CHBE 501, Transport Phenomena, Fall 2007
Meeting: 9:00-9:50 MWF, AL B-209
Instructor: George J. Hirasaki, gjh@rice.edu , ext 5416
Assistant: Gautam Kini, gck1@rice.edu
Website: http://www.owlnet.rice.edu/~chbe501/
OwlSpace:
Textbooks: Aris, Vectors, Tensors and the Basic Equations of Fluid Mechanics
Bird, Stewart, and Lightfoot, Transport Phenomena
Grading: Assigned problems and examinations; each exam, (at least one), will be 25% of the total grade.
Each assigned problem will have due date, usually one week.
Problems turned in after due date or reworked will be credited 80% of maximum score on reworked portion.
Collaborative discussions are encouraged on assigned problems. However, each student should turn in only their own work.
Some assignments will be team projects.
Assistance: If you have difficulty with lecture material or assigned problem, first discuss with another student. If two or more students can not resolve problem, see Professor Hirasaki or if he is unavailable, see assistant.
Misc.: Please point out error in notes and suggestions for improvements are welcome.
Prerequisites and text books
Scalar, vector and tensor fields
Curves, surfaces, and volumes
Coordinate systems
Continuum approximation
Densities, potential gradients, and fluxes
Definition of a vector
Examples of vectors
Scalar multiplication
Addition of vectors - Coplanar vectors
Unit vectors
A basis of non-coplanar vectors
Scalar product - Orthogonality
Directional cosines for coordinate transformation
Vector product
Velocity due to rigid body rotations
Triple scalar products
Triple vector products
Second order tensors
Examples of second order tensors
Scalar multiplication and addition
Contraction and multiplication
The vector of a antisymmetric tensor
Canonical form of a symmetric tensor
Tensor functions of time-like variable
Curves in space
Line integrals
Surface integrals
Volume integrals
Change of variables with multiple integrals
Vector fields
The vector operator del -gradient of a scalar
The divergence of a vector field
The curl of a vector field
Green's theorem and some of its variants
Stokes' theorem
The classification and representation of vector fields
Irrotational vector fields
Solenoidal vector fields
Helmholtz' representation
Vector and scalar potential
Particle paths and material derivatives
Streamlines
Streaklines
Dilatation
Reynolds' transport theorem
Conservation of mass and the equation of continuity
Deformation and rate of strain
Physical interpretation of the deformation tensor
Principal axis of deformation
Vorticity, vortex lines, and tubes
Cauchy's stress principle and the conservation of momentum
The stress tensor
The symmetry of the stress tensor
Hydrostatic pressure
Principal axes of stress and the notion of isotropy
The Stokesian fluid
Constitutive equations of the Stokesian fluid
The Newtonian fluid Interpretation of the constants l and m
Equations of motion of a Newtonian fluid
The Reynolds number
Dissipation of energy by viscous forces
The energy equation
The effect of compressibility
Resume of the development of the equations
Special cases of the equations
Boundary conditions
Scaling, dimensional analysis, and similarity
Bernoulli theorems
Classes of partial differential equations
Systems described by diffusion equation
Greens function, convolution, and superposition
Green's function for the diffusion equation
Fourier transform method
Convective-diffusion equation
Similarity transformation
Complex potential for irrotational flow
Solution of hyperbolic systems
Couette flow
Poiseuille flow
Steady film flow down inclined plane
Unsteady viscous flow
Lubrication and film flow
Laminar boundary layer
Creeping flow in wedge
Flow around particle
Boundary conditions at a fluid-fluid interface
Film drainage and deposition with Laplace pressure
The stream function - vorticity method
Finite difference approximation
Solution of linear equations
FORTRAN on Owlnet
Transients and finite Reynolds numbers
Calculation of pressure and stress
Cylindrical-polar coordinates
Flow past cylinder