Terms Of Temperature Gradient Research Articles

Investigation of irreversible losses in subsonic compressor cascade flow field: A study on viscous dissipation and temperature gradient term in entropy production rate

The entropy generation rate is a widely employed loss characterization approach in the design and optimization of fluid machinery. This approach is utilized to quantitatively determine various types of losses in the flow field, and it is considered that the temperature gradient term in the entropy generation rate can characterize irreversible losses. This research paper aims to address the question of whether the temperature gradient term in entropy production rate can represent the irreversible losses in a flow field. By employing the Reynolds-Averaged Navier-Stokes (RANS) numerical simulation method, the flow field of a subsonic compressor cascade, both with and without wall heating, was investigated. Statistical analysis was conducted to examine the contributions of viscous dissipation, the temperature gradient term in entropy production rate, wall shear stress work, and global power loss. The study reveals the distribution differences of viscous dissipation and the temperature gradient term in entropy production rate within the separated flow region. The research results demonstrate that, under wall heating conditions, viscous dissipation increased by approximately 45%, and the ratio of the temperature gradient term to global power loss increased from 4% to 125%, exceeding the mechanical energy loss in the flow field. The distribution of the temperature gradient term within the separated flow region cannot be explained by irreversible losses, and it exhibits significant discrepancies with the distribution of viscous dissipation losses. Therefore, the temperature gradient term in entropy production rate cannot represent the local irreversible losses, whereas viscous dissipation serves as an accurate measure of local irreversible losses. The research results provide theoretical support for accurately determining the irreversible losses in the flow field.

Simulation study to select optimal solid oxide fuel cells heat-up pattern from single, dual co-flow, and dual counter-flow alternatives

ABSTRACT To facilitate power generation, it is necessary to subject solid oxide fuel cells (SOFCs) to a heating process. The introduction of hot gases into the gas flow channels of fuel cells is a widely employed technique for heating purposes. Hot gases can be introduced into one channel (single-channel heating) or two channels (dual-channel heating). Dual-channel heating can have co- and counter-flow patterns. Despite the existence of several heating patterns in the literature, a comparative analysis of these patterns has not been conducted. This study uses a numerical approach to compare various heating patterns, focusing on the objectives of heat-up time, temperature gradient, and energy consumption. The findings indicate that the co-flow pattern demonstrates superior performance in terms of temperature gradient and heat-up time. However, the counter-flow pattern is more favorable in terms of energy consumption. Upon considering all the objectives concurrently through a multi-objective planning approach, the co-flow pattern, characterized by a temperature increase rate of 1 K s−1 and a gas velocity of 10 m s−1, emerges as the most optimal heat-up plan. This particular plan results in a heat-up time of 685 s, a temperature gradient of 337 K cm−1, and an energy consumption of 3856 J.

Hydraulic conductivity, microstructure and texture of compacted claystone/ bentonite mixtures saturated with different solutions

The French reference concept for the disposal of intermediate- and high-level nuclear waste in the Callovo-Oxfordian sedimentary rock formation (COX-claystone) considers the employment of crushed COX-claystone and its mixture with MX80-bentonite as potential backfill materials installed in drifts and shafts upon termination of the operational phase of the future repository. The fraction of MX80-bentonite in the mixture is limited to 30% in wet weight. Over time, the backfill will be saturated with solutions that originate in the surrounding rock formation and percolate through the concrete lining left in place. The main characteristic of the leachate will be its high pH-value. In addition to the swelling pressure, the sealing properties of the backfill are determined by the hydraulic conductivity. This laboratory experimental study aimed to understand the hydraulic conductivity evolution of potential backfill materials under realistic conditions in terms of compaction conditions, solution chemistry, temperature and hydraulic gradient, and to relate results determined at the macroscale to results of microstructural and textural analysis. Also, the impact of the solution chemistry was evaluated by these means. In the case of mixture-samples, no stabilization of hydraulic conductivity was detected, despite the duration of the experiments being about one year. There was no detectable impact of the solution chemistry in the course of experiments attributable to low reaction kinetics under imposed conditions. Subsequent microstructural analysis indicated material swelling triggering rearrangements in the pore space and lowering the fraction of hydraulic conductive voids. Interestingly, neither the saturation nor the solution chemistry had an impact on the texture of materials.

Role of Surface-Active Element Sulfur on Thermal Behavior, Driving Forces, Fluid Flow and Solute Dilution in Laser Linear Welding of Dissimilar Metals

Understanding heat and mass transfer and fluid flow in the molten pool is very helpful in the selection and optimization of processing parameters, and the surface-active element has an important effect on the heat and mass transfer in laser welding of dissimilar metals. A three-dimensional (3D) numerical model coupled with a sub-model of surface tension, which considers the influence of local temperature and the concentration of surface-active element sulfur at the gas/liquid surface, is used to analyze the thermal behavior, driving forces, fluid flow, and solute dilution during laser linear welding of 304SS and Ni. The relationship between surface tension, driving forces, and the temperature coefficient of surface tension with the spatial distribution of temperature and the surface-active element sulfur is quantitatively analyzed. The simulation results show that the molten pool is fully developed at 45 ms, and the collision of inward and outward convection, with the maximum velocity reaching 1.7 m/s, occurs at the isotherm with a temperature between 2200 K and 2500 K. The temperature-gradient term and concentration-gradient term of surface shear stress play different roles in different positions of the free surface. The local sulfur concentration changes the temperature sensitivity of the surface tension at different sides of the free surface and further determines the transition of convection. Complex fluid flow promotes solute dilution, and the distribution of solute becomes uniform from the front to the rear of the molten pool. The Ni element is transferred to 304SS mainly at the rear side. The work provides theoretical support for the control of joint quality by changing the content of surface-active elements in dissimilar welding.

Derivation and stability analysis of two-fluid model equations for bubbly flow with bubble oscillations and thermal damping

The two-fluid model with bubble oscillations, proposed by Egashira et al. (2004), can explain the properties of cavitating bubbly flow and pressure wave propagation in the bubbly liquid. However, the viscous effect as well as energy conservation leading to temperature changes inside the bubble with bubble oscillations have not yet been considered. Hence, this study aimed to incorporate the viscous (bulk viscosity and drag) and thermal effects to the previously proposed two-fluid model with bubble oscillations. Bulk viscosity was considered by averaging the shear stress term in the single-phase momentum conservation for a Newtonian fluid, and the drag was introduced by transforming the interfacial shear stress. We derived the averaged energy conservation for a general two-phase flow with a thermal conduction inside bubbles and heat transfer between the two phases, and limited this equation to that for a bubbly flow by closing the interfacial temperature gradient term via constitutive equations for a single bubble. Furthermore, we investigated the stability of our proposed one-dimensional model equations using the dispersion analysis. This analysis provided the following insight: (i) The difference in the temperature gradient models had a slight effect on the stability of the proposed model equations; (ii) the thermal conduction inside the bubbles was dominant in the thermal damping in bubbly flows rather than the heat transfer between the two phases; (iii) incorporating both the bulk viscosity and drag stabilized the proposed model equations. Our results provide insights into the development of mathematical models to investigate the thermal effects in bubbly flow with bubble oscillations, such as cavitating bubbly flow and wave propagation in bubbly liquids.

Automating the Generation of Programs Maximizing the Sustained Switching Activity in Microprocessor units via Evolutionary Techniques

During device testing, an important parameter to be considered by the test engineers is the switching activity (SWA) of the circuit under test (CUT). It is well known that the SWA must be kept to a minimum in order to avoid catastrophic scenarios on the CUTs, e.g., unacceptable peak power consumption or over-stressing that can lead to an artificial yield loss. However, there are scenarios, where the inverse, namely the switching activity maximization, can be proven beneficial. For example, this happens during Burn-In testing, when we aim at exercising the circuit under extreme operating conditions in terms of temperature and temperature gradients to accelerate aging phenomena in a controlled manner. In some cases, this is achieved by applying to the CUT stimuli in a functional manner, based on the Software-Based Self-Test (SBST) paradigm. Though, the generation of such appropriate programs for this task represents a challenge for the test engineers. In this paper we consider the scenario where the modules to be stressed are the units of a pipelined processor. We present a method, based on an evolutionary approach, that is able to automatically generate maximum stress programs, i.e., sequences of instructions achieving a high switching activity in the target module. With respect to other approaches, the generated sequences are built from the ground-up, are short and repeatable, thus guaranteeing their easy usability to stress a module (and increase its temperature). The processor we used for our experiments is the Open RISC 1200. Results demonstrate that the generated stimuli from the proposed method are effective in achieving a high value of sustained switching activity within the considered processor modules while also achieves a better results when comparing with other methods (e.g., stuck-at oriented test programs).

3D Multiphysics simulation of microwave heating of bulk metals with parametric variations

Microwave processing of metal base material is a novel and energy-efficient technique. Microwave heating of bulk metal is an emerging method with cost, time, and energy savings over conventional heating methods. This numerical study uses the finite element method-based COMSOL Multiphysics tool to analyse the microwave heating properties of a bulk metal sample. Further in this study, the effects of tooling design assembly and microwave power parameters have been analysed for temperature profile and electric field distribution. The outcome of parametric variations has been analysed in terms of electric field distribution, heating uniformity, temperature gradient, and energy requirement. Experimental results coincided with simulated results in terms of time-temperature characteristics within ±5% error. The heating uniformity of bulk metal can be achieved at low power with small-size component whereas high power creates thermal heterogeneity with high energy consumption. The cylindrical casket geometry shows uniform field distribution with rapid heating of the specimen compared to prismatic geometry. Susceptor's dielectric properties have a significant effect on the homogeneity of the process, and the heating efficiency of the irradiated specimen. The present simulation model can be used to control the heating rate of bulk metal considering various dynamic parametric properties for a complex microwave hybrid heating process.

Numerical study of viscosity and heat flux role in heavy species dynamics in Hall thruster discharge

A two- and three-dimensional velocity space axisymmetric hybrid-PIC model of Hall thruster discharge called Hybrid2D has been developed. The particle-in-cell (PIC) method was used for neutrals and ions (heavy species), and fluid dynamics on a magnetic field-aligned (MFA) mesh was used for electrons. A time-saving method for heavy species moment interpolation on a MFA mesh was developed. The method comprises using regular rectangle and irregular triangle meshes, connected to each other on a pre-processing stage. The electron fluid model takes into account neither inertia terms nor viscous terms and includes an electron temperature equation with a heat flux term. The developed model was used to calculate all heavy species moments up to the third one in a stationary case. The analysis of the viscosity and the heat flux impact on the force and energy balance has shown that for the calculated geometry of the Hall thruster, the viscosity and the heat flux terms have the same magnitude as the other terms and could not be omitted. Also, it was shown that the heat flux is not proportional to the temperature gradient and, consequently, the highest moments should be calculated to close the neutral fluid equation system. At the same time, ions can only be modeled as a cold non-viscous fluid when the sole aim of modeling is the calculation of the operating parameters or distribution of the local parameters along the centerline of the discharge channel. This is because the magnitude of the viscosity and the temperature gradient terms are negligible at the centerline. However, when a simulation’s focus is either on the radial divergence of the plume or on magnetic pole erosion, three components of the ion temperature should be taken into consideration. The non-diagonal terms of ion pressure tensor have a lower impact than the diagonal terms. According to the study, a zero heat flux condition could be used to close the ion equation system in calculated geometry.

Impact of Non-Newtonian Fluids' Rheological Behavior on Double- Diffusive Natural Convection in an Inclined Square Porous Layer

In the current study, natural convection is numerically simulated in a shallow, porous, square cavity that is filled with a non-Newtonian fluid. In terms of temperature and concentration gradients (heat and mass fluxes), the active wall was seen as uniform and constant, whereas the other walls are adiabatic and impermeable. To analyze the behavior of shear-thinning fluids, a Carreau-Yasuda model is utilized, which is suitable for many non-Newtonian fluids. It is presummated that the fluid will fulfill the Boussinesq approximation, be laminar, and be incompressible.

On the validity of the classical plasma conductivity in capacitive RF discharges

The plasma conductivity is an important input parameter for various plasma models. It is typically obtained from a simplified version of the electron momentum balance equation, where only a single inertia term and a simplified description of the collisional momentum transfer are included. The electric field is assumed to be a harmonic function of the driving frequency, higher harmonics of the current and spatial variations are neglected. Through particle-in-cell/Monte Carlo collision (PIC/MCC) simulations and analysis of the electric field generation based on velocity moments of the Boltzmann equation, the validity of this classical model is studied in capacitively coupled plasmas (CCPs). We find that these assumptions/simplifications result in significant inaccuracies of the conductivity in many cases. In single frequency CCPs, a deviation of more than an order of magnitude from the effective PIC-conductivity obtained from the simulations is found at low pressures in the discharge center and at the maximum sheath edge. In the center, this deviation is caused by neglecting the temperature gradient term in the momentum balance equation and adopting an approximation of the Ohmic term in the classical model, while at the maximum sheath edge it is induced by neglecting the density gradient term that accounts for the effect of the ambipolar electric field. The inaccuracy in the discharge center is reduced at higher pressures where the Ohmic term dominates and the approximations made in the classical model are more applicable. Better performance of the classical model is also found under conditions at which the inertia term included in the model plays an important role. Generally, neglecting higher harmonics of the current and spatial variations of plasma parameters is found to cause strong inaccuracies. Thus, the classical model can result in an inaccurate calculation of the power absorbed by electrons. Our results indicate that its applicability must be evaluated for a given set of conditions before using it to avoid introducing errors to plasma models.

Effect of thermal shear on longitudinal spin polarization in a thermal model

By including the recently introduced thermal shear term that contributes to the spin-polarization vector at local equilibrium, we determine longitudinal polarization of $\mathrm{\ensuremath{\Lambda}}$ hyperons emitted from a hot and rotating hadronic medium using the thermal model with single freeze-out. In our analysis, we consider the RHIC top energies and use the model parameters which were determined in the earlier analyses of particle spectra and elliptic flow. We confirm that, unlike the previous calculations done by using only the thermal vorticity, the thermal shear term alone leads to the correct sign of the quadrupole structure of the longitudinal component of the polarization three-vector measured in experiments. However, we find almost complete cancellation between thermal shear and vorticity terms, which eventually leads to disagreement with the data. To clarify the role played by velocity and temperature gradient terms, we present a systematic analysis of different contributions to the longitudinal polarization. Finally, replacing the mass of $\mathrm{\ensuremath{\Lambda}}$ hyperon with its constituent strange quark mass in the polarization formula we achieve agreement with the data.

Numerical simulation of three‐phase‐lag bio‐heat transfer model for generalized coordinate system amidst thermal ablation

AbstractVarious heat transmits models exhibit a thermal response in the tissue during thermal therapies. In the present work, we proposed a three‐phase‐lag (TPL) bio‐heat‐transmitting model including an external laser heating term amidst thermal treatment for the generalized coordinate system. The TPL model is based on the law of heat conduction containing heat flux, temperature gradient, and thermal displacement gradient terms. The solution is determined by implementing a discretization scheme of finite difference in the company of the Runge–Kutta (4,5) technique to examine the temperature repercussion throughout the thermal treatment of the tumor. In addition to this, the impact of various parameters such as phase lag in heat flux, temperature gradient, thermal displacement gradient, the heat generated because of blood perfusion, metabolism, and external heat source term is studied. A comparison has been shown graphically during the thermal treatment. The temperature profile is studied for different coordinate systems, and results are discussed. Moreover, validation has been made of the TPL model used in this paper with the experimental results. Thus the outcomes achieved from this study are purposeful in the therapeutical field, especially for oncologists.

Advanced sandwich structures for thermal protection systems in hypersonic vehicles: A review

A heat shield called the thermal protection system (TPS) is an important structure in hypersonic vehicles as it prevents hot air from entering vehicles and potential impacts from space debris. With the increase in demand for low-cost reusable launch vehicles as well as for searching and exploration of new planets in both unmanned and manned missions, the need for developing an effective TPS has increased across many countries. The structural design of TPSs has become more prominent in the early stage of hypersonic vehicle development. Sandwich structures that have the advantages of low density and high performance are integrated into the structural design of an effective TPS. This paper provides a comprehensive review of recent research efforts on sandwich structures for TPSs. The topics discussed in this paper include aspects of structural and material design, mechanical and thermomechanical performances, and manufacturing methods. In particular, we review and discuss the structural design as well as the material design of sandwich structures for different TPS types with various configurations, including corrugated cores, lattice cores, multilayer cores, foams, honeycomb cores, bio-inspired cores. The materials used for the sandwich structures, such as various types of laminated composite, ceramic matrix composite, and metals, are included. We also discuss the performance of the TPS sandwich structures in terms of temperature gradients, deformation limits, and mechanical strengths and provide a discussion on the manufacturing methods of TPS sandwich structures for hypersonic vehicles. Finally, further research directions and challenges of sandwich structures for TPSs are presented.

Thermal analysis of MHD convective slip transport of fractional Oldroyd-B fluid over a plate

The prime concern of this study is to analyze the generalized time-dependent magnetohydrodynamic (MHD) slip transport of an Oldroyd-B fluid near an oscillating upright plate. The plate is nested in a porous media under the action of ramped heating and nonlinear thermal radiation. Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) derivatives are utilized to constitute fractional partial differential equations that establish slip flow, shear stress, and heat transfer phenomena. Primarily, Laplace transformation is applied to dimensionless fractional models, and later Stehfest’s numerical algorithm is invoked to anticipate solutions of momentum and heat equations in principal coordinates. Moreover, computed solutions of velocity and energy fields are authenticated by Durbin’s and Zakian’s Laplace inversion algorithms. The relations for skin friction and Nusselt number are evaluated in terms of velocity and temperature gradients to efficiently anticipate shear stress and rate of heat transfer at the solid–fluid interface. The respective outcomes are manifested through tables. A critical examination of the current model is carried out and repercussions of variation in implanted parameters on temperature and momentum profiles are graphically elucidated. For the sake of comparison, three limiting fractional models, named second grade, Maxwell, and viscous models, are proposed for the isothermal and ramped temperature cases. Consequently, the observed outcomes affirm that under the isothermal condition, a generalized Maxwell fluid performs the swiftest slip transport compared to other models. Inversely, a second grade fluid specifies the highest velocity profile under ramped temperature case.

Stress–Strain Model for Freezing Silty Clay under Frost Heave Based on Modified Takashi’s Equation

In analyzing frost heave, researchers often simplify the compressive modulus of freezing soil by considering it as a constant or only as a function of temperature. However, it is a critical parameter characterizing the stress–strain behavior of soil and a variable that is influenced by many other parameters. Hence, herein several one-dimensional freezing experiments are conducted on silty clay in an open system subjected to multistage freezing by considering the compressive modulus as a variable. First, freezing soil under multistage freezing is divided into several layers according to the frozen fringe theory. Then, the correlation between the freezing rate and temperature gradient within each freezing soil layer is investigated. Takashi’s equation for frost heave analysis is modified to extend its application conditions by replacing its freezing rate term with a temperature gradient term. A mechanical model for the stress–strain behavior of freezing soil under the action of frost heave is derived within the theoretical framework of nonlinear elasticity, in which a method for determining the compressive modulus of freezing soil with temperature gradient, overburden pressure, and cooling temperature variables is proposed. This study further enhances our understanding of the typical mechanical behavior of saturated freezing silty clay under frost heave action.

Electron power absorption dynamics in a low pressure radio frequency driven capacitively coupled discharge in oxygen

We use the one-dimensional object-oriented particle-in-cell Monte Carlo collision code oopd1 to explore the properties and the origins of both the electric field and electron power absorption within the plasma bulk for a capacitively coupled oxygen discharge operated at 10 and 100 mTorr for a gap distance of 45 mm. The properties of the electric field at three different time slices as well as time averaged have been explored considering the moments of the Boltzmann equation. The electron power absorption is distinctly different at these operating pressures. The most relevant contributions to the electric field at different time steps come from the pressure terms, the ambipolar and the electron temperature gradient terms, along with the ohmic term. The same applies for the electron power absorption. At both 10 and 100 mTorr, the relative ohmic contribution to the electron power absorption remains roughly the same, while the ambipolar term contributes to power absorption and the temperature gradient term to electron cooling at 100 mTorr, and the opposite applies at 10 mTorr. At 100 mTorr, the discharge is weekly electronegative, and electron power absorption is mainly due to sheath expansion, while at 10 mTorr, it is strongly electronegative, and the electron power absorption occurs mainly within the electronegative core and the drift-ambipolar mode dominates. The agreement between the calculated values and the simulations is good for both the electric field and the electron power absorption within the plasma bulk and in the collapsed sheath region for all the cases considered.

Experimental investigation of thermally activated glass fibre reinforced gypsum roof

Switch to energy-efficient air conditioning systems and the use of eco-friendly building materials would result in significant energy savings and reductions in CO2 emissions. Thermally activated building system (TABS) is a promising low-energy cooling technology, which provides better thermal comfort than the conventional air conditioning system. In TABS, cooled water circulated in the tubes embedded in one or any combination of roof, floor slab and walls, not only reduces the heat ingress but also cools the building. Integrating TABS with eco-friendly building materials like glass fibre reinforced gypsum (GFRG) could be an intertwining solution. A hybrid system that integrates TABS with GFRG roof is investigated in this study. The thermal behavior of this thermally activated glass fibre reinforced gypsum (TAGFRG) roof is analysed experimentally in terms of diurnal temperature gradients, thermal images of the interior and exterior roof surfaces, decrement factor and water temperature variations. The reinforcement zone of the TAGFRG roof handled a higher cooling load compared to that of air cavity zones. The diurnal temperature fluctuation of interior roof surface at the air cavity and reinforcement zones is reduced by 5.1 and 6.7 °C respectively by TAGFRG roof cooling.

2D Simulation for CH4 Internal Reforming-SOFCs: An Approach to Study Performance Degradation and Optimization

Solid oxide fuel cells (SOFCs) are a well-developed technology, mainly used for combined heat and power production. High operating temperatures and anodic Ni-based materials allow for direct reforming reactions of CH4 and other light hydrocarbons inside the cell. This feature favors a wider use of SOFCs that otherwise would be limited by the absence of a proper H2 distribution network. This also permits the simplification of plant design avoiding additional units for upstream syngas production. In this context, control and knowledge of how variables such as temperature and gas composition are distributed on the cell surface are important to ensure good long-lasting performance. The aim of this work is to present a 2D modeling tool able to simulate SOFC performance working with direct internal CH4 reforming. Initially thermodynamic and kinetic approaches are compared in order to tune the model assuming a biogas as feed. Thanks to the introduction of a matrix of coefficients to represent the local distribution of reforming active sites, the model considers degradation/poisoning phenomena. The same approach is also used to identify an optimized catalyst distribution that allows reducing critical working conditions in terms of temperature gradient, thus facilitating long-term applications.

A Note for Probabilistic Model of Polymer Crystallization in Temperature Gradients

A polymer crystallization kinetics model is the most important way to characterize the crystallization rate of polymers. Because polymers are poor heat conductors, the cooling of thick-walled shapes results in temperature gradients. Piorkowska (Piorkowska, E. J. Appl. Polym. Sci., 2002, 86: 1351–1362.) derived the probabilistic analytical model of polymer crystallization in temperature gradients based on the Avrami equation. However, there are some misunderstandings when using this model. Here, isotactic polypropylene (iPP) is chosen as a model polymer and its crystallization is studied in a temperature gradient field. Based on the results of the Monte Carlo method, the probabilistic model methodology is discussed. The results show that when the product has a large temperature gradient and a large temperature difference, the probabilistic model cannot be used directly; instead, it is necessary to use the average probabilistic model. This means that the sample should be divided into several smaller parts and the probabilistic model used separately for each small part. The values are then averaged to obtain the mean conversion degree of the melt into spherulites for the whole product. The effects of the division number are also discussed. The goal of the present paper is to better understand the polymer crystallization kinetics model in terms of temperature gradients.

Xe gas bubbles evolution in UO<sub>2</sub> fuels–A phase field simulation

Owing to the large formation energy of vacancies and inert gas atoms (Xe and Kr) in nuclear fuel (UO2), the thermodynamic equilibrium concentrations of these species are extremely low in the UO2 matrix, which makes it extremely difficult to conduct quantitative study of gas bubbles evolution by phase-field method (PFM). In this study, a more physics based quantitative phase-field model has been proposed. The free energy density of the system was derived according to the principles of thermodynamics and KKS model, the UO2 tri-vacancy, Xe gas atoms and gas bubbles were considered in the system. This model enables one to study the gas bubble growth with extremely low concentrations of vacancy and Xe gas atom in the UO2 matrix. The influence of temperature, vacancy and Xe gas atom generation rates on single and multi-gas bubbles evolution were studied. At high temperature and with high generation rates of vacancies and Xe gas atoms, the gas bubbles had higher growth rate. In addition, the effect of temperature gradient on gas bubble migration was also studied by adding a temperature gradient term in the Cahn-Hillard equations. The gas bubble preferred to migrate to high temperature area. Their shape changed from initial circular shape to a prolate shape along the direction of temperature gradient, which is consistent with the experimental results. The simulation results confirmed the formation of center cavity in the nuclear fuel pellet. The simulation results are consistent with the classical rate theory and experimental observations.