The module starts by reviewing the meaning of different derivatives. A formal derivation of the balance equations is given, before a more engineering type of derivation is discussed. Different frames of references, boundary conditions, different coordinate systems and diffusion are also covered.

Module preview


  • Why distributed models
  • Partial differential equations
  • Formal derivation of balance equations
  • Engineering derivation of balance equations
  • Domain of applicability
  • Example
  • Basis of velocity
  • Frame of references
  • Coordinate systems
  • Boundary conditions (number, place and type)
  • Diffusion

Learning outcomes

At the end of this module, students should be able to derive a simple distributed model, and understand the impact of the choice of frame of reference, coordinate system and basis of velocity on the model. They should be able to determine the number of boundary conditions needed, as well as the locations and types of boundary conditions. Finally, the students should be able to include Fick’s law of diffusion in a model and understand the effect of choosing mass or mole-based velocities.

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