Heat transfer in free convection-dominated melting of a phase change material in a horizontal annulus

Heat transfer during melting in enclosures is important in the design of heat exchangers using phase change materials (PCM) for latent heat thermal energy storage. In this paper, the finite element method is employed to simulate the convection-dominated melting of a PCM in a cylindrical-horizontal annulus heated isothermally from the inside wall. The effects of Rayleigh number on the melting rate as well as the evolution of the flow pattern are examined. Results of the numerical experiments reveal that an increases in Rayleigh number promotes heat transfer rate. Multiple cellular pattern is observed at high Rayleigh numbers (10⁶).     

Accelerated melting of PCM in a multitube annulus‐type thermal storage unit using lattice Boltzmann simulation

Melting of the ice/water as the phase change material in a horizontal single‐tube annulus is sluggish when the stable stratification exists at the bottom of the configuration. To obviate this problem, three heat transfer enhancement techniques could be implemented using the enthalpy‐based lattice Boltzmann method with the double distribution function method to accelerate the process. The multifarious arrangements of the tubes in this horizontal annulus are investigated to expand the region affected by the natural convection. Also, the dispersion of the Cu nanoparticles in the base PCM could boost the thermal conductivity and melting rate. Finally, the metallic porous matrix made of nickel–steel alloys and saturated with the base PCM could be used to enhance the thermal conductivity of the base PCM. The solid–liquid phase change process is defined as the constrained melting of ice‐water in the tube heating mode. There is a thermal equilibrium between ice/water and the nickel–steel porous matrix and the Cu nanoparticles. The Prandtl number, Stefan number, Rayleigh number, and Darcy number are 6.2, 1, 10⁴–10⁵, and 10^?3, respectively. The volumetric concentric of the nanoparticles is between 0 and 0.02 and the porosity ranging from 1 to 0.9 in the representative elementary volume scale.     

Investigation on the thermal performance of phase change material/porous medium‐based battery thermal management in pore scale

With the latent heat, the phase change material (PCM) is widely used in battery thermal management (BTM) to control the temperature. In this paper, the porous medium is employed to enhance the heat transfer of PCM. The lattice Boltzmann model for PCM/porous medium in pore scale is considered, where the mesh system with porous medium (fixed point) is generated by quartet structure generation set (QSGS) method. The effects of the Rayleigh number and porosity on the heat transfer process in BTM are investigated. The results show that decreasing the porosity will accelerate the melting rate. When the porosities are 0.9, 0.8, 0.7, and 0.6, the total melting times are decreased by 23.7%, 43.3%, 58.0%, and 75.4%, compared with pure PCM. The heat is transferred through the high‐conductivity framework. The natural convection in the porous medium is weak, and the conduction is the dominated heat transfer. As a result, the area of solid–liquid interface will be increased, and the heat‐transferred rate is accelerated. However, when the Rayleigh number is raised to 10⁵, applying the porous medium with porosity of 0.9 will increase the total melting time, resulted from the stronger natural convection of PCM. The present study is helpful for design of PCM/porous medium‐based BTM.     

An analytical solution of the heat transfer process during contact melting of phase change material inside a horizontal elliptical tube

Close-contact melting processes of phase change material (PCM) inside a horizontal elliptical tube are studied. The theoretical formulas of the melting rate, thickness of liquid layer, elapsed time of solid PCM and Nusselt number during the heat melting process are obtained by analyzing. The results include those of contact melting inside a horizontal cylinder. Finally, the influences of elliptical compression coefficient and temperature difference in melting are discussed, and useful conclusions are drawn. © 1998 by John Wiley & Sons, Ltd.     

A comparative study on the performances of different shell-and-tube type latent heat thermal energy storage units including the effects of natural convection

Numerical modeling was performed to simulate the melting process of a fixed volume/mass phase-change material (PCM) in different shell-and-tube type latent thermal energy storage units with identical heat transfer area. The effect of liquid PCM natural convection (NC) on the latent heat storage performance of the pipe and cylinder models was investigated using a 3D numerical model with FLUENT software. Result shows that NC can cause a non-uniform distribution of the solid–liquid interface, which accelerates PCM melting rate. The PCM melting rate and heat storage rate in the horizontal cylinder model are higher than those in the horizontal pipe model because of the combined effects of heat conduction and NC. A comparative study was conducted to determine the effects of horizontal and vertical shell-and-tube models with different heat transfer fluid (HTF) inlets including the effects of NC. The results indicate that the vertical model with an HTF inlet at the bottom exhibits the highest PCM melting rate and heat storage rate for the pipe models. For the cylinder models, the horizontal model and the vertical model with an HTF inlet at the bottom can achieve nearly the same completed melting time. In addition, NC has minimal effect on any model with an HTF inlet at the top.     

Investigation of heat transfer during melting of a PCM by a U‐shaped heat source

An experimental study was conducted to investigate the melting process of a phase change material (PCM) and the associated convection heat transfer due to a U‐shaped heat source embedded in the PCM. The experiments were conducted at four input heat fluxes that varied from 3450 to 5840 W/m². The results showed that the heat transfer behavior, interface movement, and the heat transfer coefficients differed both axially and vertically inside the chamber. The local convective heat transfer coefficient in the inner region, enclosed by the U‐tube, was found to be about 35% higher than that in the outer region over the input heat flux range, resulting in faster melting in the inner region than in the outer region. As melted domain grew vertically from 15% to 100%, it was observed that the overall h in the inner region increased by 40–55% from the lowest to highest heat flux. The melting rate was also found comparatively high up until 65–70% of the total PCM volume melted because of the higher contribution from the inner region. It was also observed that the Rayleigh number increased by approximately 23% in the inner region and 18% in the whole domain as the heat flux increased from 3450 to 5840 W/m². A new Nusselt–Rayleigh number correlation is proposed for the heat transfer during the melting process due to a U‐shaped heat source. Copyright © 2017 John Wiley & Sons, Ltd.     

Natural convection heat transfer of microemulsion phase-change-material slurry in rectangular cavities heated from below and cooled from above

An experimental study has been conducted in dealing with natural convection heat transfer characteristics of microemulsion slurry in rectangular enclosures. The microemulsion slurry used in the present experiment was composed of water, surfactant, and fine particles of phase-change-material (PCM). The PCM mass concentration of the microemulsion slurry was varied from a maximum 30 mass% to a diluted minimum 5 mass%, and the experiments have been done separately in three subdivided temperature ranges of the dispersed PCM particles in a solid phase, two phases (coexistence of solid and liquid) and a liquid phase. The results showed that the Nusselt number increased slightly with the PCM mass concentration for the slurry in solid phase. In the phase change temperature range, the Nusselt number increased with an increase in PCM mass concentration of the slurry at low Rayleigh numbers, while it decreased with increasing PCM mass concentration of the slurry at high Rayleigh numbers. There was not much difference in natural heat transfer characteristics of the PCM slurry with low PCM concentrations (<10 mass%), however, the difference was getting greater with increasing the PCM concentration, especially for the enclosure at a lower aspect ratio (width/height of the rectangular enclosure). The enclosure height was varied from 5.5 to 24.6 mm under a fixed width and depth of 120 mm. Hence, the experiments were performed for a wide range of modified Rayleigh number from 3 × 10² to 1.0 × 10⁷. The correlation generalized for the PCM slurry in a single phase was derived in the form of Nu=0.22(1−C₁C_me^−C₂AR)Ra^1/(3n+1), where C₁ and C₂ were the optimum fitting constants obtained by the least square method. While the PCM was in a phase changing region, the correlation could be expressed as Nu=0.22(1−C₁C_me^−C₂AR)Ra^1/(3n+1)Ste^−0.25, where the Ste was the modified Stefan number.     

Numerical studies on laminar natural convection inside inclined cylinders of unity aspect ratio

The effect of cylinder inclination on thermal buoyancy induced flows and internal natural convective heat transfer is explored using CFD simulations. The cylinder’s top and bottom surfaces were maintained at different temperatures while the curved surface was adiabatic. The aspect ratio (length/diameter) of the cylinder was unity and the Prandtl number of the fluid was fixed at 0.71. The Rayleigh number of the confined fluid was varied from 10³ to 3.1 × 10⁴ by changing the specified end wall temperatures. The critical Rayleigh number was estimated to be 3800 for the vertical cylinder. Relaxing the convergence criterion caused false hysteresis in the converged results for the vertical cylinder. Typical natural convective fluid flow and temperature patterns obtained under laminar flow conditions are illustrated for various inclinations ranging from 0° to 180°. Flow visualization studies revealed complex three-dimensional patterns. Different thermal–hydrodynamic regimes were identified and were classified in terms of Rayleigh number and angle of inclination. Empirical correlations for the Nusselt number and maximum velocities in the domain as a function of the inclination angle and Rayleigh number are developed.     

Natural convection flow of Cu–Water nanofluid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method

In this paper the lattice Boltzmann method is used to investigate the effect of nanoparticles on natural convection heat transfer in two-dimensional horizontal annulus. The study consists of an annular-shape enclosure, which is created between a heated triangular inner cylinder and a circular outer cylinder. The inner and outer surface temperatures were set as hot (T_h) and cold temperatures (T_c), respectively and assumed to be isotherms. The effect of nanoparticle volume fraction to the enhancement of heat transfer was examined at different Rayleigh numbers. Furthermore, the effect of vertical, horizontal, and diagonal eccentricities at various locations is examined at Ra = 10⁴. The result is presented in the form of streamlines, isotherms, and local and average Nusselt number. Results show that the Nusselt number and the maximum stream functions increase by augmentation of solid volume fraction. Average Nusselt number increases when the inner cylinder moves downward, but it decreases, when the location of inner cylinder changes horizontally.     

Interactions between hybrid nanosized particles and convection melting inside an enclosure with partially active walls: 2D lattice Boltzmann-based numerical investigation

The ice melting is investigated inside a square cavity with two isothermally partially active walls. The concept of dispersing hybrid alumina–Cu nanoparticles and hybrid silica–multiwalled carbon nanotubes (MWCNTs) nanoparticles is recommended for thermal performance enhancement in this thermal energy storage (TES) system. The two-dimensional explicit lattice Boltzmann convection melting scheme in the single-phase model is applied to account for the natural convection flow induced in the melt region and evolution of the solid–liquid interface. The complete melting time for the pure phase change material (PCM) using case (II) is 33.3% lower compared with other cases. If the price of hybrid Al₂O₃–Cu nanoparticles and heat storage capacity is important, the full melt time diminishes by 16.6% with a volume fraction of 0.01 in case (II). Once hybrid silica–MWCNT nanoparticles with a volume fraction of 0.01 are utilized inside case (II), the lowest charging time is achieved. The complete melting time abates by 23.66% in contrast to the pure PCM melting. The use of single/hybrid nanoparticles to enhance the PCM melting is not necessarily economical as efficient positions of active parts could further lessen the charging time. The efficiency of hybrid nanoparticles is linked to the type and weight proportions of nanoparticles, and positions of thermally active parts.     

Melting of nano-enhanced phase change material in a cavity heated sinusoidal from below: Numerical study using lattice Boltzmann method

Natural convection and melting of ice as a phase change material dispersed with copper nanoparticles are numerically investigated. Square cavity filled with nano-mixture (Cu−ice) subjected to sinusoidal temperature distributions from the hot bottom boundary. The phase change process and heat transfer are formulated and solved using the enthalpy-based lattice Boltzmann method. Home-built numerical code is developed and validated. The effect of Rayleigh number (Ra = 10⁴, 10⁵, and 10⁶) and copper nanoparticle concentration (ϕ = 0%, 1%, 3%, and 5%) on the flow characteristics and thermal performance of NePCM during the melting process is examined. According to the numerical results, the melting and charging times decrease by increasing the Rayleigh number. It is also observed that increasing the volume fraction of nanoparticle decrease melting time by up to 10%.     

Seasonal thermal performance analysis of glazed window filled with paraffin including various nanoparticles

A two-dimensional heat transfer model was proposed to numerically investigate the effect of enriching phase change material (PCM) with different kinds of nanoparticles on thermal performance of glazing windows in different seasons of the year. The results were presented in terms of liquid fraction of PCM, inner surface temperature and temperature difference between interior and exterior surfaces of glass window, and their occurrence times. The results showed that adding nanoparticles into PCM can promote the melting and solidification processes, extend the total time of PCM being in the liquid state, and raise the internal surface temperature of glass. However, in summer season, the internal surface temperature decreases and the total melting time respectively reduces by 7 and 1.5 minutes by introducing TiO₂ and ZnO nanoparticles into PCM. Furthermore, the introduced nanoparticles do not have the same effect on the thermal performance of the window unit. While the inner surface temperature decreases by 0.82 K in summer by addition of TiO₂ to PCM, it increases by 0.84 K in transition season and 0.89 K in winter season by utilizing ZnO nanoparticles. Although the nano-PCM remains in the solid state in winter, the existence of nanoparticles can still increase the inner surface temperature.     

Convection-based model for a PCM vertical storage unit

This paper presents a two-dimensional axi-symmetrical model for the formulation of the problem of fusion of PCM around a vertical cylinder in the presence of natural convection. The basic equations of mass, momentum and energy were formulated in terms of the vorticity and the stream function. The numerical predictions were compared with available experimental results indicating good agreement. Additional results show the effects of the geometrical and operational parameters on the solid–liquid interface, stream function, energy stored and melt mass fraction. The model was extended to produce charts and correlations for the mean heat transfer rate, total solidification (or fusion) time in terms of the geometrical parameter, the modified Rayleigh number and the Stefan number. These charts and correlations are helpful in engineering design of PCM storage units. © 1998 John Wiley & Sons, Ltd.     

Numerical study of mixed convection nanofluid in an annulus enclosure between outer rotating cylinder and inner corrugation cylinder

Numerical investigations are presented for mixed convection problems in a concentric inner sinusoidal cylinder and an outer rotating circular cylinder, which were kept at constant hot and cold temperatures, respectively. The free space between the cylinders and the enclosure walls was filled with a water‐Cu nanofluid. The governing equations are formulated for velocity, pressure, and temperature formulation and are modeled in COMSOL5.2a, a partial differential equation solver based on the Galerkin finite element method. The governing parameters considered are the solid volume fraction, [0, 0.02, 0.04, and 0.06], Re (1, 25, 100, 200, and 300), and Ra (less than 10⁴), and the inner cylinder corrugation frequencies varied from (N = 3, 6, and 9). According to the calculations, the Reynolds number, the Rayleigh number, the nanoparticle volume fraction, and the number of corrugations play an important role of forming the stream and isothermal lines, the local and the average Nusselt number inside the annulus enclosure. The average Nusselt number decreases with increasing Reynolds number and the number of corrugations, while it increases as the Rayleigh number and the volume fraction increase.     

Numerical investigation of natural convection phenomena in a uniformly heated circular cylinder immersed in square enclosure filled with air at different vertical locations

In this model, a numerical study of two dimensional steady natural convection is performed for a uniform heat source applied on the inner circular cylinder in a square air (Pr = 0.7) filled enclosure in which all boundaries are assumed to be isothermal (at a constant low temperature). The developed mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by finite volume method. The effects of vertical cylinder locations and Rayleigh numbers on fluid flow and heat transfer performance are investigated. Rayleigh number is varied from 10³ to 10⁶ and the location of the inner cylinder is changed vertically along the centerline of the enclosure from − 0.25 L to 0.25 L upward and downward, respectively. It is found that at small Rayleigh numbers does not have much influence on the flow field while at high Rayleigh numbers have considerable effect on the flow pattern. In addition, the numerical solutions yield a two cellular flow field between the inner cylinder and the enclosure. Also, the total average Nusselt number behaves nonlinearly as a function of locations. Results are presented in terms of the streamlines, isotherms, local and average Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable agreement.     

Lattice Boltzmann simulation of natural convection heat transfer in an elliptical-triangular annulus

A numerical study for steady-state, laminar natural convection in a horizontal annulus between a heated triangular inner cylinder and cold elliptical outer cylinder was investigated using lattice Boltzmann method. Both inner and outer surfaces are maintained at the constant temperature and air is the working fluid. Study is carried out for Rayleigh numbers ranging from 1.0 × 10³ to 5.0 × 10⁵. The effects of different aspect ratios and elliptical cylinder orientation were studied at different Rayleigh numbers. The local and average Nusselt numbers and percentage of increment heat transfer rate were presented. The average Nusselt number was correlated. The results show that by decreasing the value of aspect ratio and/or increasing the Rayleigh number, the Nusselt number increases. Also the heat transfer rate increases when the ellipse positioned vertically.     

Multi-Prandtl correlating equations for free convection heat transfer from a horizontal tube of elliptic cross-section

Steady laminar free convection from a horizontal elliptic cylinder set in unbounded space is studied numerically under the assumption of uniform surface temperature. A specifically developed computer-code based on the SIMPLE-C algorithm is used for the solution of the mass, momentum and energy transfer governing equations. Simulations are performed for ratios between the minor and major axes of the elliptic cross-section of the cylinder in the range between 0.05 and 0.98, inclination angles of the major axis of the elliptic cross-section with respect to gravity in the range between 0° and 90°, Rayleigh numbers based on the major axis of the elliptic cross-section in the range between 10 and 10⁷, and Prandtl numbers in the range between 0.7 and 700. It is found that the heat transfer rate increases with increasing the Rayleigh and Prandtl numbers, while decreases with increasing the orientation angle of the cross-section of the cylinder, i.e., passing from the slender to the blunt configuration. In addition, a noteworthy fact is that in most cases the amount of heat exchanged at the cylinder surface has a peak at an optimum axis ratio which is practically independent of the Prandtl number, while may either increase or decrease with increasing the Rayleigh number depending on whether the orientation angle of the tube is above or below a critical value of approximately 67.5°. Dimensionless correlating equations are proposed both for the optimum axis ratio for maximum heat transfer and for the heat transfer rate from the cylinder surface to the undisturbed surrounding fluid reservoir.     

Thermal Performance of a Phase Change Material‐Based Latent Heat Thermal Storage Unit

An experimental analysis is presented to establish the thermal performance of a latent heat thermal storage (LHTS) unit. Paraffin is used as the phase change material (PCM) on the shell side of the shell and tube‐type LHTS unit while water is used as the heat transfer fluid (HTF) flowing through the inner tube. The fluid inlet temperature and the mass flow rate of HTF are varied and the temperature distribution of paraffin in the shell side is measured along the radial and axial direction during melting and solidification process. The total melting time is established for different mass flow rates and fluid inlet temperature of HTF. The motion of the solid–liquid interface of the PCM with time along axial and radial direction of the test unit is critically evaluated. The experimental results indicate that the melting front moves from top to bottom along the axial direction while the solidification front moves only in the radial direction. The total melting time of PCM increases as the mass flow rate and inlet temperature of HTF decreases. A correlation is proposed for the dimensionless melting time in terms of Reynolds number and Stefan number of HTF. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21120     

Thermal Energy Storage Module Design Using Energy and Exergy Analysis

In this paper, irreversibility of a thermal energy storage system is numerically investigated. The system consists of two concentric cylinders. The outer cylinder is filled with phase change material (PCM), while working fluid flows inside the inner pipe. The system works periodically. The related governing equations are solved by a control volume-based finite difference method. The effects of different parameters such as PCM size and melting point temperature are examined on the irreversibility of the system. The results show that the irreversibility of thermal storage module is strongly affected by the size of PCM (diameter and length of the external cylinder) and melting temperature. Based on the obtained results, the irreversibility of the system can be reduced by proper selection of PCM size and melting temperature.     

Numerical Analysis on a Latent Thermal Energy Storage System with Phase Change Materials and Aluminum Foam

Abstract

A latent heat thermal energy storage system with phase change material (PCM) is numerically studied. To enhance the heat transfer inside the system, a highly conductive metal foam is employed with ceramic nanoparticles. The latter method of enhancement leads to a new class of material called Nano-PCM. The system under investigation is a 70-L tank filled up with pure PCM or Nano-PCM and several pipes are situated where the heat transfer fluid (HTF) flows. The pipe surfaces are assumed at constant temperature above the PCM melting temperature to simulate the heat transfer from the HTF. The enthalpy-porosity theory is applied to simulate the PCM phase change, while the porous media formulation is assumed to describe the metal foam behavior. The nano-PCM is modeled with single-phase model where the properties are the weighted-average between the fluid base and the nanoparticles. The simulations are accomplished for charging-discharging process at different porosities and nanoparticle concentration. The results are given in term of average melting fraction evolution, average temperature as function of time, average stored energy. The metal foam significantly improves the heat transfer between PCM and HTF respect to the addition of nanoparticles, reducing the charging and discharging time more than one order of magnitude.