Equations of mass and energy conservation in integral and differential form. Conduction and diffusion. Initial and 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 a semi-infinite domain – similarity solution.
Solution methods of conduction and diffusion problems in more than one dimension in Cartesian, Cylindrical and Spherical geometries. The FFT to solve linear PDE problems. 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.
