In the end of this course, the student should:
- Comprehend the basic principles of TP, the physical significance of the relevant dimensionless numbers and their use for simplifying and solving problems.
- Be able to set the relevant microscopic and macroscopic balances, simplify them using proper assumptions and solve them analytically.
- Be able to physically and mathematically investigate TP problems, theoretically predict their results and aim at a safe and immediate technical application.
The student will have developed the following skills:
- Be able to simplify complex TP with rigorous mathematical means and solve the simplified problems using perturbation methods, FFT and similarity.
- Understand the limitations generated by the simplifications and how to alleviate them.
Required courses have not been set. The students however, must have good knowledge of Differential and Integral calculus, of methods to solve Differential eqs., and of undergraduate TP and Thermodynamics.
- Eqs of mass and energy conservation in integral and differential form. Conduction and diffusion. Initial & boundary conditions in fixed and moving boundaries.
- Conservation of species. Homo- and hetero-geneous reactions. Conduction and diffusion. Biot number. Asymptotic solution for large and small Biot.
- Fin approximation. Exact and approximate solution. Regular and singular perturbations. Mass transfer with chemical rxn. Damkohler number. Time dependent conduction in semi-infinite domain – similarity solution.
- Solution methods of conduction and diffusion problems in more than one dimension in Cartesian, Cylindrical and Spherical geometries. The finite Fourier transform (FFT). Sturm-Liouville eigenvalue problems.
- Momentum transfer. Stress and rate of deformation tensors. Newtonian fluid. Dimensionless form of the NS eqs and the Reynolds number. Initial and boundary conditions in fixed and moving boundaries.
- Momentum transfer in low Re using regular pertu-rbations. Lubrication approximation. Stream function.
- Stokes eqs & their solution using eigenfunctions. Creeping flow around a sphere. D'Alambert paradox. Oseen eqs and correction to the creeping flow eqs.
- Momentum transfer at High Re. Potential flow. The Boundary Layer (BL) and exact solution using singular perturbations and similarity. Blasius eq. and its solution, exact and approximate.
- Forced convection of heat and mass. The Prandtl, Schmidt, Peclet, Nusselt and Sherwood numbers. Solution of convection problems inside conduits. Graetz problem near and away from the conduit entrance.
- Solution of forced convection around bodies. Convection from a moving sphere at creeping flow & at high/low Peclet numbers. The BL in heat transfer.
- Heat and momentum BL at high Re. Similarity solution of heat & mass transfer at high and low Prandtl.
- Free convection around bodies. The Grasshof and Rayleigh numbers. Problems at high/low Grasshof .
Deen, Analysis of Transport Phenomena, OUP, 2011.
- Leal L.G., Advanced Transport Phenomena: Fluid Mechanics & Convective Trans. Processes, CUP, 2007.
- Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, Rev. 2nd Ed. Wiley, 2007.
- Arpaci, V.S., Conduction Heat Transfer, Addison Wesley, 1966.
- Eckert, E.R.G., and R.M. Drake, Analysis of Heat and Mass Transfer, McGraw-Hill, 1972.
- Kays, W.M. and M.E. Crawford, Convective Heat and Mass Transfer, 2nd Ed. McGraw-Hill, 1980.
- Schlichting, H., Boundary Layer Theory, 6th Edition, McGraw-Hill, 1968.
- Carslaw, H.S. and J.C., Jaeger, Conduction of Heat in Solids, 2nd Ed., Oxford, 1959.
Lectures and related problems are solved on the board. Problems are given (about 20-25) that the students are asked to solve during the semester. They are asked to solve them within a week during which they can ask for clarifications.
The course grade is determined by the exercises, 30%, the exam in the middle of the semester on conduction and diffusion topics, 35%, and the exam at the end on fluid mechanics and convection topics, 35%.