Showing papers on "Stefan number published in 2016"

Numerical investigations of solidification around a circular cylinder under forced convection

Abstract: We present numerical investigations of solidification around a cooled circular cylinder in the presence of forced convection. The numerical method is based on the front-tracking/finite difference and interpolation techniques. The solidification interface is represented by connected elements that move on a fixed, rectangular grid. The no-slip and Dirichlet temperature boundary conditions are imposed by the linear interpolation. The interpolation method was first validated through comparisons of the present results with some other numerical results for flow in an annulus, flow in an enclose with a conduction solid body and flow over a heated cylinder. We then used the method to investigate the solidification process around a cold cylinder by varying various parameters such as the Reynolds number Re, the Prandtl number Pr, the Stefan number, the thermal conductivity ratio k sl , the non-dimensional temperature of the introduced liquid θ 0, and the solid-to-liquid density ratio ρ sl . Numerical results indicate that an increase in any of Re, Pr and θ 0 results in a decrease in the area of the solidification region around the cylinder. In contrast, increasing k sl increases the region of the solid phase. Investigation on St and ρ sl reveals that the solidification rate increases with an increase in St or a decrease in ρ sl . However, St and ρ sl have a minor effect on the final product of the solidification process.

Numerical study on the melting thermal characteristics of a microencapsulated phase change plate

Abstract: The melting thermal characteristics of a microencapsulated phase change material (MEPCM) plate under constant heat flux are numerically investigated. The effective property relations of the MEPCM plate related to the parameters of base materials are first established and verified by the measured thermal properties of 10 samples. A one-dimensional phase change thermal model based on the enthalpy method is built, and the predicted results are also verified with test data. The temperature profile and phase interface movement in the MEPCM plate are discussed, and the effects of Stefan number, phase change temperature range, particle and core fraction, and additive fraction are also analyzed. Three states of solid, mushy, and fluid phases of phase change material (PCM) core divide the melting process of the MEPCM plate into five stages as follows: Fo ≤ 0.1, 0.1 < Fo ≤ 0.2, 0.2 < Fo ≤ 0.9, 0.9 < Fo ≤ 1.2, and Fo ≥ 1.2. The time point of regular regime for heat transfer in the MEPCM plate is Fo = 0.2. Th...

Mathematical simulation of melting inside a square cavity with a local heat source

Abstract: Numerical simulation of transient melting regimes inside an enclosure in the presence of a local heat source has been carried out. Mathematical model formulated in terms of dimensionless variables such as stream function, vorticity, and temperature has been numerically solved by finite difference method. Effects of the Rayleigh number 4·105 ≤ Ra ≤ 5·107, Stefan number 2.21 ≤ Ste ≤ 5.53, and dimensionless time on velocity and temperature fields as well as on the local Nusselt number along the heat source surface have been analyzed in detail. The transient effects of the considered process at high values of the Rayleigh number have been identified.

A novel method for analytical solution of transient heat conduction and Stefan problem in cylindrical coordinate

Abstract: It has been found numerical methods are very tiring and time consuming and so much dependent upon computational calculations, so in order to reduce the computational time a new eigenfunction expansion method is presented for a two dimensional case with heat generation source. This method is applicable to any combination of inhomogeneous first and second kind boundary conditions in the angular and axial direction of cylinder and can be very useful for latent heat energy based storage systems analytical analysis. Analytical problem of one phase melting/solidification of Phase Change Material was also studied with the use of dimensionless parameters using the eigenfunction expansion method. Effect of Dimensionless parameter Stefan number on the melting/solidification of PCM was studied. Results showed increase in the transition time at low Stefan value.

Studies on Multiphase, Multi-scale Transport Phenomena in the Presence of Superimposed Magnetic Field

Abstract: Multiphase transport phenomena primarily encompass the fundamental principles and applications concerning the systems where overall dynamics are precept by phase change evolution. On the other hand, multiscale transport phenomena essentially corroborate to a domain where the transport characteristics often contain components at disparate scales. Relevant examples as appropriate to multiphase and multiscale thermofluidic transport phenomena comprise solid-liquid phase change during conventional solidification process and hydrodynamics through narrow confinements. The additional effect of superimposed magnetic field over such multiphase and multiscale systems may give rise to intriguing transport characteristics, significantly unique in nature as compared to flows without it. The present investigation focuses on multiphase, multi-scale transport phenomena in physical systems subjected to the superimposed magnetic field, considering four important and inter-linked aspects. To begin with, for a multiphase system concerning binary alloy solidification, a normal mode linear stability analysis has been carried out to investigate stationary and oscillatory convective stability in the mushy layer in the presence of external magnetic field. The stability results indicate that the critical Rayleigh number for stationary convection shows a linear relationship with increasing Ham (mush Hartmann number). Magnetohydrodynamic effect imparts a stabilizing influence during stationary convection. In comparison to that of stationary convective mode, the oscillatory mode appears to be critically susceptible at higher values of  (a function of the Stefan number and concentration ratio), and vice versa for lower  values. Analogous to the behaviour for stationary convection, the magnetic field also offers a stabilizing effect in oscillatory convection and thus influences global stability of the mushy layer. Increasing magnetic strength shows reduction in the wavenumber and in the number of rolls formed in the mushy layer. In multiscale paradigm, the combined electroosmotic and pressure-driven transport through narrow confinements have been firstly analyzed with an effect of spatially varying non–uniform magnetic field. It has been found that a confluence of the steric interactions with the degree of wall charging (zeta potential) may result in heat transfer enhancement, and overall reduction in entropy generation of the system under appropriate conditions. In particular, it is revealed that a judicious selection of spatially varying magnetic field strength may lead to an augmentation in the heat transfer rate. It is also inferred that incorporating non–uniformity in distribution of the applied magnetic field translates the system to be dominated by the heat transfer irreversibility. Proceeding further, a semi-analytical investigation has been carried out considering implications of magnetohydrodynamic forces and interfacial slip on the heat transfer characteristics of streaming potential mediated flow in narrow fluidic confinements. An…

Thermally Controlled Bubble Growth

Abstract: The mathematical formulation of the heat input governed vapor bubble growth in a bulk of uniformly heated liquid is presented. Using the theory of dimensions, the structure of the solution was analyzed qualitatively. A historical survey of theoretical works devoted to the considered problem is presented. The set of degenerate solutions of the problem is obtained and studied systematically. The complete analytical solution of the problem is obtained for the first time. Formulas for the calculation of the bubble growth rate in the whole domain of possible variations in regime parameters are presented. The conclusion is made that the influence of permeability of the interface has a significant effect on the bubble growth rate. It is shown that the Plesset–Zwick formula, which is commonly accepted in computational practice, is not applicable at both small and large Jakob numbers and its good agreement with the experiment is determined to a large extent by a combination of the imperfectness of the theoretical analysis and the experimental error. The conclusion is made that, for many liquids, the ultimately achievable value of the dimensionless superheating parameter (Stefan number) can exceed unity. In this case, the regularities in the bubble growth acquire some features unexplored to date.

Investigating geometrical and flow parameters in behavior of melting phase change material in a double pipe heat exchanger

Abstract: Original Research Paper Received 26 July 2015 Accepted 25 August 2015 Available Online 09 September 2015 This paper presents numerical study on melting behavior of phase change material (PCM) in horizontal double pipe heat exchanger. The shell side is illed with RT50 as PCM and water is used as heat transfer fluid (HTF) which flows through inner tube. The aim of the study is to investigate the effect of eccentricity as geometrical parameter on melting behavior of PCM through downward movement of the inner tube. In addition, effective flow parameters such as mass flow rate and HTF inlet temperature are investigated on thermal storage performance. Enthalpy porosity method is used for modeling phase change process. At the beginning of melting process, conduction is dominant heat transfer mechanism and over time passing natural convection will be the main heat transfer mechanism. Results show that by increasing eccentricity, the dominant area for the natural convection expands and phase front penetration velocity increases which leads to considerable decrease in melting time. By increasing inlet temperature from 70 to 75 and 80 C, total melting time decreases up to 16% and 27% respectively. Although by Increasing Reynolds number from 1000 to 1500 and 2000, total melting time only decreases to 1% and 3%, respectively. These results show that Stefan number influences melting time more noticeable than Reynolds number.

Numerical simulation of solidification around a circular cylinder with natural convection

Abstract: An analysis is carried out for solidification around a cold cylinder in a rectangular cavity using numerical simulations. The transient influences of solidification accompanied by natural convection are investigated in detail. The governing equations, in terms of one-fluid formulation, including the Navier-Stokes and energy equations for incompressible Newtonian fluids are written for the whole domain. The no-slip and Dirichlet-type isothermal temperature boundary conditions are both implemented using a linear interpolation technique (immersed boundary method). The solidification interface is represented by connected elements that move on the fixed background grid. Code validations are carried out through various problems. Finally, the temporal dependence of the solid area ratio of the solid phase to the cylinder upon various dimensionless parameters, such as Rayleigh number, Prandtl number, Stefan number, thermal property ratios as well as a parameter indicating the effect of superheat is studied.