| Weeks | Topics |
| 1 |
Basic definitions, assumptions and laws: Continuum hypothesis, Conservation of energy, classical thermodynamics.
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| 2 |
Introduction to vectors and tensors. Dummy and free indices, Einstein summation convention, tensors, dyadic tensors and some identities.
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| 3 |
Motion of a deformable body. Kinematics of continuous media in Eulerian and Lagrangian frames.
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| 4 |
Velocity and material time derivatives. Rate of deformation. Reynold’s transport theorem.
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| 5 |
Conservation of mass, momentum and energy in integral and differential forms.
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| 6 |
Some exact solutions of Navier-Stokes equations. Steady flow between parallel plates and pipes, Steady flow between concentric cylinders and its special cases.
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| 7 |
Some exact solutions of Navier-Stokes equations. Impulsively started plate: Similarity solutions, Flow due to oscillating plate, High and low Reynolds number flows.
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| 8 |
Perturbation techniques and its applications in fluid dynamics. Regular and singular perturbations. Methods of asymptotic matching. Couette flow with uniform suction with the solution of regular and singular perturbation techniques.
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| 9 |
Boundary layers. Equations of boundary layers. Flow over flat plates.
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| 10 |
Instabilities. Instabilities in fluid dynamics.
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| 11 |
Introduction to turbulence. Reynolds equations. Mean equations of motion of turbulent flow.
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| 12 |
Turbulence models: Mixing length models, k-epsilon models.
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| 13 |
Compresisble flows. Basic concepts of compressible flow.
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| 14 |
Stagnation and sonic properties, Isentropic flow. Normal Shock wave.
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