- Equations of mass and energy conservation in integral and differential form. Conduction and diffusion. Initial & boundary conditions in fixed and moving boundaries.
- Conservation of species. Homogeneous and heterogeneous 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 reaction. 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 equations and the Reynolds number. Initial and boundary conditions in fixed and moving boundaries.
- Momentum transfer in low Re using regular perturbations. Lubrication approximation. Stream function.
- Stokes equations & their solution using eigenfunctions. Creeping flow around a sphere. D'Alambert paradox. Oseen equations and correction to the creeping flow equations.
- 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.
- W.M. Deen, Analysis of Transport Phenomena, Oxford Univ. Press (2011).
- L.G. Leal, Advanced Transport Phenomena: Fluid Mechanics & Convective Trans. Processes, Cambridge Univ. Press (2007).
- R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd Ed., John Wiley & Sons (2007).
- V.S. Arpaci, Conduction Heat Transfer, Addison Wesley (1966).
- E.R.G. Eckert, R.M. Drake, Analysis of Heat and Mass Transfer, McGraw-Hill (1972).
- W.M. Kays, M.E. Crawford, Convective Heat and Mass Transfer, 2nd Ed., McGraw-Hill (1980).
- H. Schlichting, Boundary Layer Theory, 6th Ed., McGraw-Hill (1968).
- H.S. Carslaw, J.C., Jaeger, Conduction of Heat in Solids, 2nd Ed., Oxford (1959).