Continuum Mechanics and Transport Phenomena

COURSE LAYOUT

Week 1: Fluid kinematics : Eulerian vs. Lagrangian; material derivative; flow visualization; system vs. control volume; Reynolds transport theorem

Week 2: Total mass balance : integral balance and applications; differential balance and applications
Week 3: Linear momentum balance : Integral balance; calculation of force
Week 4: Stress : Traction vector, stress at a point, stress element, stress tensor; Cauchy’s formula; equality of cross shears; fluids at rest; stress in fluids
Week 5: Strain : Types and measures of deformation; displacement field, displacement gradient – 1D, 3D; relationship between strain and displacement field;
displacement gradient tensor, strain tensor, rotation tensor; fluids vs. solids; strain rate tensor
Week 6: Hooke’s law; Lame’s equation; Relationship between material properties; Newton’s law of viscosity; Navier-Stokes equation
Week 7: Pascals’s law and applications; Bernoulli equation and applications; Applications of Navier-Stokes equation - Couette flow and Poiseuille flow
Week 8: Momentum transport : Shear stress as momentum flux; Navier Stokes equation; integral energy balance and applications
Week 9: Differential balance for total energy, potential energy, kinetic energy, internal energy, enthalpy, temperature; Fourier’s law; Applications of differential
energy balance - composite walls, Couette flow
Week 10:Integral component mass balance and applications (batch reactor and CSTR); Fick’s law; total flux, diffusion flux, convection flux, different average
velocities; differential component mass balance
Week 11:Applications of differential component mass balance : Diffusion through stagnant film; diffusion with homogeneous reaction
Week 12:Shell balance in cylindrical and spherical coordinates : Liquid flow through pipe; current flow through wire; sublimation of solid; concluding remarks