Analytical solutions for heat transfer during cyclic melting and freezing of a phase change material used in electronic or electrical packaging

In this paper we develop an analytical heat transfer model, which is capable of analyzing cyclic melting and solidification processes of a phase change material used in the context of electronics cooling systems. The model is essentially based on conduction heat transfer, with treatments for convection and radiation embedded inside. The whole solution domain is first divided into two main sub-domains, namely, the melting sub-domain and the solidification sub-domain. Each sub-domain is then analyzed for a number of temporal regimes. Accordingly, analytical solutions for temperature distribution within each subdomain are formulated either using a semi-infinity consideration, or employing a method of quasi-steady state, depending on the applicability. The solution modules are subsequently united, leading to a closed-form solution for the entire problem. The analytical solutions are then compared with experimental and numerical solutions for a benchmark problem quoted in the literature, and excellent agreements can be observed.

Spin Probe Signature of Freezing in Water Slow Cooling Experiment: Our Observation is Global or Local?

First systematic spin probe ESR study of water freezing has been conducted using TEMPOL and TEMPO as the probes. The spin probe signature of the water freezing has been described in terms of the collapse of narrow triplet spectrum into a single broad line. This spin probe signature of freezing has been observed at an anomalously low temperature when a milimoler solution of TEMPOL is slowly cooled from room temperature. A systematic observation has revealed a spin probe concentration dependence of these freezing and respective melting points. These results can be explained in terms of localization of spin probe and liquid water,most probably in the interstices of ice grains, in an ice matrix. The lowering of spin probe freezing point, along with the secondary evidences, like spin probe concentration dependence of peak-to-peak width in frozen limit signal, indicates a possible size dependence of these localizations/entrapments with spin probe concentration. A weak concentration dependence of spin probe assisted freezing and melting points, which has been observed for TEMPO in comparison to TEMPOL, indicates different natures of interactions with water of these two probes. This view is also supported by the relaxation behavior of the two probes.

Mixed ionic and electronic conduction in zirconia and its applications in metallurgy

Mixed ionic and electronic conduction in Zr02-based solid electrolytes was studied.The effect of impurities and second-phase particles on the mixed conduction parameter, P,, was measured for different types of ZrOZ electrolytes. The performance of solid-state sensors incorporating ZrOZ electrolytes is sometimes limited by electronic conduction in ZrOZ, especially at temperatures >I800 K. Methods for eliminating or minimizing errors in measured emf due to electronically driven transport of oxygen anions are discussed. Examples include probes for monitoring oxygen content in liquid steel as well as the newly developed sulfur sensor based on a ZrOz(Ca0) + CaS electrolyte. The use of mixed conducting ZrOZ as a semipermeable membrane or chemically selective sieve for oxygen at high temperatures is discussed. Oxygen transport from liquid iron to CO + C& gas mixtures through a ZrOZ membrane driven by a chemical potential gradient, in the absence of electrical leads or imposed potentials, was experimentally observed.

Alternating current conduction behavior of excimer laser ablated SrBi2Nb2O9 thin films

Bi-layered Aurivillius compounds prove to be efficient candidates of nonvolatile memories. SrBi2Nb2O9 thin films were deposited by excimer laser ablation at low substrate temperature (400 °C) followed by an ex situ annealing at 750 °C. The polarization hysteresis behavior was confirmed by variation of polarization with the external applied electric field and also verified with capacitance versus voltage characteristics. The measured values of spontaneous and remnant polarizations were, respectively, 9 and 6 μC/cm2 with a coercive field of 90 kV/cm. The measured dielectric constant and dissipation factors at 100 kHz were 220 and 0.02, respectively. The frequency analysis of dielectric and ac conduction properties showed a distribution of relaxation times due to the presence of multiple grain boundaries in the films. The values of activation energies from the dissipation factor and grain interior resistance were found to be 0.9 and 1.3 eV, respectively. The deviation in these values was attributed to the energetic conditions of the grain boundaries and bulk grains. The macroscopic relaxation phenomenon is controlled by the higher resistive component in a film, such as grain boundaries at lower temperatures, which was highlighted in the present article in close relation to interior grain relaxation and conduction properties.

Measurement of probability-distribution functions sensitive technique for the study of conduction phenomena in liquid dielectrics

The paper outlines a technique for sensitive measurement of conduction phenomena in liquid dielectrics. The special features of this technique are the simplicity of the electrical system, the inexpensive instrumentation and the high accuracy. Detection, separation and analysis of a random function of current that is superimposed on the prebreakdown direct current forms the basis of this investigation. In this case, prebreakdown direct current is the output data of a test cell with large electrodes immersed in a liquid medium subjected to high direct voltages. Measurement of the probability-distribution function of a random fluctuating component of current provides a method that gives insight into the mechanism of conduction in a liquid medium subjected to high voltages and the processes that are responsible for the existence of the fluctuating component of the current.

Numerical analysis of transpiration cooling in carbon dioxide atmosphere at hypersonic Mach numbers

The numerical solutions are obtained for skin friction, heat transfer to the wall and growth of boundary layer along the flat plate by employing two dimensional Navier-Stokes equations governing the hypersonic flow coupled with species continuity equations. Flow fields have been computed along the flat plate in CO2 atmosphere in the presence of transpiration cooling using air and carbon dioxide.

Scaling Analysis of Solidification of Liquid Aluminum Alloy Flowing on Cooling Slope

Among all methods of metal alloy slurry preparation, the cooling slope method is the simplest in terms of design and process control. The method involves pouring of the melt from top, down an oblique and channel shaped plate cooled from bottom by counter flowing water. The melt, while flowing down, partially solidifies and forms columnar dendrites on plate wall. These dendrites are broken into equiaxed grains and are washed away with melt. The melt, together with the equiaxed grains, forms semisolid slurry collected at the slope exit and cast into billets having non-dendritic microstructure. The final microstructure depends on several process parameters such as slope angle, slope length, pouring superheat, and cooling rate. The present work involves scaling analysis of conservation equations of momentum, energy and species for the melt flow down a cooling slope. The main purpose of the scaling analysis is to obtain a physical insight into the role and relative importance of each parameter in influencing the final microstructure. For assessing the scaling analysis, the trends predicted by scaling are compared against corresponding numerical results using an enthalpy based solidification model with incorporation of solid phase movement.

Microstructural Evolution of A356 Al Alloy During Flow Along a Cooling Slope

Cooling slope (CS) has been used in this study to prepare semi-solid slurry of A356 Al alloy, keeping in view of slurry generation on demand for Rheo-pressure die casting process. Understanding the physics of microstructure evolution during cooling slope slurry formation is important to satisfy the need of semi-sold slurry with desired shape, size and morphology of primary Al phase. Mixture of spherical and rosette shaped primary Al phase has been observed in the samples collected during melt flow through the slope as well as in the cast (mould) samples compared to that of dendritic shape, observed in case of conventionally cast A356 alloy. The liquid melt has been poured into the slope at 650 A degrees C temperature and during flow it falls below the liquidus temperature of the said alloy, which facilitates crystallization of alpha-Al crystals on the cooling slope wall. Crystal separation due to melt flow is found responsible for nearly spherical morphology of the primary Al phase.

Effect of pouring temperature on cooling slope casting of semi-solid Al-Si-Mg alloy

Present trend of semi-solid processing is directed towards rheocasting route which allows manufacturing of near-net-shape cast components directly from the prepared semi-solid slurry. Generation of globular equi-axed grains during solidification of rheocast components, compared to the columnar dendritic structure of conventional casting routes, facilitates the manufacturing of components with improved mechanical properties and structural integrity. In the present investigation, a cooling slope has been designed and indigenously fabricated to produce semi solid slurry of Al-Si-Mg (A356) alloy and successively cast in a metallic mould. The scope of the present work discusses about development of a numerical model to simulate the liquid metal flow through cooling slope using Eulerian two-phase flow approach and to investigate the effect of pouring temperature on cooling slope semi-solid slurry generation process. The two phases considered in the present model are liquid metal and air. Solid fraction evolution of the solidifying melt is tracked at different locations of the cooling slope, following Schiel's equation. The continuity equation, momentum equation and energy equation are solved considering thin wall boundary condition approach. During solidification of the liquid metal, a modified temperature recovery scheme has been employed taking care of the latent heat release and change of fraction of liquid. The results obtained from simulations are compared with experimental findings and good agreement has been found.

Temperature dependence of spin lifetime of conduction electrons in bulk germanium

Optically generated spin polarized electrons in bulk n-type Ge samples have been detected by using a radio-frequency modulation technique. Using the Hanle effect in an external magnetic field, the spin lifetime was measured as a function of temperature in the range 90 K to 180 K. The lifetime decreases with increasing temperature from similar to 5 ns at 100 K to similar to 2 ns at 180 K. We show that the temperature dependence is consistent with the Elliott-Yafet spin relaxation mechanism R. J. Elliot, Phys. Rev. 96, 266 (1954)]. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4772500]