Physics of Transport Phenomena

URL study guide

https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=32PTP&collegejaar=2025&taal=en

Omschrijving

Kinematics of fluid particles:

• • Streamlines
  • Pathline
  • Streaklines

Mass and momentum conservation:

• Mass conservation:
  • Integral and differential forms
• Momentum conservation:
  • Integral and differential forms
• Stress tensor and constitutive relations
• Navier-Stokes equations
• Boundary conditions
• Hydrostatics
• Elementary flows:
  • Poiseuille
  • Couette flow

Dimensionless numbers and similarity

• Rayleigh problem and oscillating plate
• Non-dimensionalisation of Navier-Stokes equations
• Dynamic similarity and the meaning of dimensionless numbers
• Buckingham Pi theorem

Inviscid flows

• Euler equations
• Bernoulli equations
• Irrotational flow
• Vorticity, and circulation
• Stream functions and velocity potential
• Elementary potential flows

Viscous flows and boundary layers

• Boundary layer equations
• Steady flow over flat plates
• Creeping flows:
  • Thin film equation
  • Lubrication flows

Mass transfer

• Multicomponent flows:
  • Convection and diffusion
• Mass conservation and Fick’s law for diffusive flux
• Diffusion equation (Fick’s second law)
• Convective mass transfer
• Convection-diffusion equation
• Non-dimensionalisation:
  • Peclet number
• Diffusion boundary layers and Schmidt number

Heat transfer

• Energy equation
• Fourier’s law for heat conduction
• Boundary conditions
• Heat sources
• Cylindrically symmetric and spherical conduction
• Unsteady conduction
• Convective heat transfer:
  • Thermal entrance length and boundary layers
  • Convective heat transfer coefficient and Nusselt number
• Relevant dimensionless numbers:
  • Nusselt
  • Prandtl
  • Peclet

Mathematical concepts and tools

• Vector Calculus:
  • Vector fields
  • Nabla operator
    • Gradient
    • Divergence
    • Curl
    • Laplacian
• Coordinate Systems:
  • Cartesian coordinates
  • Spherical coordinates
  • Cylindrical coordinates
• Differentiation:
  • Tangent lines
  • Partial derivatives
  • Product rule
• Integration:
  • Multidimensional integrals
  • Change of variables
• Differential Equations:
  • Solving ODEs analytically
  • Solving PDEs analytically with simplifications
  • Initial value problems
• Linear Algebra:
  • Matrices and tensors
  • Eigenvalues and eigenvectors

Doelstellingen

After the end of this course, you (the student) will be able to:

1. Provide a kinematic description of the motion and deformation of fluid elements. 
2. Apply the concepts of integral mass and momentum conservation on a control volume to determine the average flow characteristics.
3. Apply the concept of integral energy conservation to determine average heat flows through a control volume.
4. Determine the forces exerted by fluids on solid boundaries and immersed objects.
5. Apply the concepts of dimensional analysis and similarity to identify relevant dimensionless groups to design scale experiments and determine the dominant terms in the Navier-Stokes and energy equations.
6. Solve the Navier-Stokes and energy equations for elementary geometries and boundary conditions and analyze the results. 
7. Explain and apply analogies between heat and mass transfer.

Beoordelingsmethode

Written examination