs) compounds. The stable phonon dispersion spectrum affirms dynamical stability, whereas the enthalpy of formation and tolerance factor evaluated collectively verify structural stability. Considering the Tran Blaha modified Becke Johnson potentials (mBJ), the predicted direct band gaps along the symmetry point are 3.19 eV for K2GeSnF6, 3.16 eV for Rb2GeSnF6 and 3.12 eV Cs2GeSnF6. According to an in-depth examination of the optoelectronic features, A2GeSnF6 (A = K, Rb, and Cs), double perovskites are assuring contenders for optoelectronic devices due to their suitable bandgap. The extremely high figure of merit values (0.94–0.97) obtained from the numerical calculation of power factor and thermal conductivity suggest the intriguing prospects of these compositions for thermoelectric devices. These studies offer a perceptive comprehension of the materials for their potential applications in the future.

Thermal conductivity of irregularly shaped nanoparticles from equilibrium molecular dynamics

The computation of thermal conductivity for finite nanoparticulate systems, particularly those of irregular shapes, poses significant challenges. The nonequilibrium molecular dynamics (NEMD) methods has been extensively utilized in numerous prior studies for the computation of thermal conductivity of nanoparticles. One of our recent works (Dong et al 2021 Phys. Rev. B 103 035417) proposed that equilibrium molecular dynamics (EMD) methods can be used for the simulation of thermal conductivity of finite-scale systems and demonstrated their equivalence to NEMD methods. In this study, we investigated the application of the (EMD) approach for the computation of thermal conductivity in zero-dimensional nanoparticles. In our initial step, we merged both methodologies to substantiate the equivalence in thermal conductivity calculation for cube and cylinder nanoparticles. After filtering the data, we confirmed the usefulness of EMD for evaluating the thermal conductivity of zero-dimensional materials. The NEMD method faces challenges in accurately predicting thermal conductivity in nanoparticle systems with a varying cross-sectional area along the transport direction, whereas EMD methods can be utilized to estimate thermal conductivity when the volume is known. In a subsequent study, we used the state-of-the-art machine learning potential to calculate the thermal conductivity of spherical nanoparticles and compared the results with those obtained using the classical Tersoff potential. Ultimately, we predicted the thermal conductivity of nanoparticles with various geometries in all directions. Our findings collectively demonstrate the simplicity and effectiveness of employing EMD methods for calculating thermal conductivity in nanoparticle systems, thereby opening up new avenues for investigating thermal transport properties in particle systems as well as nanopders.

A moment tensor potential for lattice thermal conductivity calculations of α and β phases of Ga2O3

Calculations of heat transport in crystalline materials have recently become mainstream, thanks to machine-learned interatomic potentials that allow for significant computational cost reductions while maintaining the accuracy of first-principles calculations. Moment tensor potentials (MTPs) are among the most efficient and accurate models in this regard. In this study, we demonstrate the application of MTP to the calculation of the lattice thermal conductivity of α and β-Ga2O3. Although MTP is commonly employed for lattice thermal conductivity calculations, the advantages of applying the active learning methodology for potential generation are often overlooked. Here, we emphasize its importance and illustrate how it enables the generation of a robust and accurate interatomic potential while maintaining a moderate-sized training dataset.

Theoretical study on the effective thermal conductivity of silica aerogels based on a cross-aligned and cubic pore model

Abstract Aerogel nanoporous materials possess high porosity, high specific surface area, and extremely low density due to their unique nanoscale network structure. Moreover, their effective thermal conductivity is very l1ow, making them a new type of lightweight and highly efficient nanoscale super-insulating material. However, predicting their effective thermal conductivity is challenging due to their uneven pore size distribution. To investigate the internal heat transfer mechanism of aerogel nanoporous materials, this study constructed cross-aligned and cubic pore model (CACPM) based on the actual pore arrangement of SiO2 aerogel. Based on the established cross-aligned and cubic pore model (CACPM), the effective thermal conductivity expression for aerogel was derived by simultaneously considering gas-phase heat conduction, solid-phase heat conduction, and radiative heat transfer. The derived expression was then compared with available experimental data and the Wei structure model. The results indicate that, according to the model established in this study for the derived thermal conductivity formula of silica aerogel, for powdery silica aerogel under the conditions of T=298K, a 2=0.85, D 1=90μm, ρ=128kg/m3, within the pressure range of 0-105Pa, the average deviation between the calculated values and experimental values is 10.51%. In the pressure range of 103-104Pa, the deviation between calculated values and experimental values is within 4%. Under these conditions, the model has certain reference value in engineering verification. This study also makes a certain contribution to the research of aerogel thermal conductivity heat transfer model and calculation formula.

Anisotropic Lattice Thermal Conductivity in Highly Ordered PEDOT Fibers

AbstractWhen it comes to sustainable and efficient energy solutions, organic semiconductors can play an important role in thermoelectric applications, since they are non‐toxic, cheap, made of abundant chemical species, and show intrinsically low thermal conductivities. Their electrical conductivity can be optimized via doping. Yet, thermal conduction should be as low as possible and, to this end, the atomic scale mechanisms behind heat transport –e.g. the correlation between morphology and thermal conductivity or the role of doping– should be understood in detail. Fully atomistic molecular dynamics calculations of the lattice thermal conductivity of doped poly(3,4‐ethylenedioxythiophene) (PEDOT) highly ordered, quasi‐crystalline nanofibers are presented here. It is found that the conductivity along the backbone direction is not necessarily the highest, but it depends on the length of the PEDOT chains, thus the degree of anisotropy depends on the the aspect ratio of the nanofiber. Indeed, transport along the lamellar direction can be of the same order or higher than that of the backbone if their lengths are comparable. These results challenge the usual expectation that thermal conduction along the backbone largely exceeds those along the lamellar and π − π direction and have the important consequence that the anisotropy could be leveraged in thermal management applications.

Calculation of Equivalent Thermal Conductivity of Motor Winding Based on Conductor Distribution

Abstract To improve the calculation accuracy of motor thermal field, this paper proposes a method for calculating the equivalent thermal conductivity of winding based on conductor distribution, and a 24-slot 26-pole outer-rotor permanent magnet synchronous motor is taken as an example to verify the method. First, the equivalent thermal conductivity of winding is calculated by traditional equivalent methods, namely the equivalent insulation layer method and the area weighting method. Second, the equivalent thermal conductivity of the slot winding and end winding in the three-dimensional (3D) direction is derived using the conductor distribution method. Third, the 3D finite element models corresponding to three equivalent methods are established, and the temperature of the motor under different operating conditions is simulated and compared. Finally, an experimental platform is built to verify the accuracy of the proposed conductor distribution method.

Pore structure characterization and effective thermal conductivity modeling of fibrous building thermal insulation materials based on X-ray tomography

The existing structural characterization methods of building materials as well as thermal conductivity calculation models can not be directly applied when considering fibrous building thermal insulation materials with intricate skeletons. In this study, rock wool is considered the research object, and the X-ray tomography method is used to characterize the pore structure and extract structural parameters. Based on the actual pore morphology of the material, the pores in the representative elementary volume (REV) are reasonably assumed to be cubic. Additionally, considering the contact thermal resistance of fibers and the randomness of pore distribution, the curved pattern of heat conduction pathway with the ever-changing diameter is reasonably simplified into a series-parallel form of the curved heat chain with the same diameter. On this basis, the fractal models of effective thermal conductivity are established in horizontal and vertical directions. Finally, a modified formula for the effective thermal conductivity calculation of fiber thermal insulation materials is proposed, taking into account the influence of fiber orientation on the material thermal conductivity. It was shown that the relative deviation between the calculated correction value and the experimental value of the effective thermal conductivity is all less than 16.13%.

Thermal transport and thermoelectric properties of transition metal dichalcogenides MoX 2 from first-principles calculation

The properties of two-dimensional (2D) materials have been extensively studied and applied in various applications. Our interest is to theoretically investigate the thermal transport and thermoelectric properties of the 2D transition metal dichalcogenides MoX 2 (X=S, Se, Te). We employ density functional theory and Boltzmann transport theory with relaxation-time approximation to calculate the electronic and transport properties. We also implemented the kinetic-collective model to improve the calculation of lattice thermal conductivity. Our calculations indicate that MoTe2 has the highest ZT of 2.77 among the other MoX 2 at 550 K due to its low thermal conductivity and high electrical conductivity. Consequently, we suggest that MoX 2 monolayers hold promise as materials for energy conversion devices due to their relatively high ZT. Moreover, these results could be beneficial to design 2D material-based high-performance thermoelectric devices.

Construction of the Aerogel Thermal Conductivity Model based on k×k Sierpinski Carpet Fractal Units

With the characteristics of low density, high specific surface area, and high porosity, aerogel boasts prominent advantages in the field of thermal protection. The thermal insulation performance of aerogel has a significant relationship with its internal microstructure. In this study, the thermal conduction model of Sierpinski aerogel filled with solid in ga
 With the characteristics of low density, high specific surface area, and high porosity, aerogel boasts prominent advantages in the field of thermal protection. The thermal insulation performance of aerogel has a significant relationship with its internal microstructure. In this study, the thermal conduction model of Sierpinski aerogel filled with solid in gas is established based on the equivalent circuit method. We calculated the optimal fractal unit structure of the aerogel via its porosity, applied it to the thermal conductivity calculation of four types of aerogels, and revealed the average relative error of less than 11.58%, which is lower than the calculation results of the thermal conductivity model of the aerogel with the fractal unit structure of , indicating the effectiveness and reliability of the proposed thermal conductivity prediction model.
 s is established based on the equivalent circuit method. We calculated the optimal fractal unit structure of the aerogel via its porosity, applied it to the thermal conductivity calculation of four types of aerogels, and revealed the average relative error of less than 11.58%, which is lower than the calculation results of the thermal conductivity model of the aerogel with the fractal unit structure of , indicating the effectiveness and reliability of the proposed thermal conductivity prediction model.

Numerical estimation of effective thermal conductivity of reconstructed 2D structures of cement-based building materials

Cement-based building materials are fundamental for constructing modern buildings, and accurate determination of their thermal conductivity is crucial for calculating building energy consumption. In this study, random growth theory is used to reconstruct the two-dimensional pore structures of cement-based building materials in different forms. Furthermore, heat transfer simulations and calculations of effective thermal conductivity based on the finite element method are conducted for these pore structures. The effect of pore structure parameters on the effective thermal conductivity of cement-based building materials is investigated by this method. The results indicate that porosity, pore size, and the degree of pore regularity can all influence the effective thermal conductivity of cement-based building materials. At a porosity of 0.3, the fluctuations in the effective thermal conductivity caused by variations in pore sizes and degrees of pore regularity are most drastic.

Enhanced Heat Dissipation for Macroscopic Metals Achieved by a Single‐Layer Graphene

AbstractThe increasing demand for high‐performance devices on heat dissipation makes it approach the bottleneck even for metals with high thermal conductivities. The coating of only one layer of graphene, the heat dissipation performances of Cu, Ag, and Al can be further enhanced, e.g., with a maximum temperature reduction by ≈9% for a Cu foil is demonstrated. Molecular dynamics (MD) analysis of spectral phonon transmission reveals that low‐frequency phonons play a significant role in the thermal transport within the Cu/single‐layer graphene (SLG) system, and the high‐frequency phonons exhibit substantial mismatch. It suggests that the thermal anisotropy of graphene enables a rapid heat dispersion in the in‐plane direction and provides an effective thermal insulation in the out‐of‐plane direction. The thermal conductivity calculations demonstrate an enhanced participation of phonons in heat conduction by the graphene layer, indicating a novel heat conduction mechanism in the Cu/single‐layer graphene system. These findings highlight the positive impact of graphene on the heat conduction of metals, and they will hold crucial implications for the design and application of graphene‐based thermal devices is believed.

A wide-bandgap graphene-like structure C6BN with ultra-low dielectric constant.

This study introduces a new wide-bandgap graphene-like structure, denoted as C6BN, achieved by incorporating an eight-electron BN pair, substantially modifying its electronic properties. Utilizing extensive density functional calculations, we comprehensively analyzed the stability, electronic structure, mechanical properties, and optical-electrical characteristics of C6BN. Our investigations reveal the material's exceptional thermodynamic, mechanical, and dynamic stability. Notably, the calculated wide bandgap of 2.81 eV in C6BN, supported by analyses of energy levels, band structures, and density of states, positions it as a promising two-dimensional wide-bandgap semiconductor. Additionally, C6BN exhibits isotropic mechanical features, highlighting its inherent flexibility. Remarkably, our calculations indicate an ultra-low dielectric constant (k = 1.67) for C6BN, surpassing that of well-established third-generation semiconductors. Further exploration into the thermoelectric properties of C6BN demonstrates its promising performance, as evidenced by calculations of thermal conductivity (κ), power factor (P), and Seebeck coefficient (S). In summary, our findings underscore the significant potential of the proposed C6BN structure as a flexible two-dimensional material poised to drive future advancements in electronic and energy-related technologies.

Heat accumulation and phase transition induction in a VO2 thin film by a femtosecond pulse-periodic radiation.

The kinetics of optical switching due to the insulator-metal phase transition in a VO2 thin film is studied experimentally at different laser pulse repetition frequencies (PRFs) in the NIR range and compared with temperature kinetics obtained through the thermal conductance calculations. Two switching processes have been found with characteristic times <2 ms and <15 ms depending on the PRF; the former is explained by the accumulation of metallic domains remaining after a single-pulse phase transition, and the latter is referred to the heat accumulation in the film. Consequently, the dynamics of the microscopic domains is leading in the initiation of phase transition under pulse-periodic conditions compared to the macroscopic heat transfer. The reverse transition at the radiation turn-off depends on the PRF with a time coefficient of 17.5 µs/kHz and is determined by the metallic domains' decay in the film. The results are important for understanding the nature of the insulator-metal transition in thin films of VO2 as well as using them in all-optical switches of pulse-periodic laser radiation.

Ultralow thermal conductivity of W-Janus bilayers (WXY: X, Y = S, Se, and Te) for thermoelectric devices.

Lattice thermal conductivity (κ) in tungsten dichalcogenide Janus (WXY, where X, Y = S, Se, and Te) monolayers and heterostructures (HSs) have been investigated using ab initio DFT simulations. Tungsten-based Janus monolayers show semiconducting behavior with the bandgap in the semiconducting range for WSSe (1.70 eV), WSTe (1.26 eV), and WSeTe (1.34 eV). When Janus monolayers are stacked to form HSs with weak van der Waals (vdW) interactions, the bandgap reduces to 0.19 eV, 0.40 eV, and 0.24 eV, respectively, for WSeTe/WSTe, WSSe/WSTe, and WSSe/WSeTe HSs. Thermal vibrational characteristics of Janus monolayers are modified when these are stacked in 2D HSs with the introduction of interlayer hybrid phonon modes. Large longitudinal-transverse optical (LO-TO) splitting is noticed at the Brillouin zone-center (Γ-point): 135 cm-1, 140 cm-1, and 150 cm-1 for WSeTe/WSTe, WSSe/WSeTe and WSSe/WSTe HSs, respectively. Thermal conductivity calculations show ultra-low κ values for WSeTe/WSTe (0.01 W m-1 K-1), WSSe/WSTe (0.02 W m-1 K-1) and WSSe/WSeTe HS (0.004 W m-1 K-1) at 300 K. The results can be attributed to the hybrid phonon modes with frequencies very close to acoustic modes at the gamma point, low Debye temperature (θD) and specific heat capacity. Our results highlight the possible applications of these HSs in designing thermoelectric interfaces at the nanoscale.

Investigating the thermal properties of CrN: Theoretical insights and real ceramics

Ab-initio calculations of lattice heat capacity and phonon thermal conductivity have been performed for CrN of rock-salt structural type (paramagnetic) and for the orthorhombic antiferromagnetic (AFM) phase below TN ≈ 285 K. The comparison with experimental data below ≈30 K unveils that in contrary to the theoretically calculated heat capacity following the βT3 term with Debye temperature ΘD = 830 K, a large excess of experimental heat capacity in a form of δT2 is observed. This additional heat capacity is ascribed to magnons in the specific layered-type AFM arrangement of CrN. The experimental thermal conductivity shows a similar low-temperature excess of T2-dependence. Considering that mean free path of heat carriers is essentially limited by the grain size and calculated phonon conductivity itself is very low below ≈30 K, such additional contribution can be ascribed again to AFM magnons though theoretical model of such conductivity is still to be assessed. In spite of this complexity, our model of phonon thermal conductivity reproduces well the maximum of 7.2 Wm−1K−1 at 150 K followed by a decline tied to phonon-phonon scattering (Umklapp process). Nonetheless at higher temperatures, the experimental data evidence sudden drop at TN to ≈2 Wm−1K−1 with only slightly varying thermal conductivity at elevated temperatures, which reminds rather a behavior of amorphous or defective solids. It is proposed that atomic displacements that stabilize spin-parallel and spin-antiparallel Cr pairs in the orthorhombic AFM phase persist partially as fluctuating ones in the cubic paramagnetic state above TN, which gives rise to dynamic strain fields that cause strong phonon scattering.

Structural, electronic, optical, and thermoelectric properties of CsPbI3-yBry (y = 0.5, 1.5, 2.5) compounds: First-principle study

BackgroundAmong photovoltaic materials, halide-based perovskites, such as CsPbI3, have been the subject of many research papers due to their suitable and direct bandgap, very good optical properties, and remarkable thermoelectric properties. Enhancing optoelectronic and thermoelectric properties can be achieved by combining halide atoms intelligently. The purpose of this article is to examine the physical properties of Br substitution at different concentrations in CsPbI3 perovskite. MethodsThe structural, electrical, and optical properties of CsPbI3-yBry (y = 0.5, 1.5, 2.5) compounds have been investigated by using the QUANTUM-ESPRESSO/PWSCF computational package which is based on the density functional theory and the pseudo-potential technique. The thermoelectric properties of CsPbI3-yBry perovskites were calculated by solving the Boltzmann transport equations within the constant relaxation time approximation as employed in the BoltzTraP package. Significant findingsThe structural investigation reveals that when the I atom is substituted by Br, the lattice constant decreases, increasing the bulk modulus and stiffness of compounds. The calculated negative formation energy confirmed the thermodynamic stability of CsPbI3-yBry compounds, and the stability improved with an increase in Br concentration. The electronic investigation indicates the semiconductor nature of compounds with a direct band gap, with a slight increase in electronic band gap as Br concentration increases. The noticeable optical absorption coefficient in the visible range of the electromagnetic spectrum, along with high and tunable optical conductivity, confirms the capability of the compounds for use in optoelectronic devices. The positive value of the Seebeck coefficient revealed the p-type semiconducting nature of CsPbI3-yBry perovskites. Lattice thermal conductivity calculation reveals that this quantity is decreased because of the increase in phonon-phonon interaction due to rising temperature. Thermoelectric investigation indicates that a precise mixture of halide I and Br atoms significantly enhances the electrical and thermal conductivity of perovskites. Also, the substitution of halide I atoms by Br can improve the figure of merit (ZT). The maximum value of ZT at room temperature is equal to 0.99, justifying the brilliant thermoelectric properties of the studied compounds.

Elevated temperature properties of foam concrete: Experimental study, numerical simulation, and theoretical analysis

Foam concrete, as an inorganic cellular material possessing exceptional thermal insulation and fire resistance properties, emerges as a promising candidate for thermal insulation. To achieve a more precise evaluation of its performance under elevated temperatures, the present study comprehensively investigates the thermal characteristics of foam concrete with a combined experimental, numerical, and theoretical approach. Firstly, a high-temperature test is conducted to investigate the influence of temperature and foam concrete density on its macroscopic appearance and internal temperature distribution. Meanwhile, the thermal conductivity of foam concrete at various densities and temperatures is directly measured with a thermal conductivity analyzer. Subsequently, to acquire comprehensive specific heat and thermal conductivity parameters of foam concrete, with a numerical model established within ABAQUS, the genetic algorithm is applied to identify these thermal parameters based on the measurement data from the elevated temperature test. In addition, CT scanning and 3D reconstruction of foam concrete before and after exposure to elevated temperatures are utilized to extract pore characteristics. This facilitates the thermal conductivity calculation using theoretical models, enabling the determination of the thermal conductivity of foam concrete above 600 °C. Through a comparison of the experimental, numerical, and theoretical results, it is recommended to consider the variation of specific heat in three dehydration stages due to the observed notable dehydration. Due to the effect of cracks, the numerically determined thermal conductivity is slightly higher compared to the experimentally and theoretically determined thermal conductivity. Based on the analysis, an improved formula predicting the specific heat of foam concrete, and a formula determining the thermal conductivity of foam concrete subjected to elevated temperature are proposed.

Numerical simulation of transient boiling and void cross flow in non-uniformly heated 5 × 5 rod bundle

A multi-dimensional numerical simulation has been conducted for a transient boiling experiment by applying rapid and non-uniform power to fluid in a 5×5 bundle channel simulated a BWR fuel assembly in atmospheric pressure. The experiment is to investigate thermal hydraulic behavior in applying transient power to subcooled reactor coolant in a stand-by mode of a nuclear power plant such as reactivity initiated accident (RIA). The numerical simulation has been conducted by TRACE (version 5.0 / patch 5) which is a nuclear system analysis code to solve thermal hydraulics of boiling two phase flow by a two fluid model. The bundle channel in the upward vertical direction has been simulated by a three dimensional component with the Cartesian coordinate system attaching heat structures to simulate heating rods for thermal conduction and heat transfer calculation. It has been revealed that the numerical result is possible to simulate the void cross flow through the sub-channel in the bundle channel qualitatively as observed in the experiment. However, there was room for improvement for a wall heat transfer model in TRACE because the numerical result is larger than the experimental result in terms of the rising rate of the rod temperature during the rapid initial increasing of applied power, and it has been inferred that the evaluation model for an onset of nucleate boiling in TRACE also has to be improved because the void initiation time in the numerical result was earlier than the experimental result. Therefore, TRACE has been optimized by modifying the two physical models described above. The numerical results with the modified TRACE have been in better agreement with the experimental results than those with the original TRACE. Using the modified TRACE, a numerical experiment has been conducted putting an inlet velocity and subcooling of fluid and applied power as parameters in addition to the experimental conditions. The results have shown that there is a square law correlation between a void cross flow and applied power to the fluid. The experiments and analyses in this study have elucidated the behavior of transient boiling two phase flow in a fuel assembly of a nuclear power plant at the transient event such as RIA.