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 Academic Year: | 2018/9 |
| Owning Department/School: | Department of Mathematical Sciences |
| Credits: | 6 [equivalent to 12 CATS credits] |
| Notional Study Hours: | 120 |
| Level: | Masters UG & PG (FHEQ level 7) |
| Period: |
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| Assessment Summary: | EX 100% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| Requisites: | Before taking this module you must take MA30253 |
| Description:
| Aims: To describe viscous flow phenomena and analyse these with the necessary mathematical theory. Learning Outcomes: Students should be able to derive the Navier-Stokes equations for the flow of viscous fluids and analyse these in different flow situations using asymptotic analysis and partial differential equation theory. Skills: Numeracy T/F, A Problem Solving T/F, A Written Communication F (on problem sheets). Content: Review of Lagrangian and Eulerian descriptions: Jacobian, Euler's identity and Reynold's transport theorem. The continuity equation and incompressibility condition. Cauchy's stress theorem and properties of the stress tensor. Cauchy's momentum equation. Constitutive law for a Newtonian viscous fluid. The incompressible Navier-Stokes equations. Vorticity and Helmholtz's theorems. Energy. Exact solutions for unidirectional flows; Couette and Poiseuille flow. Dimensional analysis, Reynolds number. Derivation of equations for high and low Reynolds number flows. Further topics chosen from the following: Boundary layer theory: thermal boundary layer on a semi-infinite flat plate. Derivation of Prandtl's boundary-layer equations and similarity solutions for flow past a semiinfinite flat plate. Discussion of separation and application to the theory of flight. Jeffrey-Hamel flows. Slow flow: Slow flow past a cylinder and sphere. Non-uniformity of the two-dimensional approximation; Oseen's equation. Flow around corners and eddies. Lubrication theory: bearings, squeeze films, thin films; Hele-Shaw cell and Saffman-Taylor instability. |
| Programme availability: |
MA40255 is Optional on the following programmes:Department of Mathematical Sciences
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Notes:
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