P. Rath

Discrete Transfer Method Applied To Transient Radiative Transfer Problems in Participating Medium

Application of the discrete transfer method is extended to solve transient radiative transport problems with participating medium. A one-dimensional gray planar absorbing and aniso-tropically scattering medium is considered. Both boundaries of the medium are black. The incident boundary of the medium is subjected to pulse-laser irradiation, while the other boundary is cold. For radiative parameters such as optical thickness, scattering albedo, anisotropy factor, transmittance, and reflectance at the boundaries are found. Results obtained from the present work are compared with those available in the literature. The discrete transfer method has been found to give an excellent agreement.

A total concentration fixed-grid method for two-dimensional wet chemical etching

A total concentration fixed-grid method is presented in this paper to model the two-dimensional wet chemical etching. Two limiting cases are discussed, namely—the diffusion-controlled etching and the reaction-controlled etching. A total concentration, which is the sum of the unreacted and the reacted etchant concentrations, is defined. Using this newly defined total concentration, the governing equation also contains the interface condition. A new update procedure for the reacted concentration is formulated. For demonstration, the finite-volume method is used to solve the governing equation with prescribed initial and boundary conditions. The effects of reaction rate at the etchant–substrate interface are examined. The results obtained using the total concentration method, are compared with available results from the literature.

Modeling Convection-Driven Diffusion-Controlled Wet Chemical Etching Using a Total-Concentration Fixed-Grid Method

A total-concentration fixed-grid method is presented to model the convection-driven wet chemical etching process. The proposed method is analogous to the enthalpy method used in the modeling of melting and solidification problems. A total concentration which is the sum of the unreacted etchant concentration and the reacted etchant concentration is defined. The governing equation based on the newly defined total concentration includes the interface condition. Hence the etchfront position can be found implicitly using the proposed method. The reacted etchant concentration is used to predict the etch front position while etching progresses. Since the grid size is fixed, there is no grid velocity, unlike the case with existing moving-grid approaches. Cartesian grids can be used to capture the complicated etch front evolved during etching. In this article, a two-dimensional, incompressible, Newtonian fluid with an infinitely fast reaction at the interface is considered. For demonstration purposes, a finite-volume method is used to solve the momentum equations, the continuity equation, and the convection-driven mass diffusion equation with prescribed initial and boundary conditions. The etch front evolution obtained using the proposed method is compared with the existing moving-grid method, and good agreement is found.

Numerical Study of Cyclic Melting and Solidification of Nano Enhanced Phase Change Material Based Heat Sink in Thermal Management of Electronic Components

The Present investigation has been carried out to study the performance of nano enhanced phase change material (NEPCM) based heat sink for thermal management of electronic components. Enthalpy based finite volume method is used for the analysis of phase change process in NEPCM. To enhance the thermal conductivity of phase change material (PCM), copper oxide nano particles of volume fractions 1%, 2.5% and 5% are added to PCM. A heat flux of 2500 W/m2 is taken as input to the heat sink. The thermal performance of the heat sink with PCM is compared with NEPCM for each volume fraction of nano particle for both finned and unfinned configurations. It is observed that the nano particle volume concentration plays a major role in removing the heat from the chip in case of unfinned heat sink configuration. However, for finned heat sink configuration, the volume concentration effect is not appreciable. In addition, the performance of NEPCM based finned heat sink is studied under cyclic loading in both natural and forced convection boundary conditions. It is observed that under forced convection the solidification time is reduced.Copyright

A Conduction-Radiation Mixture Model for Laser-Assisted Phase Change of Semitransparent Material

A one-dimensional transient coupled conduction-radiation numerical model is developed to investigate the laser melting of semitransparent material under a continuous collimated laser pulse in a convective cooling environment. The medium is considered absorbing, emitting, and scattering. The thermophysical properties are taken to be different for different phase fields. Volumetric radiation is incorporated in the proposed model. The radiation information is obtained by solving the equation of transfer. The temperature field is obtained by solving the energy equation with internal radiation source. The finite-volume method is used to discretize both the equation of transfer and the energy equation. The enthalpy formulation is adopted to capture the continuously evolving solid–liquid interface during the phase change. The laser source is approximated with the collimated radiation source. Collimated intensity is captured directly (without splitting the total intensity into two parts: diffuse and collimated) by adjusting the control angles. The present model is first validated with the existing phase-change model in the literature. Then the effects of different parameters such as optical thickness, scattering albedo, and the conduction–radiation parameter on the liquid fractions and temperature distribution in the medium are studied. It is observed that when the radiation is dominant, the temperature in the medium is high and hence the liquid fraction is more, in contrast to conduction-dominated phase change.

Hybrid Cooling System for Electronics Equipment During Power Surge Operation

The performance of a hybrid phase-change material (PCM)-based cooling system is investigated experimentally to meet the requirement of power surge effect in electronics equipment. The normal cooling operation of the electronic equipment for a long period using heat sink is also studied. The thermal performance of the hybrid heat sink is studied with three different PCMs: Eicosane, 1-Hexadecanol, and Paraffin. The hybrid PCM-based heat sink is studied for different orientations of PCM and convective cooling area in the heat sink to protect electronic components from the potentially dangerous and disruptive power surge operations. The performance of the hybrid PCM-based heat sinks is compared with conventional air-based heat sinks with and without a fan. In case of hybrid PCM-based heat sink, the fan is operated at 6 V all the time irrespective of the normal or power surge operation. Whereas, in case of air-based heat sink (without PCM), the fan is operated at 12 V during power surging and at 6 V during normal operation time. It is observed that the hybrid PCM-based heat sink with fan performs better than conventional air-based heat sink with fan during surging operation by reducing the peak temperature of 5.6 °C. However, their performance is comparable during post-surging operation. Thus, the power consumption, as well as the noise, gets reduced using hybrid PCM-based heat sink with fan during surging operation. Besides, the life of fan used in hybrid PCM-based heat sink increases, which in turn increases the service life of electronic components.

Divergence of Radiative Heat Flux in Ultra-Short Time Scale in Axisymmetric Geometry With its Implications

An axisymmetric transient radiative heat transfer model is developed taking into account the new formulation of divergence of radiative heat flux in ultrashort time scale. In order to predict the medium temperature, divergence of radiative heat flux is coupled with the energy equation. The conventional quasi steady divergence of radiative heat flux is modified taking into account the transient effect of photon transport. An axisymmetric domain is taken as a physical model in the present analysis. A critical examination revealed that even for pure scattering medium, the diveregence of flux is a non-zero quantity due to the inclusion of the new term called as propagation term in the formulation of the divergence of radiative heat flux in ultrashort time scale. A two-dimensional scheme is proposed to solve the radiative transfer equation (RTE) in an axisymmeric cylindrical domain. The step spatial scheme is used for discretizing the spatial term in the RTE. The medium is assumed to be absorbing, emitting and isotropically scattering. The walls are assumed as diffuse and gray. It is observed that the conventional quasi-steady divergence of radiative heat flux underpredicts the temperature of the medium in the time scale of the order of characteristic time scale of photon where transient radiation effect is predominant.© 2013 ASME

A numerical model for etching through a circular hole

A numerical model based on the total concentration of etchant is proposed to model the wet chemical etching through a circular hole. The reaction at the etchant-substrate interface is assumed to be infinitely fast i.e. etching is controlled by the diffusion of etchant to the interface. The proposed model is based on a fixed-grid approach analogous to the enthalpy method. The total concentration of etchant is the sum of the unreacted etchant concentration and the reacted etchant concentration. The reacted concentration of etchant is a measure of the etchfront position during etching. The governing mass diffusion equation based on the total concentration of etchant includes the interface condition. The etchfront position is found implicitly using the proposed approach. The computational domain is fixed, which includes the whole etchant and substrate domain including the mask region. For demonstration purposes, the finite volume method is used to solve the governing mass diffusion equation with prescribed initial and boundary conditions. The effect of mask thickness and initial etchant concentration on the shape evolution of etchfront is studied.

A Total Concentration Fixed-Grid Method for Two-Dimensional Diffusion-Controlled Wet Chemical Etching

This article presents a total concentration method for two-dimensional wet chemical etching. The proposed procedure is a fixed-grid approach. It is analogous to the enthalpy method used for modeling melting/solidification problems. The governing equation is formulated using the total concentration of the etchant. It includes the reacted and the unreacted concentrations of the etchant. The proposed governing equation includes the interface condition. The reacted concentration is used to capture the etchant-substrate interface implicitly. Since the grids are fixed, a diffusion problem remains a diffusion problem unlike the moving grid approach where the diffusion problem becomes the convection-diffusion problem due to the mesh velocity. For demonstration purposes, the finite volume method is used to solve for the transient concentration distribution of etchant. In this article, two-dimensional diffusion-controlled wet chemical etching processes are modeled. The results obtained from the proposed total concentration method are compared with available “analytic” solutions and solutions from moving-grid approach.Copyright