Two-phase Mixture Model Research Articles

Numerical investigation of grain size effect on velocity-skewed oscillatory sheet flow

Wave-induced sheet flow leads to intense sediment transport. Fine sand and medium/coarse sand exhibit opposite directions of net sediment transport under velocity-skewed oscillatory sheet flows. A newly developed two-phase mixture model is employed to simulate the sediment transport under these conditions. The model accounts for particle stress, two-phase momentum exchange, and turbulence modulation. The effects of grain size on flow characteristics and sediment transport are primarily investigated. The model effectively reproduces the spatial and temporal distributions of two-phase velocities and sediment concentration as well as the periodic distribution of erosion depth. Comparisons between configurations with medium and fine sand demonstrate that the grain size impacts sediment transport in two main ways. First, the grain size influences the periodic variations in erosion depth and the quantity of suspended sediment. A decrease in the grain size increases the phase residual and phase lag, enhancing offshore sediment transport. Second, suspended sediments modulate the flow dynamics within the oscillatory boundary layer. Through the mobile bed effect and density stratification, the grain size affects two-phase velocities, turbulence, and net sediment transport.

Thermal and Entropic analyses of free convection of nanofluid in a partially heterogeneous porous chamber using the two-phase mixture model

Entropy generation and convection heat transfer in a partially porous chamber with different side wall temperatures using CuO–H2O have been investigated. The importance of this issue is wide application of the results in solar collectors, thermal extrusion systems, heat exchangers, bio-medicine, nuclear waste disposal, etc. The innovation of the present work is related to the investigation of fluid and heat fields and entropy generation by using a matrix with subordination of porosity to the vertical axis and permeability, thermal conductivity, and viscosity with subordination of porosity. To obtain accurate results, the two-phase mixture model was used, and thermal conductivity and viscosity of nanofluid were simulated by experimental models by temperature and volume fraction dependence. Governing equations are solved by the FVM. The main findings indicate that the best and worst optimization factor will occur in the porous matrix ε = ε(y2) and ε = -ε(y2), respectively, which is 113 % and 86 % of NH of the homogeneous matrix, respectively. Also increasing the filling of the cavity, highly improves NH, so that the NH will reach from 1.19 to 1.82 with the increase of S from 0.25 to 1.

An approach for topology optimization of heat sinks for two-phase flow boiling: Part 1 – Model formulation and numerical implementation

Two-phase flow boiling in heat sinks and cold plates is attractive for various thermal management applications due to high effective heat capacity rates and high heat transfer coefficients compared to single-phase operation. In addition, multi-physics topology optimization is sought for generation of high performance thermal management components. Yet, the design of heat sinks using topology optimization has been restricted to single-phase flow physics, due to incompatibility between available two-phase flow models and traditional single-phase topology optimization approaches. Interface-capturing two-phase flow models are too computationally expensive for optimization; mixture and two-fluid models that treat the liquid and vapor phases as an interpenetrating continuum with interfacial transport phenomena captured through empirical correlations are computationally tractable for heat-sink-scale optimization. However, the penalization approaches commonly used to define the structures formed during topology optimization results in arbitrary fin and channel geometries for which a universal two-phase flow correlation is not available. To enable coupling with two-phase mixture models, this work leverages a homogenization approach to topology optimization wherein heat sink designs are represented using spatially varying microstructures with optimized dimensions. A predefined microstructure geometry is chosen for which two-phase flow correlations exist and therefore topology optimization can be performed. This work is the first to develop a topology optimization algorithm using a mixture model for simulating two-phase flow boiling to design heat sinks and cold plates. Part 1 of this study develops and implements the algorithm to investigate topology optimized heat sinks at various heat inputs, topology optimization grid sizes, and maximum vapor quality constraints. Topology optimized heat sinks designed for single-phase versus two-phase flow are compared. There are significant differences in hydraulic and thermal responses of the single-phase and two-phase designs due to high effective heat capacity rates and high heat transfer coefficients of flow boiling. A companion paper (Part 2) focuses on manufacturing, model calibration, and experimental validation of the topology optimized heat sinks under two-phase flow boiling. The algorithm demonstrated in this work extends the capabilities of topology optimization to two-phase flow physics, and thereby enables the design of various two-phase flow components such as evaporators, condensers, heat sinks, and cold plates.

An approach for topology optimization of heat sinks for two-phase flow boiling: Part 2 – Model calibration and experimental validation

Flow boiling offers increased heat transfer coefficients and effective heat capacity rates that can be leveraged by topology optimization (TO) to generate high-performance microchannel heat sinks. Topology optimization of heat sinks having two-phase flows can be accomplished using the homogenization approach wherein designs are represented as spatially varying distributions of microstructures, as demonstrated in Part 1 of this two-part study. Flow and heat transfer within the microstructures are captured using a two-phase mixture model featuring an effective porous medium formulation. However, closure of these governing equations requires empirical correlations for pressure drop and heat transfer that are specific to the operating conditions, geometry, and surface finish. Therefore, it must be demonstrated these available correlations can be successfully calibrated over a range of microstructural variations present within the homogenization framework, so as to attain the required prediction generality and accuracy needed to ensure the resulting designs achieve Pareto-optimality. This Part 2 of our study successfully demonstrates a comprehensive end-to-end process for two-phase flow model calibration, topology optimized design generation, and experimental validation of optimized performance for flow boiling heat sinks. To this end, a TO algorithm with the homogenization approach and a two-phase mixture model is implemented using available flow boiling correlations for microchannels. A set of uniform pin fin calibration samples are additively manufactured and experimentally tested under flow boiling at various flow rates and heat inputs for model calibration. All of the unknown/free coefficients in the adopted correlations are determined by minimizing the error between the model predictions and the experimental measurements using gradient-based optimization. The calibrated topology optimization algorithm is then used to generate a Pareto-optimal set of heat sinks optimized for minimum pressure drop and thermal resistance during flow boiling. Experimental characterization of these additively manufactured heat sinks, unseen during the model coefficient calibration process, reveals that the measured Pareto optimality curve matches that predicted by the topology optimization algorithm. Lastly, a heat sink design is generated for a design space involving multiple hot spots and background heating to showcase the capability of the experimentally calibrated two-phase topology optimization algorithm at handling complex boundary conditions. The optimized heat sink intelligently distributes an adequate amount of coolant flow to each of the heated regions to avoid local dry-out. This work demonstrates a complete framework for two-phase topology optimization of heat sinks through experimental calibration of flow boiling correlations to the porous medium used by the homogenization approach.

Effect of Marangoni flow during the solidification of a Fe-0.82wt.%C steel alloy

A two-phase Mixture model is proposed to simulate the liquid-solid phase transition of a Fe-0.82wt%C steel alloy under the effect of Marangoni flow. This model simplifies computations by solving a single momentum and enthalpy equation for the mixture phase using a three-dimensional finite volume method. The simulation involves solidifying a rectangular ingot (100 × 10 × 100 mm3) from the cold bottom surface towards the hot-free surface at the top. To facilitate heat exchange with the surrounding environment, a high heat transfer coefficient of h = 600 W/m2/K was applied on the bottom surface to establish an upward solidification direction. However, a lower heat transfer coefficient of 20 W/m2/K was applied on the top free surface, which was considered flat. This study aims to examine the effect of Marangoni flow generated by surface tension on flow and segregation patterns. The results show that the Marangoni flow emerges at the free surface and penetrates into the liquid depth, leading to the formation of hexagonal patterns along the liquid thickness. Upon full solidification, macro-segregation also exhibits hexagonal structures, mirroring the stationary hexagonal shapes generated by Marangoni flow.

Mixed Convection in an Open Cavity with an Internal Fin Filled with Nanofluid in a Porous Medium Using Two-Phase Mixture Model

Mixed Convection in an Open Cavity with an Internal Fin Filled with Nanofluid in a Porous Medium Using Two-Phase Mixture Model

Investigation of the effect of fins and magnetic field on flow maldistribution and two-phase mixture model simulation of nanofluid heat transfer in microchannel heat sink

Investigation of the effect of fins and magnetic field on flow maldistribution and two-phase mixture model simulation of nanofluid heat transfer in microchannel heat sink

A modified local thermal non-equilibrium model of transient phase-change transpiration cooling for hypersonic thermal protection

Aiming to efficiently simulate the transient process of transpiration cooling with phase change and reveal the convection mechanism between fluid and porous media particles in a continuum scale, a new two-phase mixture model is developed by incorporating the local thermal non-equilibrium effect. Considering the low-pressure and high overload working conditions of hypersonic flying, the heat and mass transfer induced by capillary and inertial body forces are analyzed for sub-cooled, saturated and super-heated states of water coolant under varying saturation pressures. After the validation of the model, transient simulations for different external factors, including spatially-varied heat flux, coolant mass flux, time-dependent external pressure and aircraft acceleration are conducted. The results show that the vapor blockage patterns at the outlet are highly dependent on the injection mass flux value and the external pressure, and the reduced saturation temperature at low external pressure leads to early boiling off and vapor blockage. The motion of flying has a large influence on the cooling effect, as the inertial force could change the flow pattern of the fluid inside significantly. The comparison of the results from 2-D and 3-D simulations suggests that 3-D simulation shall be conducted for practical application of transpiration cooling, as the thermal protection efficiency may be overestimated by the 2-D results due to the assumption of an infinite width length of the porous plate.

Thermo-hydraulic and entropy generation analysis of nanofluid flow with variable properties in various duct cross sections: a 3-D two-phase approach

A three-dimensional computational fluid dynamics (CFD) study is carried out to explore the effect of duct cross section on the thermo-hydraulic performance of various ducts. A finite volume-based scheme with an SST k-omega model and mixture model (two-phase model) was used to obtain more realistic results. A two-phase mixture model was used to consider the movement between base fluid and nanoparticles. Al2O3 nanoparticle having a volume fraction of 0.01% and 42 nm as particle size, the heat transfer and friction factor characteristic are studied for turbulent flow regime (3000 < Re < 9000) with variable thermo-physical properties. A maximum enhancement of 86% in heat transfer rate is obtained for the serpentine duct compared to the conventional circular duct at Re = 4500. Owing to a significantly lower increase in pressure drop, the elliptical duct has the highest thermo-hydraulic performance parameter of 1.54 relative to the circular duct. Further, to analyze the heat transfer quality, the entropy generation rate is studied, and it is observed that the square duct reported the highest with an increase of 60% and the elliptical duct the lowest with a reduction of 54% relative to the circular duct. This study can aid in choosing the duct geometry to enhance the heat transfer rate with nanofluid for applications such as solar-thermal, heat exchangers, etc.

The Impact of Marangoni and Buoyancy Convections on Flow and Segregation Patterns during the Solidification of Fe-0.82wt%C Steel.

Due to the high computational costs of the Eulerian multiphase model, which solves the conservation equations for each considered phase, a two-phase mixture model is proposed to reduce these costs in the current study. Only one single equation for each the momentum and enthalpy equations has to be solved for the mixture phase. The Navier-Stokes and energy equations were solved using the 3D finite volume method. The model was used to simulate the liquid-solid phase transformation of a Fe-0.82wt%C steel alloy under the effect of both thermocapillary and buoyancy convections. The alloy was cooled in a rectangular ingot (100 × 100 × 10 mm3) from the bottom cold surface to the top hot free surface by applying a heat transfer coefficient of h = 600 W/m2/K, which allows for heat exchange with the outer medium. The purpose of this work is to study the effect of the surface tension on the flow and segregation patterns. The results before solidification show that Marangoni flow was formed at the free surface of the molten alloy, extending into the liquid depth and creating polygonized hexagonal patterns. The size and the number of these hexagons were found to be dependent on the Marangoni number, where the number of convective cells increases with the increase in the Marangoni number. During solidification, the solid front grew in a concave morphology, as the centers of the cells were hotter; a macro-segregation pattern with hexagonal cells was formed, which was analogous to the hexagonal flow cells generated by the Marangoni effect. After full solidification, the segregation was found to be in perfect hexagonal shapes with a strong compositional variation at the free surface. This study illuminates the crucial role of surface-tension-driven Marangoni flow in producing hexagonal patterns before and during the solidification process and provides valuable insights into the complex interplay between the Marangoni flow, buoyancy convection, and solidification phenomena.

Flow and irreversible mechanism of pure and hybridized non-Newtonian nanofluids through elastic surfaces with melting effects

Abstract The significance of nanofluid research in nanotechnology, pharmaceutical, drug delivery, food preparation, and chemotherapy employing single- and two-phase nanofluid models has drawn the attention of researchers. The Tiwari–Das model does not capture the diffusion and random movement of nanoparticles (NPs) when they are injected into complex functional fluids. In order to fix the peculiar behavior of NPs, more complex models like the Buongiorno model are coupled with the single-phase model. To examine the heat-mass transfer attributes of nanofluids, a single- and two-phase mixture model is coupled for the first time. The effect of hybrid NPs on the hemodynamic properties of the blood flow through a stretched surface with interface slip in the neighborhood of the stagnation point is examined. Due to their significance in medicinal uses and nominal toxicity, blood is loaded with zinc–iron ( ZnO − F e 2 O 3 ) {\rm{ZnO}}\left-{\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3}) NPs. However, blood is speculated to have the hematocrit viscosity of the Powell–Eyring fluid. The single-phase model predicts an improvement in heat transport due to an increased volumetric friction of NPs, while the two-phase models provide closer estimates of heat-mass transfer due to Brownian and thermophoretic phenomena. Entropy evaluation predicts the details of irreversibility. The mathematical structures are effectively solved with a Runge–Kutta fourth-order algorithm along with a shooting mechanism. The Eyring–Powell parameters decrease the drag coefficient and mass/thermal transport rate. A higher estimation of the slip, material, and magnetic parameters decreases the flow behavior. The Bejan number increases with the diffusion parameter and decreases as the magnetic and Brinkman numbers increase. The effect of iron oxide ( F e 2 O 3 ) \left({\rm{F}}{{\rm{e}}}_{2}{{\rm{O}}}_{3}) is observed to be dominant.

Improving lithium battery cooling: analyzing the impact of air flow, nanofluid flow, and phase change materials

In this study, a finite element analysis is employed to numerically investigate the thermal behavior of a battery pack comprising cylindrical lithium-ion cells. The system incorporates air cooling with phase change material (PCM) surrounding the batteries and nanofluid (NFD) circulating within the PCM through tubes of varying diameters (ranging from 2 mm to 6 mm) at flow rates (FRT) spanning 5 mL/min to 20 mL/min. A two-phase mixture model is applied to analyze the behavior of the NFD as it changes phase. The transient simulation covers a 1-h period to assess temperature variations of the NFD, batteries, surrounding air, PCM, and the phase change process within the PCM. Our results indicate that variations in NFD flow rate (NFFR) do not significantly affect the PCM’s molten fraction during PCM melting, coinciding with an increase in battery temperature (TBT). However, during the PCM refreezing phase, a FRT of 15 mL/min results in the highest quantity of solid PCM. The outlet temperature (TOT) of the NFD demonstrates a cyclical pattern of increase and decrease over time. We observe that when the NFD temperature is elevated, the lowest TOT of the NFD is associated with a FRT of 5 mL/min. Conversely, when the NFD temperature is lowered, this FRT leads to the highest TOT of the NFD. The TBT exhibits some sensitivity to changes in FRT within the initial half-hour, with a subsequent decline, particularly with a FRT of 15 mL/min.

Numerical investigation on pillow plate heat exchangers: Effects of nanofluid and geometry

The current research involves a comprehensive numerical simulation of nanofluid flow within a pillow-plate heat exchanger. Al2O3-water nanofluid and water are used as the working fluids, simulated using a two-phase mixture model. The study explores the influence of geometric properties on the heat exchanger’s hydrodynamic and thermal performance. It also delves into the utilization of nanofluids as the working medium and its impact on dimensionless pressure drop, Nusselt numbers, and dimensionless temperature. An innovative aspect of this research lies in the integration of artificial intelligence (AI) techniques for heat exchanger design optimization. Specifically, a Random Forest Regressor (RFR) AI model is employed to predict crucial parameters, including heat transfer coefficient (HTC) and pressure drop, based on input design variables. Key findings reveal that non-linear hole layouts in heat exchangers significantly improve Nusselt numbers by up to 25 percent. Conversely, larger holes result in higher pressure drops. The use of nanofluids enhances thermal efficiency by up to 10% while increasing pressure drop by around 7%.

The effect of alphabet-shaped twisted tape on thermo-fluidic properties in a shell-tube type heat exchanger: A comparative study utilizing a two-phase mixture model

In the present Computational Fluid Dynamic (CFD) simulation, the impact of various shapes of alphabet twisted tape in a shell –tube type of heat exchanger on the pressure drop, temperature, velocity distribution, and heat transfer coefficient was studied numerically. The best shape of the twisted tape was selected by thermo-hydraulic analysis. SIMPLE algorithm and Finite Volume Method (FVM) were then implemented to solve the conversion formulas. Conversion equations were discretized using second-order upwind discretization. Comparing the results of different types of twisted tape, Case I (W-shaped tape) exhibited the best performance and the utmost pressure differences. Furthermore, the utmost heat transfer factor was obtained by W shape twisted tape. Also, the helical baffles illustrated the best performance of the shell-part baffles in the shell-tube type of heat exchanger. Comparison between single and two-phase flow by utilizing mixture model for heat transfer factor and pressure difference reveal the negligible changes. On the quant part, FOM amount have been shown a great significance (1.3439) in the shell part for helical baffle type.

Numerical investigation on the double-layer porous plate of transpiration cooling with phase change under different heat flux

Transpiration cooling is a potential active thermal protection method for aircraft under severe thermal environment. Though it is cooling efficiency that is of concern in most structural designs, the injection pressure is equally critical for transpiration cooling especially when using liquid as coolant. To enhance the cooling performance of transpiration cooling with phase change, double-layer porous plate that upper and lower layers have different porosities is presented and adopted. A new numerical simulation model, modified Two-Phase Mixture Model with Local Thermal Non-Equilibrium is used to investigate two-phase flow and fluid-solid coupled heat transfer under different heat flux. The results reveal that overall pressure drop of the porous plate is mostly dependent on vapor region which has higher flow resistance, so designing larger porosity for the upper layer where is occupied by vapor region can effectively reduce the coolant injection pressure. Besides, since the specific heat of liquid is larger than that of vapor, designing smaller porosity for the lower layer where liquid region is located can lead to lower surface temperature when increasing coolant mass flow. Moreover, designing a thinner lower layer in the region exposed to high heat flux could obtain desired coolant distribution. The double-layer porous plate with unequal thickness can reduce the injection pressure by 20.8 % and improve its relative uniformity by 33.3 % while decreasing the surface temperature at the same time. The new evaluation of cooling performance and the new structure have important guidance and practical significance of transpiration cooling in the actual application of aircraft in severe thermal environment.

Effect of Magnetic Field and Impingement Jet on the Thermal Performance and Heat Transfer of Hybrid Nanofluids

In this paper, we focus on modeling the flow and heat transfer behavior of SiO2–CuO/water hybrid-nanofluid impingement jet used for CPU cooling, where this flow is subject to a magnetic field. For this purpose, a new geometry has been adopted that contributes to the processor’s cooling while controlling the dynamic field and making it stable. The assessments were performed using two-phase mixture model under laminar forced convection flow setting. The working liquid consists of SiO2 and CuO nanoparticles with a diameter of 20 nm dispersed in the base fluid. The flow field, heat transfer, thermal efficiency, loss pressure and entropy production were analyzed in terms of volumetric concentration, Hartmann number, and Reynolds number. The simulation approach was applied to compare previous research findings, and a considerable agreement was established. Results indicate that the use of outside magnetic forces aids in maintaining the working fluid’s stability. Boosting the Hartmann number to maximum values increases pressure drop and pumping power while lowering system efficiency by 5%, 5% and 19%, respectively. Compared to pure water, hybrid nanofluids yield to a considerable drop in mean CPU temperature up to 10 K. The hybrid nanofluid’s efficiency improves as the Reynolds number and nanoparticle volume fraction rise, where the improvement in the best conditions reaches up to 21% and 27%, respectively. Using the following nanoparticles: SiO2, CuO and SiO2–CuO improves the Nusselt number of the base fluid by 15%, 36% and 30%, respectively. While the pressure drop values increase by 5%, 17% and 11%. Regarding the entropy production, the results reveal that the total entropy values increase slowly with the volume fraction of the nanoparticles, and the maximum increase does not exceed 5% in the best case. On the other hand, the increase in the total entropy values reaches 50% when Ha = 20. Lastly, two correlations for the Nusselt number and the friction factor are suggested, with errors of no more than ±9% and ±7%, respectively.

Heat transfer and thermal efficiency enhancement using twisted tapes in sinusoidal wavy tubes with nanofluids: a numerical study

PurposeThe purpose of the study is to propose a novel implementation of twisted tape in sinusoidal wavy-walled tubes to enhance the rate of heat transfer without compromising thermal efficiency. The study numerically investigates the fluid flow characteristics and analyzes the effect of different geometrical configurations, including wall wave amplitude, tape twist angles and nanoparticle volume fractions, on heat transfer improvement and performance factor.Design/methodology/approachThis problem is numerically investigated using computational fluid dynamics, and the method is the finite volume method. A two-phase mixture model is used for nanofluid modeling.FindingsThe study investigated the effect of wall waviness, twisted tape, and nanoparticles on forced convective heat transfer and friction factor behavior in laminar pipe flow in three different Reynolds number regimes. The results showed that implementing twisted tape in wavy tubes significantly increased the rate of heat transfer and the performance factor, with the best twist ratio between 90 and 180°. Adding nanoparticles also enhanced heat transfer and performance factor, but to a lesser extent than wavy wall-twisted tape combinations. The study suggests selecting a proper combination of wavy wall and twisted tape at each Reynolds number to achieve an optimum solution.Originality/valueTo the best of the authors’ knowledge, the implementation of the selected passive methods in sinusoidal wavy tubes has not been studied before, and no previous studies have taken into account such a mix of heat transfer improvement techniques.

Numerical investigation of the effect of two-phase hybrid nanofluids on thermal-hydraulic performance and PEC of parabolic solar collectors

This study investigated the effect of hybrid nanofluids Al₂O₃-SiO₂/water and Al₂O₃-CuO/water on heat transfer (HT) in parabolic solar collectors. The results revealed that, in general, the Nusselt number (Nu) and pressure drop enhance with increasing total volume fraction (ϕtot). The Two-phase Mixture model and SST k-ω turbulence model have been used for simulations. The Reynolds number range is 5000 to 30,000. At a constant ϕtot, the Nu increases with the volume fraction (ϕ) enhancement of Al₂O₃ and CuO in their corresponding hybrid nanofluids, but the pressure drops for both hybrid nanofluids do not follow the same trend as the Nu with the increment of nanoparticle concentration. Their performance coefficient does not show a uniform trend compared to the percentage of nanoparticles composition in hybrid nanofluids. For example, the value of the performance coefficient (PEC) for the percentage of Al₂O₃ (0.1%) - CuO (0.4%) and Al₂O₃ (0.75%) - CuO (0.25%) is almost equal. The maximum enhancement of Nu in Al₂O₃ (0.25%) - CuO (0.75%) /water is about 47%, and this value is 33% for the other hybrid nanofluid at the same ϕtot. Also, in addition to the total volume fraction, the performance coefficient strongly depends on the percentage of nanoparticles in the hybrid nanofluid at a fixed volume fraction. Nu increases of 26% and 48% indicate the total volume fractions of 0.5% and 1%, respectively, compared to the base fluid.

Numerical investigation of the effect of perforation inclination angle on the performance of a perforated pin-fin heatsink using two-phase mixture model

The numerical analysis of water/silver nanofluid (NF) flow in a perforated pin-fin heatsink (PFHS) is performed considering the nanoparticle concentration (φ) of 1% and seven different perforation inclination angles (γ). The configuration with the best hydrothermal performance and the lowest entropy generation rate at different values of Reynolds number (Re) is determined using the two-phase mixture technique. According to the results, the γs of 45º and -45º exhibit the highest heat transfer coefficient (h) and the lowest thermal resistance factor and mean CPU temperature at four studied Res of 500, 1000, 1500, and 2000. Consequently, the highest hydrothermal performance evaluation criterion (PEC) was obtained for the heatsink with γ of 45º followed by γ of -45º at Re of 500; the increase in Re reduced the PEC due to the pressure drop. PEC of the heatsink with γ of 45º was almost 11.06–16.63% higher than that with γ of 0º. In addition, γ of -15º and 45º provided the lowest frictional and thermal entropy generation rates (S˙fr and S˙th) at Re of 1500 and then 2000. S˙fr and S˙th for γ of 45º were 1401% and 97% lower than those for γ of 0º at Re=1500.

Oscillation and evolution characteristics of nanofluid thermocapillary convection in rectangular cavity

To analyze the oscillation and evolution characteristics of nanofluid thermocapillary convection instability, a two-phase mixture model was utilized to simulate nanofluid thermocapillary convection in a rectangular cavity and investigate the impact of nanoparticle volume fraction on the oscillatory flow. The results indicate that the two-phase mixture model has a lower critical temperature difference compared to the single-phase model, and the oscillation mode exhibits distinct changes for small nanoparticle volume fractions. At a high Marangoni number, the thermocapillary convection displays periodic oscillatory behavior, with the flow field composed of several dynamic convection vortices. An increase in nanoparticle volume fraction results in a decrease in the critical temperature difference, as well as the amplitude and variation range of temperature oscillation. However, the oscillation period shows an approximate linear increase. Furthermore, there is a non-uniform distribution of nanoparticles at the vicinity of solid wall, especially a significant concentration gradient near the side wall.