Stefan number

About: Stefan number is a research topic. Over the lifetime, 482 publications have been published within this topic receiving 32056 citations.

Numerical investigation and correlations for heat diffusion through planar ablative thermal protection systems

Abstract: In the present study, heat diffusion through a planar ablative Thermal Protection System (TPS) is numerically investigated by modeling the problem as one-dimensional transient heat conduction equation in Cartesian coordinates subject to the adiabatic back wall and aerodynamic heating on the other surface. The surface exposed to aerodynamic heating undergoes sensible heating until the surface temperature reaches an ablative temperature of the material. Further exposure of the material to heat flux results in material getting ablated. Ablation is modeled as Stefan-type wherein layers of material are immediately removed upon melt after reaching ablative temperature. Boundary immobilization method is used to fix the moving boundary and the governing equations are solved using finite difference scheme in space and Crank-Nicolson semi-implicit scheme in time, after expressing them in non-dimensional form. A FORTRAN code is developed to solve the set of equations using Tri-Diagonal Matrix Algorithm (TDMA). Parametric studies are conducted and new correlations are developed for predicting the amount of material ablated as a function of non-dimensional heat flux, Stefan number and non-dimensional time. Correlations are also developed to predict the non-dimensional time when back-wall that protects the vehicle interiors from extreme heat flux environment attains non-dimensional temperature 0.1. Results show that the developed correlations predict the parameter very well and errors are within acceptable limits.

Latent Heat Phase Change Heat Transfer of a Nanoliquid with Nano–Encapsulated Phase Change Materials in a Wavy-Wall Enclosure with an Active Rotating Cylinder

Abstract: A Nano-Encapsulated Phase-Change Material (NEPCM) suspension is made of nanoparticles containing a Phase Change Material in their core and dispersed in a fluid. These particles can contribute to thermal energy storage and heat transfer by their latent heat of phase change as moving with the host fluid. Thus, such novel nanoliquids are promising for applications in waste heat recovery and thermal energy storage systems. In the present research, the mixed convection of NEPCM suspensions was addressed in a wavy wall cavity containing a rotating solid cylinder. As the nanoparticles move with the liquid, they undergo a phase change and transfer the latent heat. The phase change of nanoparticles was considered as temperature-dependent heat capacity. The governing equations of mass, momentum, and energy conservation were presented as partial differential equations. Then, the governing equations were converted to a non-dimensional form to generalize the solution, and solved by the finite element method. The influence of control parameters such as volume concentration of nanoparticles, fusion temperature of nanoparticles, Stefan number, wall undulations number, and as well as the cylinder size, angular rotation, and thermal conductivities was addressed on the heat transfer in the enclosure. The wall undulation number induces a remarkable change in the Nusselt number. There are optimum fusion temperatures for nanoparticles, which could maximize the heat transfer rate. The increase of the latent heat of nanoparticles (a decline of Stefan number) boosts the heat transfer advantage of employing the phase change particles.

Numerical investigation of the melting process in a half horizontal cylinder with radial fins

Abstract: In the present study, the melting phenomenon in a half horizontal cylinder cavity with rectangular heat sources is investigated using numerical lattice Boltzmann method. The cylinder is modeled two dimensionally and its boundaries are insulated. Also, the high temperature rectangular heat sources with constant area are located in radial position on cavity. The enthalpy-based lattice Boltzmann method is used for simulating the phase change problem in the cavity. Melting of lead with Stefan number of 0.86 and Prandtl number of 0.0236 is simulated in the cavity. The effects of pertinent parameters such as the aspect ratio of the fins 1, 2.5 ,5, 7.5 , the Rayleigh number 103,104,105 and the angular position of the heat sources 0,15,45 are studied on the melting phenomenon. The results show that increasing the aspect ratio of the fin with constant area reduces the melting time and increases the liquid fraction at the same time. Also higher value of the Rayleigh number improves the natural convection effect and raises the rate of melting. Finally, it is observed that the highest rate of melting is obtained when two fins are positioned at 45 degrees with aspect ratio of 7.5 at Rayleigh number of 105.

An experimental study of steam injection into a uniform water flow through porous media

Abstract: An experimental study of steam injection into a porous media was carried out in a 2-dimensional plane porous channel. The steam was injected into a uniform downward water flow in a vertically aligned porous channel. The steam-water interface was carefully observed to understand the underlying physics. Two steam injection rate bounds were found for a given water flow rate and water subcooling. The upper bound is the steam flow rate at which the steam zone grows without limit and the lower bound is the steam flow rate at which a steam zone is just initiated. The bounds were determined experimentally for a porous channel with different permeabilities and thermal conductivities. For large particle size, chaotic oscillation of steam water interface was observed. The oscillation is believed to enhance heat and momentum transfer mechanisms. The steam zone size and shape were measured to evaluate heat transfer characteristics. The average Nusselt number is presented in terms of steam and water Reynolds numbers and the Stefan number.