Function Of Fourier Number Research Articles

Effect of filling configurations on melting heat transfer characteristic of phase change materials partially filled with metal foam

Metal foam embedded in phase change materials (PCM) has been shown to significantly improve the storage of latent heat thermal energy. Nonetheless the presence of metal foam also reduces natural convection, energy storage and increases cost. To address this issue, we modelled the internal flow of heat transfer in a PCM, paraffin wax, filled with metal foam at the top or the bottom, with filling height ratio ξ of 0.25, 0.5 and 0.75. The liquid-solid phase transition was studied by numerical simulations. Results show that natural convection in the pure paraffin wax area is higher, and melting time is shorter, in the bottom-filled than in the top-filled configuration. These differences increase with filling height ratio. By contrast, in metal foam-paraffin composite region, melting time is longer in the bottom-filled configuration due to heat loss. Interestingly, we observed significant changes in the interface shape of liquid-solid PCM at the junction of the pure paraffin and the metal foam-paraffin composite region. The liquid fraction formulas for different metal foam filled configurations are established as the function of Fourier number, Rayleigh number and filling height ratio.

Phase-Change Process Inside a Small-Radii Cylinder Subjected to Cyclic Convective Boundary Conditions: A Numerical Study

Abstract We numerically investigate the melting and solidification behavior of phase-change materials (PCMs) encapsulated in a small-radii cylinder subjected to a cyclic convective boundary condition (square-wave). First, we explore the effects of the Stefan and Biot numbers on the nondimensionalized time required for a PCM initially held at Tcold to melt and reach the crossflow temperature Thot (i.e., reference Fourier number T̃ref). The increase in either Stefan or Biot number decreases T̃ref which can be predicted accurately using the correlation developed in this work. The variations of the PCM melt fraction, surface temperature, and heat transfer rate as a function of Fourier number are reported and analyzed. We further study the effect of the cyclic Fourier number T̃ on the periodic melting and freezing process. The melting or freezing front initiates at the outer periphery of the PCM and propagates toward the center. At higher frequencies, multiple two-phase interfaces are generated (propagating inward), and the surface temperature oscillates in the vicinity of the melting temperature. This increases the effective temperature difference with the crossflow and leads to a higher overall heat transfer.

Experimental study on solidification process of a phase change material containing TiO2 nanoparticles for thermal energy storage

The solidification process of n-octadecane as a phase change material (PCM) with dispersed titanium dioxide (TiO2) nanoparticles was experimentally studied. Experiments were performed in a rectangular enclosure cooled from one vertical side corresponding to the solid Stefan numbers in the range 0.17–0.239. The Rayleigh numbers at the initial of experiment were in the range 0.92–18.3×106. The rheological behavior of liquid PCM/TiO2 samples at higher concentrations tended to Bingham fluids, thus the solidification experiments were conducted for Bingham numbers in the range 0–2.17. The solidification process was characterized by visualizing the progression of solid-liquid interface as well as recording the temperature distribution inside the enclosure. Experimental results showed that heat conduction was the dominant mode of heat transfer during the solidification. Dispersing TiO2 nanoparticles led to enhance in thermal conductance and consequently the increase in solidified volume. An increase of 7%, 9% and 18% in solidified volume fraction was observed at the end of solidification for the mass fractions of 1wt.%, 2wt.% and 4wt.%, respectively. A universal correlation was proposed to predict the solidified volume fraction as a function of Fourier number, Rayleigh number, solid Stefan number, Bingham number and mass fraction of nanoparticles with an error below 11%.

Experimental investigation on heat transfer characteristics during melting of a phase change material with dispersed TiO2 nanoparticles in a rectangular enclosure

This paper presents an experimental investigation on the melting process of n-octadecane as a phase change material (PCM) with dispersed titanium oxide (TiO2) nanoparticles. Experiments were performed in a rectangular enclosure heated at constant rates from one vertical side corresponding to Rayleigh numbers in the range 0.57×108–43.2×108 and Stefan number in the range 5.7–23.8. The rheological behavior of liquid PCM/TiO2 at the mass fractions of 2 and 4% tended to Bingham fluids, thus the melting experiment was conducted for Bingham numbers in the range 0–31.1. Heat transfer during melting was characterized by visualizing the solid-liquid interface as well as recording the temperature distribution in the enclosure. Experimental results showed that at the initial stage of melting, heat transferred by conduction, and at later times, natural convection dominated heat transfer. Dispersing TiO2 nanoparticles led to increase in Bingham number and consequently the natural convection and melting rate deteriorated. Two correlations were proposed to predict the Nusselt number and melted volume fraction as a function of Fourier number, Rayleigh number, Stefan number, Bingham number and mass fraction of nanoparticles.

Mass transfer enhancement at deformable droplets due to Marangoni convection

One of the key design parameters in liquid/liquid extraction is the mass transfer coefficient. A complex list of parameters including fluid dynamics, drop size distribution, chemical properties of the involved species, local interfacial instabilities (Marangoni convection) is required in order to determine the transient evolution of the mass transfer coefficient. The influence of Marangoni convection on single drop mass transfer cannot yet be described in an analytical manner, and empirical correlations available in literature fail to predict the mass transfer process. In the present study, experimental investigations on deformable single droplets in the toluene/acetone/water system are presented which shows strong interfacial instabilities. Parameters varied are the drop diameter, the initial solute concentration and the mass transfer direction. Experimental results are compared with the well-known models by Kronig and Brink and Handlos and Baron. The Kronig and Brink model cannot describe Marangoni dominated systems, but comparisons reveal the influence of deformation on the mass transfer enhancement. In contrary, with a slight modification to the Handlos and Baron model, the mean droplet concentration of the transferred component was successfully modelled as a function of Fourier number.

A cracked plate under transient thermal stresses due to surface heating

The transient thermal stresses in a cracked plate due to sudden surface heating are investigated. The plate is assumed to be insulated on one face and heated on the other. A ramp heating function is assumed at the boundary, which is more realistic than a step function. It is shown that, in the case of an edge crack, the situation of a heated surface is very different to that of a cooled surface. When the surface of the plate is heated, compressive transient thermal stresses occur close to the surface, causing the crack surfaces to come into contact with each other over a certain contact length, but when the surface of the plate is cooled, high tensile stresses take place close to the surface which tend to open the crack. If the contact between the crack surfaces is not taken into account, the stress intensity factors will always yield negative values, but when the contact length is taken into account the resulting calculations produce positive stress intensity factors. So, the problem is reduced to a non-linear crack contact problem which is formulated in terms of a singular integral equation from the embedded crack problem with smooth closure conditions of the crack surfaces. The numerical results are obtained for stress intensity factors and the crack contact length is obtained as a function of Fourier number, crack length, and the duration of the heating rate.

ASYMPTOTIC SOLUTIONS OF TRANSIENT TEMPERATURE AND THERMAL STRESSES FOR A SURFACE-CRACKED HOLLOW CYLINDER SUBJECTED TO THERMAL SHOCK

The transient temperature and stress fields in a hollow cylinder with an axial surface crack subjected to thermal shock are considered. It is found that the temperature boundary effect exists in a thin layer close to the cooled surface, if the nondimensional Fourier number is not very large. For the third kind of boundary condition ( convection boundary condition) due to thermal shock on the inner surface, the asymptotic solutions of temperature fields are deduced for various values of Biot number. The resulting thermal stresses in the uncracked cylinder, which are necessary for the determination of the stress intensity factor, are solved by quasi-static formulation. By introducing the line spring model considering the arbitrary loads on crack surfaces, the numerical results of the stress intensity factors for a semi-elliptical axial surface crack are obtained as a function of Fourier number and the parametric angle of ellipse for various values of Biot number.