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Indian Institute of Technology Madras

Continuum Mechanics and Transport Phenomena

Indian Institute of Technology Madras and NPTEL via Swayam


This is a unique course which introduces continuum mechanics and transport phenomena to the second year student. The main objective of this course is to relate the laws of physics to the conservation equations of transport phenomena. Continuum mechanics brings out the analogy between solid and fluid mechanics. Transport phenomena brings out the analogy between the transport of momentum, energy and mass.

INTENDED AUDIENCE: III or IV semester undergraduate students in Chemical Engg., Mechanical Engg., BiotechnologyPREREQUISITES: Engineering physics, I year Engineering mathematics, Chemical process principles, Engineering thermodynamics
INDUSTRY SUPPORT: Any process industry



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

Taught by

Prof.T. Renganathan

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