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This book deals with an important topic in rational continuum physics, thermodynamics.Although slim, it is fairly well self-contained; some basic notions in continuum mechanics, which a well-intentioned reader should but may not be familiar with, are collected in a final appendix. Modern continuum thermodynamics is a field theory devised to handle a large class of processes that typically are neither spatially homogeneous nor sequences of equilibrium states. The most basic chapter addresses the continuum theory of heat conduction, in which the constitutive laws furnish a mathematical characterization of the macroscopic manifestations of those fluctuations in position and velocity of the microscopic matter constituents that statistical thermodynamics considers collectively. In addition to a nonstandard exposition of the conceptual steps leading to the classical heat equation, the crucial assumption that energy and entropy inflows should be proportional is discussed and a hyperbolic version of that prototypical parabolic PDE is presented. Thermomechanics comes next, a slightly more complex paradigmatic example of a field theory where microscopic and macroscopic manifestations of motion become intertwined. Finally, a virtual power format for thermomechanics is proposed, whose formulation requires that temperature is regarded formally as the time derivative of thermal displacement. It is shown that this format permits an alternative formulation of the theory of heat conduction, and a physical interpretation of the notion of thermal displacement is given. It is addressed to mathematical modelers – or mathematical modelers to be – of continuous material bodies, be they mathematicians, physicists, or mathematically versed engineers.

Mathematics --- Thermodynamics --- thermodynamica --- wiskunde

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This book provides a comprehensive overview of protection schemes used for power transformers and describes the internal fault conditions and external abnormalities that may disrupt the operation of a power transformer. It also highlights the issues of current protective schemes, which pose several challenges in terms of the detection of internal faults and abnormalities, including computational burden, reduced accuracy, difficulty to implement, increased cost, computational complexity, impermeability to high resistance faults (HRF), and malfunction in conditions like cross-country fault. To address these problems, the book develops an effective novel transformer protection scheme that can eliminate all the said difficulties using an innovative algorithm. Given its scope, it is a useful resource for researchers and practitioners working in the field of power system protection, allowing them to design novel protection schemes, and providing insights into the hardware validation of developed technique.

Thermodynamics --- Electronics --- energietechniek --- vermogenselektronica

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vuur --- verbranding --- motoren --- Thermodynamics --- Inorganic chemistry --- fysica

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Thermodynamics --- Mechanical properties of solids --- thermodynamica --- warmteoverdracht

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Partial differential equations --- Thermodynamics --- differentiaalvergelijkingen --- thermodynamica