Introduction Introduction Governing Equations of Fluid Flow and Heat Transfer Mathematical Properties of Entropy and Exergy Governing Equations of Entropy and the Second Law Formulation of Entropy Production and Exergy Destruction Statistical and Numerical Formulations of the Second Law Introduction Conservation Laws as Moments of the Boltzmann Equation Extended Probability Distributions Selected Multivariate Probability Distribution Functions Concave Entropy Functions Statistical Formulation of the Second Law Numerical Formulation of the Second Law Predicted Irreversibilities of Incompressible Flows Introduction Entropy Transport Equation for Incompressible Flows Formulation of Loss Coefficients with Entropy Production Upper Entropy Bounds in Closed Systems Case Study of Automotive Fuel Cell Design Case Study of Fluid Machinery Design Measured Irreversibilities of Incompressible Flows Introduction Experimental Techniques of Irreversibility Measurement Case Study of Magnetic Stirring Tank Design Case Study of Natural Convection in Cavities Measurement Uncertainties Entropy Production in Microfluidic Systems Introduction Pressure-Driven Flow in Microchannels Applied Electric Field in Microchannels Micropatterned Surfaces with Open Microchannels Numerical Error Indicators and the Second Law Introduction Discretization Errors of Numerical Convection Schemes Physical Plausibility of Numerical Results Entropy Difference in Residual Error Indicators Numerical Stability and the Second Law Introduction Stability Norms Entropy Stability of Finite Difference Schemes Stability of Shock Capturing Methods Entropy Transport with Phase Change Heat Transfer Introduction Entropy Transport Equations for Solidification and Melting Heat and Entropy Analogies in Phase Change Processes Numerical Stability of Phase Change Computations Thermal Control of Phase Change with Inverse Methods Entropy Production with Film Condensation Entropy Production in Turbulent Flows Introduction Reynolds Averaged Entropy Transport Equations Eddy Viscosity Models of Mean Entropy Production Turbulence Modeling with the Second Law
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