Compressible Flow with Applications to Engines, Shocks and Nozzles by Luis Manuel Braga da Costa Campos, Luis Antonio Raio Vilela (Hardcover, 2021)

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This book is part of the series Mathematics and Physics Applied to Science and Technology that combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. The volume V presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions, and includes applications to acoustic, elastic, water, electromagnetic and other waves and to the diffusion of heat, mass and electricity, and to their interactions. The first book 10 of volume V starts with the classification of partial differential equations and proceeds with similarity methods that apply in general to linear equations with constant coefficients and all derivatives of the same order, such as the Laplace and Biharmonic equations without and with forcing. The similarity solutions are also applied to Burger 's non-linear diffusion equation. Firstorder linear and quasi-linear partial differential equations with variable coefficients are considered, with application to the representation of conservative I non-conservative, solenoidal I rotational and Beltrami I helical vector fields by one, two or three scalar and/or one vector potential in relation with exact, inexact and non-integrable differentials. The latter appear in the first and second principles of thermodynamics, that specify the constitutive and diffusive properties of matter as concerns thermal, mechanical, elastic, flow, electrical, magnetic and chemical phenomena and their interactions. The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical and other branches of engineering dealing with advanced technology, and also in the physical sciences and applied mathematics.