Cooling of a composite slab in a two-fluid medium

A mixed boundary value problem associated with the diffusion equation that involves the physical problem of cooling of an infinite parallel-sided composite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speedv. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming the front layer of the fluid to be of finite width and the back layer of infinite extent. The main problem is solved through a three-part Wiener-Hopf problem of a special type and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Numerical estimation of hotspot temperatures in electrodes subjected to pulsed electron beam heating in vacuum

A numerical solution for the transient temperature distribution in a cylindrical disc heated on its top surface by a circular source is presented. A finite difference form of the governing equations is solved by the Alternating Direction Implicit (ADI) time marching scheme. This solution has direct applications in analyzing transient electron beam heating of target materials as encountered in the prebreakdown current enhancement and consequent breakdown in high voltage vacuum gaps stressed by alternating and pulsed voltages. The solution provides an estimate of the temperature for pulsed electron beam heating and the size of thermally activated microparticles originating from anode hot spots. The calculated results for a typical 45kV (a.c.) electron beam of radius 2.5 micron indicate that the temperature of such spots can reach melting point and could give rise to microparticles which could initiate breakdown.

Cooling of an infinite slab in a two-fluid medium

A mixed boundary-valued problem associated with the diffusion equation, that involves the physical problem of cooling of an infinite slab in a two-fluid medium, is solved completely by using the Wiener-Hopf technique. An analytical solution is derived for the temperature distribution at the quench fronts being created by two different layers of cold fluids having different cooling abilities moving on the upper surface of the slab at constant speed. Simple expressions are derived for the values of the sputtering temperatures of the slab at the points of contact with the respective layers, assuming one layer of the fluid to be of finite extent and the other of infinite extent. The main problem is solved through a three-part Wiener - Hopf problem of a special type, and the numerical results under certain special circumstances are obtained and presented in the form of a table.

Numerical and experimental study of the thermal behaviour of coining and upsetting processes

A numerical simulation technique has been employed to study the thermal behavior of hot-forging type forming processes. Experiments on the coining and upsetting of an aluminum billet were conducted to validate the numerical predictions. Typical forming conditions for both the coining and upsetting processes were then studied in detail. an electrical analogy scheme was used to determine the thermal contact resistance. This scheme can conviniently provide the interface characteristics for typical processing conditions, which normally involve high pressures and temperatures. A single forging cycle was first considered, and then a batch of twenty-five forgings was studied. Each forging cycle includes the billet mounting, ascent, loading, dwelling, unloading, descent, and billet removal stages. The temperature distribution in the first forging to be formed is found to be significantly different from that at the end of the batch. In industry, forging is essentially a batch operation. The influence of forming speed and reduction on thermal characteristics was investigated also. The variations that can occur in the process design by considering differences in temperature characteristics are discussed also.

Studies on helium flow in experimental loops with different impedances operated with fountain effect pumps

An experimental flow loop with He II flow driven by fountain effect pumps (FEPs) is studied with respect to operation at different flow impedances and with thermal loads applied at different positions. The measured values of temperature, flow rate and pressure drop are compared with calculations resulting from a simplified model which assumes ideal performance of the porous plug and of the heat exchangers and which does not take into account Gorter-Mellink (GM) conduction. The main features of the loop are shown to be well described by this model. Refined calculations with a more complex model, including GM conduction of the He II, are only required for predicting the temperature distribution in some discrete regions of the loop.

Role of surface tension driven convection in pulsed - laser melting and solidification

Surface melting by a stationary, pulsed laser has been modelled by the finite element method. The role of the surface tension driven convection is investigated in detail. Numerical results are presented for a triangular laser pulse of durations 10, 50 and 200 ms. Though the magnitude of the velocity is high due to the surface tension forces, the present results indicate that a finite time is required for convection to affect the temperature distribution within the melt pool. The effect of convection is very significant for pulse durations longer than 10 ms.

Control of transient thermal response during sequential open-die forging: A trajectory optimization approach

A trajectory optimization approach is applied to the design of a sequence of open-die forging operations in order to control the transient thermal response of a large titanium alloy billet. The amount of time tire billet is soaked in furnace prior to each successive forging operation is optimized to minimize the total process time while simultaneously satisfying constraints on the maximum and minimum values of the billet's temperature distribution to avoid microstructural defects during forging. The results indicate that a "differential" heating profile is the most effective at meeting these design goals.

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.

Computational and experimental studies of fluid flow and heat transfer in a Calandria based reactor

CFD investigations are carried out to study the heat flux and temperature distribution in the calandria using a 3–Dimensional RANS code. Internal flow computations and experimental studies are carried out for a calandria embedded with a matrix of tubes working together as a reactor. Numerical investigations are carried on the Calandria reactor vessel with horizontal inlets and outlets located on top and the bottom to study the flow pattern and the associated temperature distribution. The computations have been carried out to simulate fluid flow and convective heat transfer for assigned near–to working conditions with different moderator injection rates and reacting heat fluxes. The results of computations provide an estimate of the tolerance bands for safe working limits for the heat dissipation at different working conditions by virtue of prediction of the hot spots in the calandria. The isothermal CFD results are validated by a set of experiments on a specially designed scaled model conducted over a range of flows and simulation parameters. The comparison of CFD results with experiments show good agreement.

Down-to-earth temperatures: The mechanics of the thermal environment

This lecture describes some recent attempts at unravelling the mechanics of the temperature distribution near ground, especially during calm, clear nights. In particular, a resolution is offered of the so-called Ramdas paradox, connected with observations of a temperature minimum some decimetres above bare soil on calm clear nights, in apparent defiance of the Rayleigh criterion for instability due to thermal convection. The dynamics of the associated temperature distribution is governed by radiative and convective transport and by thermal conduction, and is characterised by two time constants, involving respectively quick radiative adjustments and slow diffusive relaxation. The theory underlying the work described here suggests that surface parameters like ground emissivity and soil thermal conductivity can exert appreciable influence on the development of nocturnal inversions.

Theoretical estimation of electromigration in metallic carbon nanotubes considering self-heating effect

In this paper, we estimate the solution of the electromigration diffusion equation (EMDE) in isotopically pure and impure metallic single-walled carbon nanotubes (CNTs) (SWCNTs) by considering self-heating. The EMDE for SWCNT has been solved not only by invoking the dependence of the electromigration flux on the usual applied static electric field across its two ends but also by considering a temperature-dependent thermal conductivity (κ) which results in a variable temperature distribution (T) along its length due to self-heating. By changing its length and isotopic impurity, we demonstrate that there occurs a significant deviation in the SWCNT electromigration performance. However, if κ is assumed to be temperature independent, the solution may lead to serious errors in performance estimation. We further exhibit a tradeoff between length and impurity effect on the performance toward electromigration. It is suggested that, to reduce the vacancy concentration in longer interconnects of few micrometers, one should opt for an isotopically impure SWCNT at the cost of lower κ, whereas for comparatively short interconnects, pure SWCNT should be used. This tradeoff presented here can be treated as a way for obtaining a fairly well estimation of the vacancy concentration and mean time to failure in the bundles of CNT-based interconnects. © 2012 IEEE.

Natural convection in a series of thermally interacting cavities with wall mounted heaters

Laminar natural convection in a series of thermally interacting cavities is numerically studied. Each cavity consists of a conducting bottom wall with a surface mounted heater. The side walls of the cavities are isothermally cooled. Each cavity thermally interacts with its adjacent cavities through the conducting walls. Flow and heat transfer characteristics are studied in detail for various Rayleigh numbers. The convection characteristics in multiple cavities are compared with those in single independent cavity. The thermal interaction between the cavities results in lower temperatures compared with those in independent cavities. While heat is rejected into the adjacent upper cavity through some portion of the conducting wall, heat is received from the adjacent cavity through the remaining portion of the wall. The influence of substrate conductivity on heat exchange between adjacent cavities are examined. Substrate conductivity shows strong effect on temperature distribution. When cooling at both vertical sides is changed to one side cooling, the heat transfer characteristics are changed drastically and many interesting flow features are observed. Effects of cavity aspect ratio is studied and higher heat transfer rates are observed at higher aspect ratios. Correlations for dimensionless temperature maximum and average Nusselt number are presented in terms of Rayleigh number.

Eulerian two-phase flow simulation and experimental validation of semisolid slurry generation process using cooling slope

Experimental and numerical studies of slurry generation using a cooling slope are presented in the paper. The slope having stainless steel body has been designed and constructed to produce semisolid A356 Al alloy slurry. The pouring temperature of molten metal, slope angle of the cooling slope and slope wall temperature were varied during the experiment. A multiphase numerical model, considering liquid metal and air, has been developed to simulate the liquid metal flow along the cooling channel using an Eulerian two-phase flow approach. Solid fraction evolution of the solidifying melt is tracked at different locations of the cooling channel following Schiel's equation. The continuity, momentum and energy equations are solved considering thin wall boundary condition approach. During solidification of the melt, based on the liquid fraction and latent heat of the alloy, temperature of the alloy is modified continuously by introducing a modified temperature recovery method. Numerical simulations has been carried out for semisolid slurry formation by varying the process parameters such as angle of the cooling slope, cooling slope wall temperature and melt superheat temperature, to understand the effect of process variables on cooling slope semisolid slurry generation process such as temperature distribution, velocity distribution and solid fraction of the solidifying melt. Experimental validation performed for some chosen cases reveals good agreement with the numerical simulations.

Model-free simulations for compressible mixing layer

Confined supersonic mixing layer is explored through model-free simulations. Both two- and three-dimensional spatio-temporal simulations were carried out employing higher order finite difference scheme as well as finite volume scheme based on open source software (OpenFOAM) to understand the effect of three-dimensionality on the development of mixing layer. It is observed that although the instantaneous structures exhibit three-dimensional features, the average pressure and velocities are predominantly two-dimensional. The computed wall pressures match well with experimental results fairly well, although three-dimensional simulation underpredicts the wall pressure in the downstream direction. The self-similarity of the velocity profiles is obtained within the duct length for all the simulations. Although the mixing layer thicknesses differ among different simulations, their growth rate is nearly the same. Significant differences are observed for species and temperature distribution between two- and three-dimensional calculations, and two-dimensional calculations do not match the experimental observation of smooth variations in species mass fraction profiles as reported in literature. Reynolds stress distribution for three-dimensional calculations show profiles with less peak values compared to two-dimensional calculations; while normal stress anisotropy is higher for three-dimensional case.

A model of coupled thermal, mechanical, and electrostatic field effects in III-N thin film heterostructures

A one-dimensional coupled multi-physics based model has been developed to accurately compute the effects of electrostatic, mechanical, and thermal field interactions on the electronic energy band structure in group III-nitrides thin film heterostructures. Earlier models reported in published literature assumes electro-mechanical field with uniform temperature thus neglecting self-heating. Also, the effects of diffused interface on the energy band structure were not studied. We include these effects in a self-consistent manner wherein the transport equation is introduced along with the electro-mechanical models, and the lattice structural variation as observed in experiments are introduced at the interface. Due to these effects, the electrostatic potential distribution in the heterostructure is altered. The electron and hole ground state energies decrease by 5% and 9%, respectively, at a relative temperature of 700 K, when compared with the results obtained from the previously reported electro-mechanical model assuming constant and uniform temperature distribution. A diffused interface decreases the ground state energy of electrons and holes by about 11% and 9%, respectively, at a relative temperature of 700 K when compared with the predictions based on uniform temperature based electro-mechanical model. (C) 2013 AIP Publishing LLC.