Convective Phase Research Articles

Positive Solutions for Convective Double Phase Problems

Positive Solutions for Convective Double Phase Problems

Grey‐zone simulations of shallow‐to‐deep convection transition using dynamic subgrid‐scale turbulence models

AbstractWe examine the ability of two dynamic turbulence closure models to simulate the diurnal development of convection and the transition from dry to shallow cumuli and then to deep convection. The dynamic models are compared with the conventional Smagorinsky scheme at a range of cloud‐resolving and grey‐zone resolutions. The dynamic schemes include the Lagrangian‐averaged, scale‐dependent dynamic Smagorinsky model and a Lagrangian‐averaged, dynamic mixed model. The conventional Smagorinsky model fails to reproduce the shallow convection stage beyond the large‐eddy simulation regime, continuously building up the convective available potential energy that eventually leads to an unrealistic deep convection phase. The dynamic Smagorinsky model significantly improves the representation of shallow and deep convection; however, it exhibits issues similar to the conventional scheme at coarser resolutions. In contrast, the dynamic mixed model closely follows the large‐eddy simulation results across the range of sub‐kilometre simulations. This is achieved by the combined effect of an adaptive length scale and the inclusion of the Leonard terms, which can produce counter‐gradient fluxes through the backscatter of energy from the subgrid to the resolved scales and enable appropriate non‐local contributions. A further sensitivity test on the inclusion of the Leonard terms on all hydrometeor fluxes reveals the strong interaction between turbulent transport and microphysics and the possible need for further optimisation of the dynamic mixed model coefficients together with the microphysical representation.

Numerical simulation on reservoir stimulation assisted depressurization development of hydrate bearing layers based on embedded discrete fractures

As the global demand for energy escalates, the increasing severity of environmental pollution underscores the urgent need for efficient development of hydrates—a promising, clean energy source with vast reserves. It is imperative to carry out reservoir stimulation on low-permeability hydrate reservoirs to enhance fluidity. In order to simulate the geometric morphology of complex fractures, based on the bifurcation fracture morphology in existing laboratory experiments, combined with embedded discrete fracture model and tree fractal theory, the multiphase and multi-component seepage mechanism, thermal conduction, thermal convection, and hydrate phase change in hydrate-bearing layers were comprehensively considered. Based on the TOUGH code, a TOUGH-EDFM module is developed to realize numerical simulation of three-dimensional four-phase four-component hydrate reservoir stimulation assisted depressurization development. We clarify the production capacity change characteristics, main methane dissociation zones, and gas-water migration trends after reservoir stimulation. The results indicate that in the multi-level branching fracture area, the increase in hydrate production in the primary fracture area of the reservoir is greater than that in the secondary fracture branching area. When the fractal scale factor is 0.56, the increase in production in the secondary branch fracture zone is 48% of that in the primary fracture zone. The cumulative gas production after the reservoir stimulation of Class III hydrate reservoirs can surpass that of the basic depressurization scheme by a remarkable 2.21 times, and the overall hydrate dissociation proportion has increased by 60%, indicating the ability of the reservoir to effectively utilize the energy within hydrate reservoirs, thereby significantly improving its depressurization development potential.

Inhibiting Leidenfrost phenomenon with granulated polymer film

Inhibiting Leidenfrost phenomenon has been conventionally mediated by texturing materials to facilitate the solid-liquid contact or by arranging vapor channels to promote vapor evacuation. However, it remains challenging to break the trade-off between the high Leidenfrost point and the high heat transfer efficiency because elevating Leidenfrost point is often accompanied by the increase of thermal resistance. We propose a method using Rayleigh-Bénard-Marangoni convection and non-solvent induced phase separation to create granulated matrices that prevent the Leidenfrost effect at temperatures up to 400 °C. These matrices offer strong capillary adhesion, ensuring water droplets remain pinned and provide effective cooling. Additionally, the unique bubble dynamics prevent film boiling and Leidenfrost levitation. The matrices are mechanically robust and thermally stable, making them suitable for cooling high-power electronic devices at high temperatures. These results highlight the potential of using polymer matrices for cooling devices at elevated temperatures, potentially advancing cooling technologies.

Enhanced numerical modeling of natural heat convective phase change for generalized non-Newtonian fluids at high Rayleigh number

Numerical modeling of convective heat transfer employing non-Newtonian fluids is a key issue and represent an interesting challenge in many engineering applications. For this reason, this work develops an enhanced numerical model to predict fast and accurately the convective phase change for generalized non-Newtonian fluids. The strongly thermally coupled model is solved by an improved pressure-correction algorithm (SIMPLERnP) and the Finite Volume Method with accuracy of the third order for the transient terms and second order for the convective boundary conditions and the velocity gradients that allows to calculate the apparent viscosity. The study examines the natural heat convective solidification of the ternary Al-27 %Cu-5.25 %Si alloy with the Herschel-Bulkley rheology at a high Rayleigh number (>107). In addressing the main problem, four crucial aspects are discussed: the validation of the numerical scheme with numerical and experimental results; the modeling of the non-linear temperature variation of the liquid phase change fraction; the non-Newtonian effects of the power index (0.1 ≤ n ≤ 1.9) and yield stress (0≤τ0≤5 Pa) on the heat transfer mechanisms; and finally, the time of computation with the high-order numerical scheme and the enhanced pressure-correction algorithm. The main finding is that FVM/SIMPLERnP provides a significant reduction in the time of computation compared to reliable pressure-correction schemes (SIMPLER and IDEAL), being a robust, accurate and efficient scheme to solve complex natural heat convective phase change problems involve generalized non-Newtonian fluids at high-Rayleigh numbers.

Lattice Boltzmann modeling of convective heat and solute transfer in additive manufacturing of multi-component alloys

Additive manufacturing (AM) is a remarkable breakthrough technology, allowing for the direct fabrication of three-dimensional components through the layer-by-layer stacking of materials. A novel free Surface lattice Boltzmann (LB) model is developed to simulate the heat and solute transfer in AM of multi-component alloys. The behavior liquid phase is described by using the free surface LB model, and the phase transitions between solid and liquid are modeled by using the LB-enthalpy method. A LB equation is directly constructed, which accounts for solute transfer in a certain multi-component alloys system. The thermodynamic information used in the calculation of phase transitions are determined by an extensive thermodynamic database. The model is validated via several benchmark examples of fluid flow and heat transfer. The characteristics of convective heat and solute transfer within various AM are investigated. Finally, the non-equilibrium convective heat transfer, phase transitions, and macroscopic segregation are discussed within the AM melt pools. The melt pool expands and convective heat transfer is enhanced by the Marangoni effect. Thus there is a consistent decrease in solute segregation. The solute segregation is more severe near the surface of the deposit layer. Additionally, the thermal convection experiences cyclic intensification attributed to the successive impact of multiple droplets in wire feeding and melting AM. This continuous impact serves to diminish the solute segregation. The results underscore the significant potential and advantages of LB method in accurately simulating the AM, which provides valuable insights for understanding the underlying mechanism of heat and solute transfer in materials and manufacturing.

Convection and phase change in a lid-driven trapezoidal vented cavity with encapsulated PCM under non-uniform magnetic field by using ternary nanofluid

In this study, a novel configuration of lid-driven vented cavity system equipped with encapsulated phase change materials is studied where applications are relevant in drying, material processing, and electronic cooling. For controlling the convective heat transfer and phase transition, combined utilization of non-uniform magnetic field with ternary nanofluid is offered. Upper wall is inclined and moving with constant speed while ternary nanofluid up to a loading of 0.03 is used. Galerkin weighted residual finite element method is considered as the solution technique. A range of parameters for Reynolds number (Re, 200–1000), wall velocity (Rep, 0–1500), Hartmann number (Ha, 0–30), inclination parameter (yd, 0–0.4H), non-uniform amplitude (Af, 0–0.3), and nanoparticle loading (ϕ, 0–0.03) are considered in the analysis. When Re is increased, transition time (tf) is generally reduced for moving wall case. Reduction of tf up to 65% is obtained at the highest Re when moving wall is used at Rep=1000. For stationary wall case, the behavior of tf with Re is non-monotonic while at the highest Re, tf is reduced. The phase transition process is strongly influenced by the moving wall velocity while first increment and decrement of tf with wall velocity is observed. Thermal performance rises by around 58% and 22%, respectively by using the highest Re for stationary and moving walls. There is a significant increase in heat transfer, of around 211%, as wall velocities rise from Rep=0 (stationary) to Rep=1500. The tf for the moving wall is decreased by around 43.7% at the highest Ha. According to the stationary scenario, tf rises by around 33% until Ha=15 and falls by roughly 39.2% between Ha=15 and Ha=30. Amplitude of non-uniform magnetic field results in variation of tf between 4.5% and 19%. When imposing magnetic field at maximum strength, thermal performance is improved by 44.75% with a moving wall while it is just 5% in a stationary scenario. While raising the value of upper wall’s inclination (yd) increases the thermal performance, it also influences the phase change process. More loading of nanoparticles in base fluid results in a faster transition; the corresponding decreases in tf are 24.5% and 12.7% for stationary and moving wall setups, respectively. The increases in thermal performance for stationary and moving wall cases are 36.3% and 33.7%, respectively.

Microwave-Assisted Hydrothermal Synthesis of Pure-Phase Sodalite (>99 wt.%) in Suspension: Methodology Design and Verification.

Despite numerous studies focused on the hydrothermal (HT) synthesis of fly ash zeolites (FAZs), this method still has many limitations, the main of which is the low yield of zeolites. Hydrothermally synthesized zeolites are typically multiphase and exhibit low purity, which limits their applicability. Pure-phase zeolites have been primarily prepared from filtrates after alkaline mineralization of fly ashes, not directly in suspension. In addition, the published methodologies have not been tested in a wider set of samples, and thus their reproducibility is not confirmed. The aim of the study is to propose a reproducible methodology that overcomes the mentioned limitations. The influence of the Si/Al ratio (1.3:1-1:2), the type and concentration of the activator (2/4 M NaOH/KOH/LiOH), the reagent (30% LiCl), the duration (24-168 h), and the temperature (50-180 °C) of the synthesis phases were studied. The sequence of the synthesis phases was also optimized, depending on the type of heat transfer. The fly ashes were analyzed by wavelength-dispersive X-ray fluorescence (WD XRF), flame atomic absorption spectrometry (F-AAS), and X-ray diffraction (XRD). The energy intensity of the synthesis was reduced through the application of unique microwave digestion technology. Both microwave and combined (microwave and convection) syntheses were conducted. FAZs were identified and quantified by XRD analysis. This study presents a three-stage (TS) hydrothermal synthesis of pure-phase sodalite in suspension. Sodalite (>99 wt.%) was prepared from nine fly ashes under the following conditions: I. microwave phase: 120 °C, 150 min, solid-to-liquid ratio (S/L) 1:5, Si/Al ratio 1:1.5, and 4 M NaOH; II. convection phase: 120 °C, 24 h, S/L 1:40, and the addition of 30 mL of 30% LiCl; and III. crystallization: 70 °C for 24 h. The formation of rhombododecahedral sodalite crystals was confirmed by scanning electron microscope (SEM) images.

Thermocapillary convection modes and phase change heat transfer characteristics of three-dimensional metal foam composited phase change materials with different aspect ratios under microgravity

This work aims to investigate the flow, heat transfer and phase change characteristics of porous media composite phase change materials with different aspect ratios in the thermocapillary mode under microgravity. A three-dimensional hydrodynamic model of thermocapillary-enhanced phase change heat transfer in the composite is developed. The model considers the shear stress boundary conditions on the porous free surface, employing the enthalpy-porosity method and the Darcy–Forchheimer model to describe the phase change process and fluid flow within the porous matrix, respectively, and the local thermal non-equilibrium model to describe the transient heat energy transfer between the paraffin and copper foam. The effects of different Marangoni numbers (Ma), aspect ratios (AR), Darcy numbers (Da) and porosities (ε) on the phase change heat transfer are compared. The results show that the increase of Ma from 6 × 104 to 2 × 105 accelerates the thermocapillary effect, and positively affect the thermal transport inside the cavity. The total melting time of the composite is reduced by 22.6 %, the heat storage efficiency is improved by 31.1 %, and secondary vortices appear in the convection zone. The large AR is favorable to the development of thermocapillary convection, but it also causes the reduced temperature gradient and heat transfer area of the heat source as well as the increased heat transfer distance. Compared to AR = 1, the total melting time increased by 34.4 % and 46.9 % for AR of 1.95 and 2.25 at a larger Ma, while the heat storage efficiency decreased by 26.5 % and 33.7 %, respectively. For a fixed ε, the decrease in Da hinders the development of convection, thus weakening the heat transfer and storage performance of the composite, and also causes heat conduction to dominate the phase change process in advance.

Photo-Activated Growth and Metastable Phase Transition in Metallic Solid Solutions.

Laser processing in metals is versatile yet limited by its reliance on phase transformation through heating rather than electronic excitation due to their low absorptivity, attributing from highly ordered structures. Metastable states (i.e., surfaces, glasses, undercooled liquids), however, present a unique platform, both energetically and structurally to enable energy landscape tuning through selective stimuli. Herein, this ansatz is demonstrated by exploiting thin passivating oxides to stabilize an undercooled state, followed by photo-perturbation of the near surface order to induce convective Marangoni flows, edge-coalescence and phase transition into a larger metastable solid bearing asymmetric composition between the near surface and core of the formed structure. The self-terminating nature of the process creates a perfectly contained system which can maintain a high relaxation energy barrier hence deep metastable states for extended periods of time.

The Diurnal Cycle of Rainfall and Deep Convective Clouds Around Sumatra and the Associated MJO‐Induced Variability During Austral Summer in Himawari‐8

AbstractThe effects of the diurnal cycle and large‐scale atmospheric disturbances dominate rainfall and cloud variability in the Maritime Continent. This study examines the modulation of the Austral Summer diurnal cycle by the Madden–Julian Oscillation (MJO) using cloud populations through precipitation and deep convective cloud derived from satellite measurements. Using Rainfall Potential Areas from Himawari‐8 Advanced Himawari Imager as a proxy for deep convection, our analysis shows that convective clouds are present ∼55% of the time over land in Sumatra during the afternoon and night. Cloud signatures reveal semi‐diurnal structures of deep convective clouds off the West Coast of Sumatra. In contrast, the East Coast exhibits explicit sea‐ward propagation patterns of deep convective controlled by the coastal effects around the Strait of Malacca and Java Sea, together with the influence of synchronized diurnal forcing between islands. We show that the MJO drives the enhanced convective phases, changing the cloud top type distribution, moisture convergence, and moisture transport over the equatorial Indian Ocean. The cold cloud area also increases during the MJO active phases, which is linked to frequent deep convective cloud development near the mountain ranges of Sumatra and the adjacent ocean. The analyses of cloud variations based on the rainfall potential areas and cloud top type provide evidence of the effects of convective processes on the diurnal cycle of ice and water vapor distribution in the troposphere.

Importance of Seasonally Evolving Near‐Surface Salinity Stratification on Mixed Layer Heat Budget During Summer Monsoon Intraseasonal Oscillation in the Northern Bay of Bengal in 2019

AbstractThe discharge of freshwater from major rivers into the northern Bay of Bengal (BoB) increases dramatically during the summer monsoon season, reaching a peak in August–September, and there is a corresponding increase in the vertical salinity gradient in the upper ocean. Here we study the impact of seasonally evolving near‐surface salinity stratification on the response of ocean mixed layer temperature (MLT) to Summer Monsoon Intraseasonal Oscillations (MISO), using accurate surface fluxes and high vertical resolution (∼2 m) hydrographic measurements from a mooring in the northern BoB (17.8°N, 89.5°E) during June–September 2019. Prominent MLT warming and cooling with a range of 1.5°C is observed between suppressed (clear skies, calm winds) and active (cloudy, windy) phases of MISO convection. However, the intraseasonal MLT response to the active phase of a late‐season MISO event is minimal compared to MISO events in early summer. We infer this is primarily due to the much smaller contribution from oceanic vertical processes (∼6 Wm−2) in late summer 2019, compared to their role in early summer (−15 to −55 Wm−2). During the active phase of the MISO event of late summer 2019, the combined effect of reduced entrainment and weak vertical temperature gradients associated with a barrier layer inhibits near‐surface cooling. Conversely, the near‐surface salinity stratification and the barrier layer are weak during MISO events in the early summer of 2019—these hydrographic conditions lead to enhanced MLT cooling in response to MISO, apparently through a freer turbulent exchange of cool thermocline water with the surface layer.

Comprehensive performance analysis and structural improvement of latent heat thermal energy storage (LHTES) unit using a novel parallel enthalpy-based lattice Boltzmann model

Latent heat thermal energy storage (LHTES) utilizing phase change material (PCM) is one of the critical enablers in developing sustainable and low-carbon energy systems. To fill the knowledge gap, this paper presents an enthalpy-based solid–liquid model through the lattice Boltzmann method (LBM) with a multi-relaxation-time (MRT) approach, aiming to simulate convective phase change in LHTES units with and without porous media in Cartesian or axisymmetric domains. To improve accuracy and efficiency, the model integrates a differential scanning calorimetry (DSC) correlated equation for enthalpy modeling, couples with a 1D heat-transfer-fluid (HTF) model for boundary treatment of HTF side, and employs a parallel LBM scheme for efficient parametric studies. The validation demonstrates the model’s success in predicting PCM phase change, with errors below 10%. A comprehensive numerical analysis is then conducted to quantitatively evaluate the effect of convection on PCM melting. Novel metrics, such as acceleration rates (ac) of PCM melting and threshold Rayleigh numbers (Radc) at various aspect ratios, are introduced. Furthermore, PCM melting in the porous cylindrical unit is explored. Findings reveal up to 86% acceleration in melting compared to pure PCM at 80% energy storage, and the porous media with porosity above 0.9 is recommended for thermal enhancement. Moreover, this paper analyzes the negative effect of uneven temperature distributions caused by convection on LHTES unit efficiency. A modified LHTES unit geometry is proposed to offset this negative effect, and the study demonstrates successful mitigation of uneven temperature distributions, achieving up to 57 % acceleration in PCM melting.

Topology optimization of HCM/PCM composites for thermal energy storage

In this paper, we have applied topology optimization (TO) to the latent heat based thermal energy storage (LHTES) device design. The high conductivity materials (HCM) are added to the phase change materials (PCM) to increase the overall thermal conductivity. Distribution of HCM in PCM is optimized by the TO method to maximize the charging speed of the LHTES device at the different charging periods. The time-dependent Navier–Stokes (NS) equations, involving natural convection and PCM phase change, are chosen as the governing equations of fluid motion. The energy equation including latent heat is strongly coupled with the NS equation. The adjoint method is utilized to derive and calculate the sensitivity. Several 2D numerical examples with different charging periods and different HCM volume fractions have been studied with this TO method. The charging period showed a huge influence on the optimized TO structures. The short charging period designs exhibit more conductive structures while the long charging period designs show convective structures. A pareto front of the topologically optimized designs has been constructed, which shows up to 110.7% of improvement in the charging speed over the parallel-fin design with the same root fin width.

Directional Crystallization in the Presence of a Mushy Layer with Applications to the Earth’s Inner Core Boundary

We formulate the mathematical model of directional crystallization of a binary melt with a mushy layer (region) between purely solid and liquid phases. This model is complicated by melt convection and pressure-dependent phase transition temperature. Approximate analytical solutions to this nonlinear moving-boundary problem are constructed. Namely, the concentration of impurity, fraction of solid phase, mushy region thickness, average fluid velocity, primary interdendritic spacing, mean radius of a chimney, and a characteristic distance between chimneys in a mushy region are found. Using this analytical solution, we describe the mushy region structure near the inner core boundary of the Earth, which is consistent with computer simulations and estimates existing in recent literature. A scheme illustrating the mushy region arrangement with chimneys at the inner core boundary of the Earth is presented. This arrangement based on the developed theory represents the novelty and importance of our study.

Multiscale Influences on Rainfall in Northeast Australia

Abstract This study examines the multiscale modulation of mean and extreme rainfall in Northeast (NE) Australia under different background modes of variability, which is a new aspect given the high-resolution and long-term observational datasets. Daily rainfall probability is significantly modified by the Madden–Julian oscillation (MJO), and its influence varies with the seasons and is associated with atmospheric circulation anomalies. Rainfall generally decreases during El Niño and increases during La Niña years; however, there is a notable spatial nuance to El Niño–Southern Oscillation (ENSO)-associated extreme rainfall, with some locations showing the opposite precipitation response to the typical ENSO–rainfall relationship. Despite more precipitation overall in La Niña years, the mean and extreme precipitation responses to the MJO appear to be stronger and more often statistically significant during El Niño compared to La Niña periods. The impact of ENSO on the MJO–rainfall relationship is stronger than the variation of the MJO itself with ENSO, and likely reflects a change in the MJO modulation of rain-bearing atmospheric processes. During El Niño periods, diurnal rainfall amplitude is generally stronger in the central and southern subtropical parts of the study area than during La Niña periods, while the opposite tendency occurs in the northern tropical part. The diurnal cycle of both mean and extreme precipitation is amplified during suppressed convection phases compared to enhanced convection phases of the MJO. In general, the peak time of diurnal cycle does not change with MJO regimes, but there are some notable differences in rainfall propagation between enhanced and suppressed MJO phases. Significance Statement This study presents a new perspective on the relationship between precipitation in Northeast (NE) Australia and two important climate modes, the Madden–Julian oscillation (MJO) and El Niño–Southern Oscillation (ENSO). Rainfall in NE Australia is strongly influenced by the MJO, ENSO, and their interaction, suggesting that climate models need to capture both individual climate modes and their interactions for reliable rainfall projections. These findings have societal climate risk implications, as NE Australia is an area prone to catastrophic flooding due to extreme rainfall.

The Impact of the Madden‐Julian Oscillation on the Formation of the Arabian Sea Monsoon Onset Vortex

AbstractDuring certain years, a synoptic scale vortex called the monsoon onset vortex (MOV) forms within the northward advancing zone of precipitating convection over the Arabian Sea. The MOV does not form each year and the reason is unclear. Since the Madden‐Julian Oscillation (MJO) is known to modulate convection and tropical cyclones in the tropics, we examined its role in the formation of the MOV. While the convective and transition phases of the MJO do not always lead to MOV formation, the suppressed phase of the MJO hinders the formation of the MOV more consistently. This asymmetric relationship between the MJO and MOV can be partially explained by the modulation of the large‐scale environment, measured by a tropical cyclone genesis index. It also suggests that the Arabian Sea is generally near a critical state that is favorable for MOV formation during the monsoon onset period.

Influence of the Madden-Julian Oscillation on the diurnal cycles of convection and precipitation over the Congo Basin

The Congolese rainforest is a hotspot for convection where thunderstorms and rainfall exhibit a strong diurnal cycle. Previous studies have shown that various modes of variability such as the Madden-Julian Oscillation (MJO), the leading mode of intraseasonal variability in the tropics, can impact the diurnal cycles of precipitation and convection over tropical land areas. Thus, this study analyzes the influence of the MJO on diurnal variations of convection and precipitation over the Congo and explores possible mechanisms leading to the observed changes, using Gridded Satellite (GridSat-B1), Tropical Rainfall Measuring Mission (TRMM), and ERA5 reanalysis data. Results show that convection and precipitation are increased during the MJO enhanced convective phase (RMM phases 1 and 2) and decreased during the suppressed convective phase (RMM phases 5 and 6), where the differences are found to be largest during the morning hours when convection is weakest. Convection is generally deeper during the enhanced phase and shallower during the suppressed phase, accompanied by a slower decay of convective clouds and anvils during the enhanced phase. Furthermore, the influence of the MJO was found to be stronger on stratiform precipitation compared to convective precipitation. While the diurnal cycles of convective precipitation fractions are similar during both MJO phases, the fraction of stratiform precipitation is higher during the enhanced phase, mainly in the morning hours. Suggested atmospheric drivers contributing to the observed differences between the two MJO phases include enhanced upward air motion in the mid- and upper levels and strong divergence in the upper levels during the enhanced phase, and strong mid-level divergence and upper- to mid-level subsidence during the suppressed phase, mainly during the nighttime and morning hours. Furthermore, decreased mid-level wind speed, increased upper-level wind speed, and enhanced relative humidity may be contributing factors to the increased formation of stratiform precipitation during the enhanced phase. These results enhance our understanding of the MJO's impacts on precipitation and convection variability, ultimately improving predictions of MJO modulated rainfall over the Congo.

Mathematical modeling of unsteady convective flow analysis of water and nano-encapsulated phase change particles in composite enclosure subject to rotation

Free convection heat transfer in water and hybrid particles in an enclosure is studied. A layer of porous material with various thickness and permeability is attached to the enclosure. Both fluid and porous layers rotate with a specific speed. Hybrid particles are formed by a polyurethane (PU) and an N-nonadecane (ND). PU acts as shell and ND goes through a phase change and it capables of preserving and releasing a considerable amount of latent heat. The enclosure movement can be controlled through a rotation speed. The Brinkman-Forchheimer extended Darcy model is used for governing the flow within a fully saturated porous layer. The governing equations for the convective flow and phase change heat transfer, including specific heat capacity and permeability, were introduced and solved by FEM. The impact of the porous thickness, permeability, fusion temperature and rotation speed on the heat capacity ratio, streamline and isotherms structures were investigated. The results showed that a high Darcy number and thin porous thickness were a good candidate for the improvement of average heat transfer rate since reinforcing the melting process and heat transmitting.

Existence and uniqueness for a convective phase change model with temperature–dependent viscosity

In this article, we consider a class of phase change model with temperature–dependent viscosity, convection and mixed boundary conditions on a bounded domain that reflect melting and solidification in a variety of real-world applications, such as metal casting and crystal growth. The mathematical model, which is based on the enthalpy formulation, takes into consideration the thermophysical differences between the liquid and solid states. The moving liquid-solid interface is explicitly fulfilled as the energy and momentum equations are solved over the full physical domain. Under particular assumptions, we derive various a priori estimates and prove well-posedness results. Numerical simulation of the model employed in the paper is presented as an illustration of an example of a melting problem.