G.F. Naterer

Heat Transfer in Single and Multiphase Systems

INTRODUCTION Vector and Tensor Notations Fundamental Concepts and Definitions Eulerian and Lagrangian Descriptions Properties of a System Conductive Heat Transfer Convective Heat Transfer Radiation Heat Transfer Phase Change Heat Transfer Conservation of Energy Problems CONDUCTION HEAT TRANSFER Introduction One-Dimensional Heat Conduction Thermal and Contact Resistances Fins and Extended Surfaces Multidimensional Heat Conduction Graphical Solution Methods Analytical Methods Transient Heat Conduction Combined Transient and Spatial Effects References Problems CONVECTIVE HEAT TRANSFER Introduction Convection Governing Equations Velocity and Thermal Boundary Layers External Forced Convection Internal Forced Convection Free Convection Second Law of Thermodynamics Turbulence Modelling References Problems RADIATIVE HEAT TRANSFER Introduction Fundamental Processes and Equations Radiation Exchange Between Surfaces Thermal Radiation in Enclosures with Diffuse Gray Surfaces Solar Energy References Problems PHASE CHANGE HEAT TRANSFER Introduction Processes of Phase Change Mixture and Two-Fluid Formulations Interface Tracking References Problems GAS (VAPOR) - LIQUID SYSTEMS Introduction Boiling Heat Transfer Condensation Heat Transfer Devices with Vapor - Liquid Phase Change References Problems GAS - SOLID (PARTICLE) SYSTEMS Introduction Classification of Gas - Solid Flows Dynamics of Gas - Solid Flows Fluidized Beds References Problems LIQUID - SOLID SYSTEMS Introduction One-Dimensional Solidification and Melting Phase Change with Convection Phase Change with Coupled Heat and Mass Transfer Problems in Other Geometries Multi-Dimensional Solidification and Melting Dynamics of Liquid - Solid Flows Applications References Problems GAS -LIQUID - SOLID SYSTEMS Introduction Droplet Flows with Phase Change Gas Flows with Solidification and Melting Chemically Reacting Systems Multiphase Byproducts of Reacting Flows References Problems HEAT EXCHANGERS Introduction Tubular Heat Exchangers Cross-Flow and Shell-and-Tube Heat Exchangers Effectiveness - NTU Method of Analysis Condensers and Evaporators References Problems COMPUTATIONAL HEAT TRANSFER Finite Difference Methods Weighted Residual Methods Finite Element Method Hybrid Methods Numerical Methods for Other Applications Accuracy and Efficiency Improvements References Problems APPENDICES INDEX

Modeling of Entropy Production in Turbulent Flows

We present new modeling of turbulence correlations in the entropy transport equation for viscous, incompressible flows. An explicit entropy equation of state is developed for gases with the ideal gas law, while entropy transport equations are derived for both gases and liquids. The formulation specifically considers incompressible forced convection problems without a buoyancy term in the y-momentum equation, as density variations are neglected. Reynolds averaging techniques are applied to the turbulence closure of fluctuating temperature and entropy fields. The problem of rigorously expressing the mean entropy production in terms of other mean flow quantities is addressed. The validity of the newly developed formulation is assessed using direct numerical simulation data and empirical relations for the friction factor. Also, the dissipation (e) of turbulent kinetic energy is formulated in terms of the Second Law. In contrast to the conventional e equation modeling, this article proposes an alternative method by utilizing both transport and positive definite forms of the entropy production equation.

Establishing heat–entropy analogies for interface tracking in phase change heat transfer with fluid flow

Abstract In this paper, entropy is presented as an important variable in effectively describing and predicting various phase change processes. An interfacial entropy constraint, downward concavity condition and Second Law formulation are obtained. Modelling of interfacial momentum interactions and thermal recalescence are based on heat–entropy analogies. It is shown that deeper insight into phase change processes with fluid flow can be realized through consideration of the analogy variable (entropy). Also, an entropy-based approach provides effective guidelines for interface tracking and numerical stability in phase change computations involving a control volume-based finite element method (CVFEM) formulation.

Unified Approach to Exergy Efficiency, Environmental Impact and Sustainable Development for Standard Thermodynamic Cycles

The exergy efficiency of three standard thermodynamic cycles, i.e., Brayton, Rankine and Otto cycles, are developed and the corresponding analytical equations are derived accordingly. The resultant expressions are applied to typical operating conditions and numerical results are obtained, when the heat of each engine is supplied by burning natural gas as a fuel with 100 percent theoretical air. A common result is the significant effect of the maximum cycle temperature, which causes an increase of exergy efficiency. It is shown that the compression ratio of the Brayton and Otto cycles, as well as the turbine inlet pressure in a steam power plant, raise the exergy efficiency. Moreover, increasing the ambient temperature has a negative influence on the exergy efficiency in the Brayton and Otto cycles, which occurs due to ambient air fed to these systems, thereby decreasing the deviation of the system from ambient conditions and reducing the exergy efficiency. Further findings include an optimal performance point of the Brayton and Rankine cycle, with a high sustainability and exergy efficiency. For instance, at the optimal operating point of the Brayton cycle with a compression ratio of 8 (or 12 for a second case), the exergy efficiency is 73 (60) percent, CO2 emissions is 530 (590) g/kWh and the sustainability index is 3.8 (2.8). The optimal operating point for an example of a Rankine cycle is found to be 50 percent for the exergy efficiency, with 440g/kWh of emitted CO2 and a sustainability index of two.

Slip-flow irreversibility of dissipative kinetic and internal energy exchange in microchannels

The mechanisms of near-wall velocity slip and their effects on energy conversion of fluid motion in microchannels are investigated. Unlike large-scale channels with no-slip boundary conditions, this paper predicts how streamwise temperature gradients and transverse velocity gradients contribute to velocity slip during intermolecular interactions near a microchannel wall. A numerical formulation is developed with a mass-weighted convection scheme (called NISUS; non-inverted skew upwind scheme) in a SIMPLEC finite volume method. The new convection scheme provides accurate upstream interpolation of convection variables, including robust pressure/velocity coupling near the slip-flow boundary. Numerical predictions of entropy production characterize the near-wall dissipation of kinetic energy. Effects of varying pressure ratios, accommodation coefficients, flow rates and channel aspect ratios are presented for nitrogen gas flows between Re = 0.001 and 0.003. This paper gives new insight regarding dissipative kinetic and internal energy exchange in microchannels, due to slip-flow behavior.

Adaptive Surface Microprofiling for Microfluidic Energy Conversion

Adaptive microprofiling is a newly proposed technique of embedding open microchannels within a surface to take advantage of resulting slip-flow behavior and drag reduction. The objective of this paper is to predict the optimal geometrical profiles of such microchannels, particularly for minimizing entropy production in convective heat-transfer problems. A theoretical slip-flow formulation (within microchannels) is developed for Knudsen numbers between about 0.02 and 0.07. These values fall within the range governed by the Navier-Stokes equations with slip-flow boundary conditions. Numerical results show that a fourth-order geometrical profile yields lower entropy production than a linearly diverging microchannel. With rapid advances in micromachining technology, it is viewed that adaptive microprofiling can become a useful alternative technique of drag reduction, while increasing heat-transfer effectiveness. These combined objectives can be realized through the newly formulated approach with entropy-based microprofiling, which establishes the optimal microgroove patterns by minimizing entropy production over the surface

Applying heat–entropy analogies with experimental study of interface tracking in phase change heat transfer

Abstract Heat–entropy analogies are applied to problems involving phase change heat transfer with fluid flow. In the experimental studies, entropy is not measured directly, but temperature and other measurements yield associated entropy results for improved understanding of the phase change processes. The entropy-based framework is shown to serve an important role in modelling of momentum phase interactions and thermal recalescence, as well as numerical stability in the computations. Numerical and experimental results indicate that entropy can serve as an effective variable in describing and predicting various interfacial processes during phase change.

Performance study of mode-pursuing sampling method

Since the publication of the authors’ recently developed mode-pursing sampling method, questions have been asked about its performance as compared with traditional global optimization methods such as the genetic algorithm and when to use mode-pursing sampling as opposed to the genetic algorithm. This work aims to provide an answer to these questions. Similarities and distinctions between mode-pursing sampling and the genetic algorithm are presented. Then mode-pursing sampling and the genetic algorithm are compared via testing with benchmark functions and practical engineering design problems. These problems can be categorized from different perspectives such as dimensionality, continuous/discrete variables or the amount of computational time for evaluating the objective function. It is found that both mode-pursing sampling and the genetic algorithm demonstrate great effectiveness in identifying the global optimum. In general, mode-pursing sampling needs much fewer function evaluations and iterations than the genetic algorithm, which makes mode-pursing sampling suitable for expensive functions. However, the genetic algorithm is more efficient than mode-pursing sampling for inexpensive functions. In addition, mode-pursing sampling is limited by the computer memory when the total number of sample points reaches a certain extent. This work serves the purpose of positioning the new mode-pursing sampling method in the context of direct optimization and provides guidelines for users of mode-pursing sampling. It is also anticipated that the similarities in concepts, distinctions in philosophy and methodology and effectiveness as direct search methods for both mode-pursing sampling and the genetic algorithm will inspire the development of new direct optimization methods.

Multiphase flow with impinging droplets and airstream interaction at a moving gas/solid interface

Abstract Multiphase flows with droplets involving gas (air), liquid (droplets) and solid (ice) phases are examined in this paper. The external multiphase flow is predicted in conjunction with a moving phase interface arising from solidification of impinging supercooled droplets. A scalar transport form of the droplet flow equations is solved separately from the viscous main (air) flow solver. This approach provides an effective alternative to tracking of individual droplet trajectories in the freestream. Interactions between the droplet and main (air) flows appear through appropriate inter-phase expressions in the momentum balance equations within each individual phase. The numerical formulation is based on a CVFEM (Control-Volume-based Finite Element Method) with quadrilateral isoparametric elements. This model is applied to problems involving the formation of rime (dry) ice (i.e., without liquid film covering the ice surface). Experimental data provides further insight into the impingement of droplets on a cylindrical conductor. Favorable agreement between the numerical and experimental results is achieved.

Thermal-Design Options for Pressure-Channel SCWRS With Cogeneration of Hydrogen

Currently there are a number of Generation IV supercritical water-cooled nuclear reactor (SCWR) concepts under development worldwide. The main objectives for developing and utilizing SCWRs are (1) to increase the gross thermal efficiency of current nuclear power plants (NPPs) from 33-35% to approximately 45-50% and (2) to decrease the capital and operational costs and, in doing so, decrease electrical-energy costs (approximately US