Coriolis effect on the stability of convection in mushy layers during the solidification of binary alloys.

Thesis (Ph.D.)-University of Durban-Westville, 2000.We consider the solidification of a binary alloy in a mushy layer subject to Coriolis effects. A near-eutectic approximation and large far-field temperature is employed in order to study the dynamics of the mushy layer in the form of small deviations from the classical case of convection in a horizontal porous layer of homogenous permeability. The linear stability theory is used to investigate analytically the Corio lis effect in a rotating mushy layer for, a diffusion time scale used by Amberg & Homsey (1993) and Anderson & Worster (1996), and for a new diffusion time scale proposed in the current study. As such, it is found that in contrast to the problem of a stationary mushy layer, rotating the mushy layer has a stabilising effect on convection. For the case of the new diffusion time scale proposed by the author, it is established that the viscosity at high rotation rates has a destabilising effect on the onset of stationary convection, ie. the higher the viscosity, the less stable the liquid. Finite amplitude results obtained by using a weak non-linear analysis provide differential equations for the amplitude, corresponding to both stationary and overstable convection. These amplitude equations permit one to identify from the post-transient conditions that the fluid is subject to a pitchfork bifurcation in the stationary case and to a Hopf bifurcation associated with the overstable convection. Heat transfer results were evaluated from the amplitude solution and are presented in terms of the Nusselt number for both stationary and overstable convection. They show that rotation enhances the convective heat transfer in the case of stationary convection and retards convective heat transfer in the oscillatory case, but only for low values of the parameter X I = 8 Pr ~ 0 So· The parameter 1/ X I represents the coefficient of the time derivative term in the Darcy equation. For high X I values, the contribution from the time derivative term is small (and may be neglected), whilst for small X I values the time derivative term may be retained

Chaotic and periodic natural convection for moderate and high Prandtl numbers in a porous layer subject to vibrations

The analysis of natural convection for moderate and high Prandtl numbers in a fluid-saturated porous layer heated from below and subject to vibrations is presented with a twofold objective. First, it aims at investigating the significance of including a time derivative term in Darcy’s equation when wave phenomena are being considered. Second, it is dedicated to reporting results related to the route to chaos formoderate and high Prandtl number convection. The results present conclusive evidence indicating that the time derivative term in Darcy’s equation cannot be neglected when wave phenomena are being considered even when the coefficient to this term is extremely small. The results also show occasional chaotic “bursts” at specific values (or small range of values) of the scaled Rayleigh number, R, exceeding some threshold. This behavior is quite distinct from the case without forced vibrations, when the chaotic solution occupies a wide range of R values, interrupted only by periodic “bursts.” Periodic and chaotic solution alternate as the value of the scaled Rayleigh number varies.University of Pretoriahttp://link.springer.com/journal/11242hb201

Vibration effects on heat transfer during solidification of paraffin

Paper presented at the 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Malta, 16-18 July, 2012.Previous work looked at the solidification process of PCM (phase change material) paraffin wax. Experimental results were compared with numerical work done in CFD package FLUENT. In the current study, the effects of vibration on heat transfer during the solidification process of PCM in a sphere shell are investigated. Enhancement of heat transfer results in quicker solidification times and desirable mechanical properties of the solid. The amount of PCM used was kept constant during each experiment by using a digital scale to check the weight, and thermocouple to check consistent temperature. A small amount of air was present in the sphere so that the sphere was not filled completely. Commercially available paraffin wax, RT35, was used in the experiments. Experimentations were done on a sphere of 40 mm diameter, wall temperature 20°C below mean solidification temperature, and consistent initial temperature. A vibration frequency was varied from 10-300 Hz was applied to the set-up and results compared with that of no vibration. Samples were taken at different times during the solidification process and compared with respect to solid material presentdc201

Experimental study of vibration effects on heat transfer during solidification of paraffin in a spherical shell

Two effects that have been observed when metals and metal alloys are vibrated during solidification are a decrease in dendritic spacing, which directly affects density, and faster cooling rates and associated solidification times. Because these two effects happen simultaneously during solidification, it is challenging to determine the one effect independently from the other. Most previous studies were on metals and metal alloys. In these studies, the one effect, i.e., the decrease in dendritic spacing, might influence the other, i.e., the faster cooling rates, and vice versa. The direct link between vibration and heat transfer has not yet been studied independently. The purpose of this study was to experimentally investigate the effect of vibration only on heat transfer and thus solidification rate. Experiments were conducted on paraffin wax, because it had a clearly defined macroscopic crystal structure consisting of mostly large straight-chain hydrocarbons. The advantage of the large straight-chain hydrocarbons was that the dendritic spacing was not affected by the cooling rate. Experiments were done with paraffin wax inside hollow plastic spheres of 40mm diameter with 1mm wall thickness. The paraffin wax was initially in a liquid state at a uniform temperature of 608C and then submerged into a thermal bath at a uniform constant temperature of 158C, which was approximately 208C below the mean solidification temperature of the wax. Experiments were conducted in approximately 300 samples, with and without vibration at frequencies varying from 10–300 Hz. The first set of experiments was conducted to determine the solidification times. In the second set of experiments, the mass of wax solidified was determined at discrete time steps, with and without vibration. The results showed that paraffin wax had vibration independent of solid density contrary to other materials, e.g., metals and metal alloys. Enhancement of heat transfer resulted in quicker solidification times and possible control over the heat transfer rate. The increase in heat transfer leading to faster solidifcation times was observed to first occur as frequency increased and then to decrease.The University of Pretoria and Prof. J. P. Meyer.http://www.tandfonline.com/loi/ueht202017-05-31hb2016Mechanical and Aeronautical Engineerin

Vadasz Number Effects on Convection in a Vertical Rotating Porous Layer, Placed Far from Axis of Rotation, and Subjected to Internal Heat Generation and Centrifugal Jitter

The flow and heat transfer in a rotating vertical porous layer, placed far from the axis of rotation, and subjected to internal heat generation and centrifugal jitter, is considered. The linear stability theory is used to determine the convection threshold, in terms of the critical Rayleigh number. Typical liquids used in engineering applications and heavy liquid metals are used to demonstrate conditions at which the Vadasz number is sufficiently small to warrant the retention of the time derivative in the momentum equation. When considering low amplitude and high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions. In summary, when the Vadasz number is large, centrifugal jitter has no impact on the convection stability criteria. In contrast, when the Vadasz number is small, centrifugal jitter impacts the convection stability criteria