An Angular Finite Element Method for the Solution of the Even-Parity Equation

The present article introduces a new method to solve the radiative transfer equation (RTE). First, a finite element discretization of the solid angle dependence is derived, wherein the coefficients of the finite element approximation are functions of the spatial coordinates. The angular basis functions are defined according to finite element principles on subdivisions of the octahedron. In a second step, these spatially dependent coefficients are discretized by spatial finite elements. This approach is very attractive, since it provides a concise derivation for approximations of the angular dependence with an arbitrary number of angular nodes. In addition, the usage of high-order angular basis functions is straightforward. In the current paper the governing equations are first derived independently of the actual angular approximation. Then, the design principles for the angular mesh are discussed and the parameterization of the piecewise angular basis functions is derived. In the following, the method is applied to two-dimensional test cases which are commonly used for the validation of approximation methods of the RTE. The results reveal that the proposed method is a promising alternative to the well-established practices like the Discrete Ordinates Method (DOM) and provides highly accurate approximations. A test case known to exhibit the ray effect in the DOM verifies the ability of the new method to avoid ray effects.

Steam Ejector Used as a Substitute for Cooling Tower in the Ethanol Production Process

Nowadays petroleum dependency in transportation is widely discussed all over the world. Atmospheric pollution and global warming are deleterious consequences of gasoline consumption. Ethanol is a natural substitute fuel that has been increasingly used. One of the most important raw materials used for ethanol production is the sugar cane. The exothermic fermentation reaction of the sugar cane juice in the ethanol production process requires a rigorous temperature control. This control is usually made by using cooling water from cooling towers. The heat released from cooling towers not only has an economical cost as well as it contributes to the global heating. Steam ejectors can substitute cooling towers thus improving the ethanol production plant efficiency and reducing world heating. Furthermore, steam ejectors are smaller, cheaper and are very simple equipment when compared with cooling towers. Furthermore, its use provides an improved thermal efficiency of the production plant resulting in the reduction of the global warming effects. In this work the use of steam ejector is proposed for the fermentation cooling of a typical Brazilian sugar and ethanol production plant. The steam which feeds the steam ejector is obtained from the plant utilities and the low temperature obtained from steam expansion within the ejector is used for sugar cane fermentation process cooling. The steam ejector discharge heat is recovered as it is used to sugar and ethanol production process heating. The sugar and ethanol production plant overall energy fluxes either using cooling towers as well as using steam ejectors are presented and the results are compared and discussed.

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

Low-Profile Chipset Microprocessor Heatsink Optimization for Server Form Factor

We present a methodology for optimizing footprint, metal mass and thermal performance of an aluminum extruded heatsink for cooling chipset microprocessors in server form-factor. The analysis is based on predefined volume flow rate of air at a constant temperature assumed to be available upstream of the package. The front-to-back cooling assumption covers the worst case ambient conditions, typical of chipset boundary condition in servers. We present studies covering a range of heatsink footprints in order to compare and minimize the heatsink footprint, at the same time satisfying thermal specification of the chipset microprocessor. The study also focuses on the system-level assessment of the optimum 60×40 mm2 footprint and corner cases by studying the effect of motherboard thermal conductivity as well as blockages on the heatsink case-to-ambient thermal resistance.

A Numerical Study on the Slab Heating Characteristics in a Reheating Furnace With the Formation and Growth of Scale on the Slab Surface

In this work, the development of a mathematical heat transfer model for a walking-beam type reheating furnace is described and preliminary model predictions are presented. The model can predict the heat flux distribution within the furnace and the temperature distribution in the slab throughout the reheating furnace process by considering the heat exchange between the slab and its surroundings, including the radiant heat transfer among the slabs, the skids, the hot combustion gases and the furnace wall as well as the gas convection heat transfer in the furnace. In addition, present model is designed to be able to predict the formation and growth of the scale layer on the slab in order to investigate its effect on the slab heating. A comparison is made between the predictions of the present model and the data from an in situ measurement in the furnace, and a reasonable agreement is found. The results of the present simulation show that the effect of the scale layer on the slab heating is considerable.

A k-Distribution-Based Spectral Module for Radiation Calculations in Multi-Phase Mixtures

k-distribution-based approaches are promising models for radiation calculations in strongly nongray participating media. Advanced k-distribution methods were found to achieve close-to benchmark line-by-line (LBL) accuracy for strongly inhomogeneous multi-phase media accompanied by several orders of magnitude smaller computational cost. In this paper, a k-distribution-based portable spectral module is developed, incorporating several state-of-the-art k-distribution methods along with compact and high-accuracy databases of k-distributions. The module construction is flexible — the user can choose among various k-distribution methods with their relevant k-distribution databases, to carry out accurate radiation calculations. The spectral module is portable, such that it can be coupled to any flow solver code with its own grid structure, discretization scheme, and solver libraries. This open source code module is made available for free for all noncommercial purposes. This article outlines in detail the design and the use of the spectral module. The k-distribution methods included in the module are briefly described with a discussion of their advantages, disadvantages and their domain of applicability. Examples are provided for various sample radiation calculations in multi-phase mixtures using the new spectral module and the results are compared with LBL calculations.

An Experimental Investigation of Microchannel Size Effects on Flow Boiling With De-Ionized Water

The heat transfer characteristics during flow boiling of deionized water in parallel microchannels are investigated. The silicon heat sinks contain an array of integrated heaters and diodes for localized heat-flux control and temperature measurement. The channel widths for the three different test pieces range from 250 μm to 2200 μm, with a nominal depth for all channels of 400 μm. The present study investigates the effects of the channel width and mass flux on the boiling performance. This study follows a previous study using a wetting dielectric liquid, and aims to understand the role of wetting since water is relatively non-wetting. From the results of the present study, a weak dependence of the boiling curve and heat transfer coefficient on mass flux was observed. Varying the channel width also does not have a strong effect on either the boiling curve or the heat transfer coefficient. The experimental results are compared to those obtained previously for a dielectric liquid. They are also compared with predictions from several correlations from the literature.

Lumped Parameters Modeling of an Incinerator With Heat Recovery for Energy Production

This work shows the modeling of an incineration plant with energy recovery which operates in the vicinity of Pisa, Italy. The plant analysed was built formerly as an incineration plant and was recently refurbished with a heat recovery steam generator to drive a condensing steam turbine. In the foresight of an enlargement of the plant capacity, the Technical Office of the Company asked the Energetica Department of University of Pisa for an analysis of the recovery capability. The Technical Office and the Energetica Department decided to create a lumped parameter model in order to simulate the temperature behavior of the combustion products. This model was created inside Matlab/Simulink environment. The followed procedure led to the reproduction of the system interested by the cycle in steady state conditions in order to obtain a model simple enough but at the same time rigorous of the real behavior of steam cicle. After the description of the plant modeling, model calibration and validation is shown, by means of the comparison between the measured and simulated values of temperatures and mass flows in several load conditions. The model developed is currently used by the Technical Office of the Company for further developments of the plant.

Narrow-Band k-Distribution Database for Atomic Radiation in Hypersonic Nonequilibrium Flows

Full-spectrum k-distribution (FSK) and multi-group FSK approaches make it possible to evaluate radiative fluxes at a fraction of the cost needed for line-by-line calculations. However, the required k-distributions need to be assembled from accurate absorption coefficient data for each flow condition, which is computationally expensive. An accurate and compact narrow-band k-distribution database has been developed for the most important species encountered in hypersonic nonequilibrium flow. The database allows users to calculate desired full-spectrum k-distributions through look-up and interpolation. Strategies for k-distribution data generation are outlined. The accuracy of the database is tested by comparing narrow-band mean absorption coefficients and narrow-band emissivities with those obtained from line-by-line calculations. Application of the database to construct full-spectrum k-distributions accurately and efficiently is discussed, and results from a number of heat transfer calculations and cpu-time studies are presented.

On the Reduction of Wall Temperature Non-Uniformity of a Three-Dimensional Experimental Apparatus

This paper presents a detailed analysis that was performed for the design of a “uniform” temperature boundary condition imposed on a boundary of a three-dimensional cubical experimental apparatus for benchmark natural convection heat transfer study. The three-dimensional experimental apparatus was constructed with plates which were assembled to act as boundary conditions to the enclosure walls. Test measurements revealed that temperature non-uniformity along one of the plates (boundary) was significant enough that the benchmark study could not be carried out to the desired accuracy of about 1% error. A subsequent detailed mathematical analysis revealed that the temperature non-uniformity on the plate was a result of the effect of thermal spreading/constriction resistance. Modifications to the original design of the apparatus were made to reduce the temperature non-uniformity on the plate by adding a heat source around the plate where the uniform temperature setting was desired. Before the addition of this heat source, a careful mathematical analysis shows a significant reduction in temperature non-uniformity from about 4% (based on the initial design) to less than 1% (for the modified design). By examining the temperature difference between two locations on the plate, the predicted temperature difference obtained through mathematical analyses show excellent agreement with the measured temperature difference.