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HostJane seller ClaireLovesMath - Mathematics

Claire

Mathematics

Thermodynamics

Temperature scales, heat and heat engines and kinetic theory; heat transfer; thermal and chemical equilibrium; classical gases and phase transitions; geometrical optics, lenses, mirrors and optical instruments; physical optics, diffraction, interference and wave theory; Fluid statics and dynamics, first and second laws of thermodynamics and special theory of relativity. Applications in ideal gas and vapor power to refrigeration cycles; entropy and availability; second law: entropy statement and logical equivalence with Clausius and Kelvin Planck statements. Power and refrigeration cycles. Mixtures, psychrometry, chemical reactions and combustion. Conduction, convection, radiation, steady state flow systems: turbines, pumps/compressors, throttles, boilers, nozzles, diffusers, single substance mixing chambers, and heat exchangers; air-conditioning; Relationship between pressure / volume, temperature / volume, and pressure / temperature spaces; Irreversibility and definition of entropy. Got a Thermodynamics project? Hire the best Thermodynamics freelancers with the right skills and background in April 2024 to get your Thermodynamics job done quickly. Schedule a consultation with a Thermodynamics freelancer today. Read less

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This relates as a field to incompressible fluid flow. Review of control-volume approach to fluids engineering problems, with advanced applications. Differential analysis of fluid motion. Derivation of full Navier-Stokes, Euler, and Bernoulli equations. Unsteady Bernoulli equation. Velocity potential and its application to steady two-dimensional flows. Vorticity and vortex motion. Eulerian vs. Lagrangian analysis.
An introduction to the general theory of solid deformation; small deformation emphasized. Topics include: Cartesian tensors, indicial notation. Introduction to continuum mechanics: deformation of continuous media, deformation gradient, strain definitions. Stress, Cauchy's postulate, Cauchy and Piola-Kirchhoff stress tensors. Balance laws. Constitutive equations, strain energy and Green's postulate. Linear Elasticity: two-dimensional problems, Airy stress function, in-plane loading of strips, St. Venant's principle, complex variable methods, Goursat-Muskhelishvili representation, stress concentrations around holes and cracks. Three-dimensional problems, Kelvin's solution, the Boussinesq problem, Hertzian contact, Eshelby's energy-momentum tensor.

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