UE Physics 1 - 4PUGPHY1

Goal(s)

• Mathematical tools for physicists and engineers
  For an engineer or a researcher, mathematics is an indispensable toolbox for the resolution of applied problems. This lecture consequently aims in introducing to the GEN2A alumni the following advanced methods: (i) use of orthonormal function bases. These bases use special functions frequently encountered in physics; (ii) Green’s functions, a powerful mean to solve PDE with boundary conditions. Green’s functions rely on the bases presented in (i).
  The lecture requires a good knowledge in mathematics: routine use of differential and integral calculus, complex and vector analysis, series, etc. Each part of the lecture will be illustrated with a practical application.

• Thermal Radiation Heat Transfer
  This course introduces the fundamentals of thermal radiation heat transfer. The following topics are covered: basic concepts and quantities related to radiation transfer, principles governing the radiation exchange between surfaces and a brief introduction to the resolution methods for radiation transport. This course in taught in French.

Content(s)

Mathematical tools for physicists and engineers (12h CM - 8h TD dédoublés)
Thermal Radiation Heat Transfer (6h CM - 6h TD dédoublés)
Nuclear Physics 1 (8h CM - 4h TD)

• Mathematical tools for physicists and engineers (Lecture : 12h - Tutorials : 8h)
  1. Orthonormal bases of functions
     Interest in physics, Laplace eigenvalues and eigenfunctions on the: (i) cube; (ii) cylinder: Bessel functions, Fourier-Bessel series; (iii) sphere: Legendre polynomials, Fourier-Legendre series, spherical harmonics, application examples of function bases.
  2. Green’s functions
     Resolution of PDE with boundary conditions, eigenvalue expansion of Green’s functions, Laplace operator case, application examples.

• Thermal Radiation Heat Transfer (Lecture : 6h - Tutorials : 6h)
  Chapter 1 - Radiation Transfer: Processes and Properties
  Fundamental Concepts: Spectral Intensity, Emissive Power, Irradiation Power and Radiosity. Blackbody Radiation, Planck distribution and Stefan-Boltzmann law. Surface Absorption, Reflection and Transmission. Opaque versus transparent media. Kirchhoff’s Law. The Gray Surface.

Chapter 2 – Radiation Exchange Between Surfaces
View Factor integral. View Factor Relations. View factors properties. Blackbody Radiation Exchange. Radiation exchange between diffuse, gray and opaque surfaces in an enclosure (N-Surfaces)

Chapter 3 - Resolution Methods for Radiation Transport
Transfer in Participating Media. Absorbing, Emitting, Non-scattering Medium. Absorbing, Emitting and Scattering Medium. Radiative Transfer Equation. Solution of the Transfer Equation. Two-Flux Model.

• Mathematical tools for physicists and engineers
  Fundamentals in mathematics (Bachelor degree)

• Thermal Radiation Heat Transfer
  • Fundamental of heat transfer: conduction and convection
  • Linear algebra
  • Vector analysis
  • Advanced calculus, including: Gauss’s and Stokes’s theorems, Partial differential equations (PDEs), Multivariable integration and differentiation and Complex variables.

Test

Written exam. One A4 sheet of paper (front and back). Calculator required. Same conditions for the second session.

Additional Information

Bibliography

• Thermal Radiation Heat Transfer
  [1] “Fundamentals of Heat and Mass Transfer”, F. P. Incropera (Auteur), D. P. DeWitt, T. L. Bergman and A.S. Lavine, John Wiley & Sons, 2006.
  [2] “Thermal Radiative Transfer and Properties”, M.Q. Brewster, John Wiley & Sons, 1992.

• Physique nucléaire 1
  Mayet, Frédéric. Physique nucléaire appliquée. De Boeck Supérieur, 2017