Showing papers on "Stefan number published in 2020"
TL;DR: In this paper, free convection heat transfer of a suspension of nano-encapsulated phase change materials (NEPCMs) is simulated and discussed in an inclined porous cavity.
142 citations
TL;DR: In this article, the free convective flow of a nano-encapsulated phase change material (NEPCM) suspension in an eccentric annulus is investigated numerically, where the inner cylinder is heated and kept at a temperature higher than that of the outer cylinder.
Abstract: The free convective flow of a Nano-Encapsulated Phase Change Material (NEPCM) suspension in an eccentric annulus is investigated numerically. The inner cylinder is heated and kept at a temperature higher than that of the outer cylinder. The core of the NEPCM particles is made of nonadecane while the shell is made of Polyurethane. The nanoparticles are dispersed in water as the base fluid. The equations governing the flow and heat transfer of the NEPCM suspension in the annulus are developed and written in the non-dimensional form. The numerical solutions of these equations are obtained using the finite element method. The validity of the numerical method is ensured by comparing its predictions to the results of previously published studies. The main outcomes point out to the impact of the volume fraction of the NEPCM particles and Stefan number on the thermal and hydrodynamic characteristics of the suspension. A 5% volume fraction represents the optimal value for heat transfer enhancement. Heat transfer is also enhanced when the fusion temperature of the NEPCM core is far from the temperatures of the hot and cold walls. Furthermore, increasing the annulus eccentricity and moving the inner cylinder towards the top tends to inhibit heat transfer in the annulus.
120 citations
TL;DR: In this article, a two-dimensional model of the melting heat transfer process for phase change material with Paraffin wax RT58 in a finned LHS unit is developed and numerically solved to investigate the melting behaviors.
75 citations
TL;DR: In this article, the authors investigate the thermal behavior of nano-encapsulated phase change material (NEPCM) suspensions in a cylindrical cavity and investigate the effect of the fusion temperature of the particle core (θf) on heat transfer.
64 citations
TL;DR: In this article, an enthalpy-based LBM with a D2Q9-DDF 3 model at the REV 4 scale is implemented for the constrained melting of ice as a PCM in inclined elliptical annulus.
Abstract: Constrained melting of ice as a PCM 1 in inclined elliptical annulus should be studied. Efficiency of heat transfer enhancement methods such as insertion of Cu nanoparticles and metallic porous matrix in this heat storage system must be determined. Porous material is made of alloys of Nickel and Steel. The enthalpy-based LBM 2 with a D2Q9-DDF 3 model at the REV 4 scale is implemented. There is thermal equilibrium condition between porous media and PCM. Also, for NEPCM 5 melting, the single phase flow model is adopted. Particle diameter in nanofluid is equal to 100 nm. The sub-cooling of solid PCM is ignored. Prandtl number, Stefan number, Rayleigh number and Darcy number are 6.2, 1, 2 × 105 and 10−3, respectively. The volumetric concentric of the nanoparticles is between 0 and 0.02. Porosity is between 1 and 0.9. It is found that inclination of the elliptical annulus does not engender any change in the liquid fraction. Inserting nanoparticles is best effective technique to enhance liquid fraction in oblate annulus due to enhanced conduction heat transfer. Use of porous matrix is recommended for prolate and inclined configurations. It obviates considerably stable stratification at bottom of elliptical annulus as a thermal storage unit.
43 citations
TL;DR: In this article, an extensive numerical investigation of the heat transport enhancement achieved by the thermocapillary effect during the melting of phase change materials in microgravity is presented, where the phase change transition is analyzed for the high Prandtl number paraffin n-octadecane in a two-dimensional rectangular container subjected to isothermal conditions along the lateral boundaries.
31 citations
TL;DR: In this article, the thermal and hydrodynamic characteristics of a suspension with water-Nano-Encapsulated Phase Change Material (NEPCM) in an annulus of a porous eccentric horizontal cylinder are investigated.
31 citations
TL;DR: In this paper, the charging performance of a shell-and-tube LTES under fluctuating and steady heat source has been investigated and analyzed, and the effects of period and amplitude for the fluctuating heat source, as well as the Stefan number, are investigated in detail.
31 citations
TL;DR: In this article, the authors presented a mathematical model describing the inward melting process of a phase change material in the presence of convection under the most generalized boundary condition, where the material within a container have different geometrical configuration like circular cylinder or sphere.
Abstract: This article presents a mathematical model describing inward melting process of a phase change material in the presence of convection under the most generalized boundary condition. It is assumed that the material within a container have different geometrical configuration like circular cylinder or sphere. All thermophysical properties of the solid and liquid regions are assumed to be homogeneous. Initially, we convert the mathematical model into an initial value problem in the form of vector matrix representation using a finite difference technique. Two numerical methods; the operational matrix of integration for Bessel functions and finite element Legendre wavelet Galerkin method, are applied to solve the initial value problem. Thus, the obtained results from both methods analyzed for constant (or time depending) temperature or constant (or time depending) heat flux. The whole study is presented in dimensionless form. The effect of Stefan number, Peclet number, Kirpichev number and Biot number on dimensionless temperature profile and dimensionless moving front are illustrated graphically.
26 citations
TL;DR: In this paper, a 2D lattice Boltzmann model combining the enthalpy-based method (EBM) is established to investigate the ice melting process in the gas diffusion layer (GDL), the effects of GDL melting position, porosity, Rayleigh number and Stefan number on the melting rate, ending time of melting, temperature distribution and solid-liquid interface distribution are investigated.
26 citations
TL;DR: In this paper, the melting mechanism and thermal behavior of phase change material (PCM) in a slender rectangular cavity with heat transfer fluid (HTF) flowing over one side and the other sides thermally insulated.
TL;DR: It is shown that improving the porous thermal conductivity not only leads to an increase in the rate of heat transfer but also augments the fluid flow inside the cavity and opens up an avenue for further application-based studies.
TL;DR: In this paper, the authors investigate the thermal, hydrodynamic and entropy generation behavior of nano-encapsulated phase change materials (NEPCM) in a porous medium and demonstrate that the rates of heat transfer and the average Bejan number are maximum and the generated entropy is minimum when the fusion temperature of the nano-capsules is Tfu ǫ = 0.5.
TL;DR: In this paper, the deformed mesh technique was employed to track the solid-liquid interface of the phase change material (PCM) during the melting process, and the simulations showed that an increment of Stefan's number can significantly improve the melting rate.
Abstract: Non-Newtonian behavior of a Phase Change Material (PCM) inside a porous coaxial pipe is studied by utilizing the deformed mesh technique. The inner and outer pipes are subjected to the high and low temperatures of Th and Tc, while the bottom and upper surfaces are thermally insulated. The Finite Element Method (FEM), implemented in the Arbitrary Eulerian-Lagrangian (ALE) moving grid technique, is applied to solve the weakened forms of the governing equations. Stefan's condition is employed to track the solid-liquid interface of the PCM during the melting process. Grid independency test is conducted, and the verifications of the results are evaluated through comparisons with several test cases published in the literature. The simulations show that an increment of Stefan's number can significantly improve the melting rate. As the Stefan number reaches from 0.014 to 0.01, the full melting non-dimensional time declines from 1.313 to 0.937. Also, an extreme increase in the melting rate can be found while decreasing the power-law index. When the power-law index decrease from 1 to 0.6, the full melting time subsequently is reduced to 54%.
TL;DR: In this paper, the authors presented a Stefan problem including thermal conductivity and heat capacity as the functions of temperature at α = β, the exact solutions to the proposed problem are discussed for two different specific cases, i.e. m = n = 1 and m = N = 2, for the general case, estimation of the solution to the problem is deliberated with the help of shifted Chebyshev tau method.
TL;DR: In this article, the spherically symmetric dissolution of an initially cold alumina particle in a bath of molten cryolite is investigated, and asymptotic solutions valid in the limits of small-superheat and of small Stefan number are derived.
TL;DR: The thermal performance of a flat plate LHSU consisting of parallel flat plate slabs of phase change material (PCM) was investigated with analytical techniques in this paper, where an index of effective latent heat storage ratio, Er, which was defined as the ratio of the actual amount of available latent thermal energy before HTF outlet temperature reaches a specified value to the total LHSUs capacity, was proposed to evaluate the thermal performance.
TL;DR: This article develops mathematical and numerical analysis of one phase moving boundary problem with conduction and convection effect when variable thermal conductivity depends on time and temperature and also latent heat is presented as the power function of position.
TL;DR: In this article, the phase change convection of a new type of hybrid nanofluids, suspensions of nano-encapsulated phase change materials (NEPCM), was addressed in a semi-annular inclined enclosure.
Abstract: The natural phase change convection of a new type of hybrid nanofluids, suspensions of Nano-Encapsulated Phase Change Materials (NEPCM), was addressed in a semi-annular inclined enclosure. The nanoparticles consist of a polymer shell and a nonadecane shell, in which the nonadecane core can change phase at its melting temperature and absorb/release a significant quantity of latent heat. The NEPCM-suspension circulates in the enclosure due to the natural convection, and the NEPCM particles contribute to heat transfer by phase change. The equations governing the movement and heat transfer of the suspension and nanoparticles were inserted in the form of partial differential equations. The finite element method was used to numerically solve the equations. Then, the entropy generation of NEPCM suspension in the attendance of the phase change was examined. The influence of the fusion temperature and volume fraction of nanoparticles, Stefan number, Rayleigh number, and inclination angle of enclosure on the thermal behavior and entropy generation of the suspension was explored. The results showed that the contribution of phase change core of nanoparticles was significant, and the heat transfer was enhanced by the presence of NEPCM particles. The fusion temperature of particles controls the Bejan number (entropy generation) behavior of the NEPCM suspension. There is an optimum phase change temperature for nanoparticles, which results in maximum heat transfer. For a horizontal enclosure, the optimum fusion temperature is the average temperature of the active walls. This optimum phase change temperature is a function of the tilting angle of the enclosure.
TL;DR: In this paper, the authors formulate a Stefan problem appropriate when the thermophysical properties are distinct in each phase and the phase-change temperature is size or velocity dependent, and apply the governing equations to a standard one-dimensional problem and also the melting of a spherically symmetric nanoparticle.
TL;DR: In this paper, the authors studied the role played by supercooling in the solidification of binary alloys appearing in such applications and compared the results with both numerical simulations and real experimental data arising from the casting of molten metallurgical grade silicon through the water granulation process.
Abstract: We study the extended Stefan problem which includes constitutional supercooling for the solidification of a binary alloy in a finite spherical domain. We perform an asymptotic analysis in the limits of large Lewis number and small Stefan number which allows us to identify a number of spatio-temporal regimes signifying distinct behaviours in the solidification process, resulting in an intricate boundary layer structure. Our results generalise those present in the literature by considering all time regimes for the Stefan problem while also accounting for impurities and constitutional supercooling. These results also generalise recent work on the extended Stefan problem for finite planar domains to spherical domains, and we shall highlight key differences in the asymptotic solutions and the underlying boundary layer structure which result from this change in geometry. We compare our asymptotic solutions with both numerical simulations and real experimental data arising from the casting of molten metallurgical grade silicon through the water granulation process, with our analysis highlighting the role played by supercooling in the solidification of binary alloys appearing in such applications.
TL;DR: In this article, the authors analyzed the heat transfer, fluid flow and heat capacity ratio in an annulus enclosure filled with porous and saturated by a suspension of nano-encapsulated phase change materials (NEPCMs).
Abstract: In this study, the heat transfer, fluid flow and heat capacity ratio are analyzed in an annulus enclosure filled with porous and saturated by a suspension of nanoencapsulated phase change materials (NEPCMs). It consists of phase change material core and a polymer or non-polymer shell. The presence of nanoparticles in the base fluid and the phase change capability of the nanoparticle’s core improve the thermal properties of the base fluid and thermal control process. The inner cylinder wall is reserved at hot temperatures where the encapsulated particles absorb the heat, while the outer cylinder wall is reserved at cold temperatures where the encapsulated particles release the heat. A local thermal non-equilibrium model is adopted for the porous medium. The parameters studied are Rayleigh number (104 ≤ Ra ≤ 106), Stefan number (0.2 ≤ Ste ≤ ∞), melting point temperature of the core (0.05 ≤ θf ≤ 1), the concentration of the NEPCM particles (0% ≤ ϕ ≤ 5%), radius ratio (1.67 ≤ Rr ≤ 2.5), eccentricity (− 0.67 ≤ Ec ≤ 0.67), Darcy number (10−4 ≤ Da ≤ 10−1), porosity (0.3 ≤ e ≤ 0.9) and interface heat transfer coefficient (1 ≤ H ≤ 1000). The results show that the dimensionless temperature of fusion (θf) plays the main role in the improvement in NEPCM on the heat transfer process.
TL;DR: In this article, the melting dynamics of a phase change material by the action of thermocapillary driving were studied. And the authors showed that the melting properties of phase change materials follow simple power laws such as the position of the melting front, the time to full melting, and the input of energy into the system.
TL;DR: In this paper, the authors report the criterion for the onset of convection in a low Prandtl number phase-change Rayleigh-Benard (RB) system with an upward moving melt interface in a two-dimensional square box for a wide range of Rayleigh number Ra and Stefan number Ste.
Abstract: Here, for the first time, we report the criterion for the onset of convection in a low Prandtl number phase-change Rayleigh–Benard (RB) system with an upward moving melt interface in a two-dimensional square box for a wide range of Rayleigh number Ra and Stefan number Ste (defined as the ratio between the sensible heat to the latent heat). High fidelity simulations were performed to study the phenomenon of the onset of convection. Unlike the classical RB system in the phase-change RB system, it was found that the onset of convection depended on Ste and Fourier number τ, in addition to Ra. The phase-change RB system with upward moving melt interface can be classified into two groups: slow expanding phase-change RB system (Ra ≤ 104) and moderate/fast melting phase-change RB system (Ra > 104). The slow melting phase-change RB system becomes unstable when the effective Rayleigh number based on the melt height is ≈1295.78, consistent with the finding by Vasil and Proctor [“Dynamic bifurcations and pattern formation in melting-boundary convection,” J. Fluid Mech. 686, 77 (2011)]; however, moderate and fast melting phase-change RB systems become unstable when the product of the local Rayleigh number Ra based on the melt-layer height hyt and the Fourier number based on the melt-layer height reaches a threshold value. Interestingly, it is seen that the criteria for the onset of convection for moderate and fast melting phase-change RB systems show a power law kind of form such that Racrτcr = aSteb + c. In addition, during the initial conduction regime before the onset of convection, it is seen that the Nusselt number at the hot wall is Nuh ∼ τ0.5, and during the onset of convection, i.e., during the formation of the initial convection rolls, the Nusselt number at the hot wall is Nuh ∼ τd, where the value of the exponent d is 2 for low Rayleigh numbers and 4 for higher Rayleigh numbers. This study reports some general characteristics of the onset of convection and some organized behavior in the transient melting phase-change RB system, which are not yet explored and reported in the open literature. This work may lead to significant understanding of different applications of fluid-dynamical melting phase-change RB systems in both natural and engineering systems.
TL;DR: In this article, the authors investigated hydrodynamic and thermal characteristics of nanofluids, NEPCMs mixed in the host liquid, in glass balls as a porous structure.
TL;DR: In this paper, an experimental and numerical analysis of unconstrained melting of Paraffin wax-RT58 in a horizontally placed cylindrical container was carried out at constant wall temperature maintained on the lateral surface of the cylinder.
Abstract: The present study is focused on experimental and numerical analysis of unconstrained melting of Paraffin wax-RT58 in a horizontally placed cylindrical container. After the validation of numerical model with experimental results, numerical analysis is extended to constrained melting to investigate the process. The experiments are carried out at constant wall temperature maintained on the lateral surface of the cylinder. The influence of initial sub-cooling and lateral surface temperature on the melting rate is investigated. The melting process is better analyzed by the melting phase front and temperature contours as time progresses. The results show that the melting rate decreases by increasing the initial sub-cooling, and increases with increasing lateral surface temperature of the cylinder. In unconstrained melting, heat transfer by conduction governs the melting process initially, but later it is restricted to only the bottom part of the cylinder as the solid PCM at a higher density sinks due to effects of gravity. Heat transfer in the upper half of the cylinder is dominated by natural convection set up in the liquid PCM. In constrained melting, pure conduction phenomenon exists only in the beginning, and later conjugate heat transfer occurs. When subjected to similar boundary conditions, PCM melt-time is lower in unconstrained melting than in constrained melting. A correlation between melt-time and Stefan number is also developed.
TL;DR: In this paper, the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis was studied numerically, and it was shown that the number and size of voids formed are relatively insensitive to the Stefan number.
Abstract: We study numerically the melting of a horizontal layer of a pure solid above a convecting layer of its fluid rotating about the vertical axis. In the rotating regime studied here, with Rayleigh numbers of order $10^7$, convection takes the form of columnar vortices, the number and size of which depend upon the Ekman and Prandtl numbers, as well as the geometry -- periodic or confined. As the Ekman and Rayleigh numbers vary, the number and average area of vortices vary in inverse proportion, becoming thinner and more numerous with decreasing Ekman number. The vortices transport heat to the phase boundary thereby controlling its morphology, characterized by the number and size of the voids formed in the solid, and the overall melt rate, which increases when the lower boundary is governed by a no-slip rather than a stress-free velocity boundary condition. Moreover, the number and size of voids formed are relatively insensitive to the Stefan number, here inversely proportional to the latent heat of fusion. For small values of the Stefan number, the convection in the fluid reaches a slowly evolving geostrophic state wherein columnar vortices transport nearly all the heat from the lower boundary to melt the solid at an approximately constant rate. In this quasi-steady state, we find that the Nusselt number, characterizing the heat flux, co-varies with the interfacial roughness, for all the flow parameters and Stefan numbers considered here. This confluence of processes should influence the treatment of moving boundary problems, particularly those in astrophysical and geophysical problems where rotational effects are important.
01 Jun 2020
TL;DR: In this article, a comprehensive analysis of time dependent condensation model embedded in a porous medium with variations in liquid-vapour densities is presented, where both similarity and asymptotic solutions are obtained with the manifestation of various pertinent parameters.
Abstract: This article presents a comprehensive analysis of time dependent condensation model embedded in a porous medium with variations in liquid–vapour densities. Both similarity and asymptotic solutions for the unsteady liquid–vapour phase change front are obtained with the manifestation of various pertinent parameters. The obtained results are compared which congregate well as depicted clearly in graphs. Results indicate that with different diffusivity and contrast ratios, the similarity front parameter is found to be gradually declining with variation in a density ratio. We have shown for the condensation process, the ratio of sensible to latent heat is independent of time and is equal to the half of the Stefan number of the liquid phase.
TL;DR: In this paper, two dimensionless numbers, Fourier and Stefan numbers, were used to study the development of ice temperatures and the ice growth, and the overall results from simulation and experiments demonstrate that an areal scalar (convective flux) and a volumetric scalar cannot be scaled simultaneously.
TL;DR: In this paper, the growth of a vapor bubble in a uniformly superheated liquid is simulated numerically and the results of numerical calculations are in good agreement with the solution of [3] in a wide range of Jacob numbers.
Abstract: In the framework of the thermal energy scheme, the growth of a vapor bubble in a uniformly superheated liquid is simulated numerically. The results of numerical calculations are in good agreement with the solution of [3] in a wide range of Jacob numbers. The account for the interfacial surface permeability at high values of Stefan number shows a good match with the results of numerical calculations.