MA40255: Viscous fluid dynamics
Academic Year:  2019/0 
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: 

Assessment Summary:  EXTH 100%* 
Assessment Detail: 
*Assessment updated due to Covid19 disruptions 
Supplementary Assessment: 

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 NavierStokes 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 NavierStokes 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 semiinfinite flat plate. Derivation of Prandtl's boundarylayer equations and similarity solutions for flow past a semiinfinite flat plate. Discussion of separation and application to the theory of flight. JeffreyHamel flows. Slow flow: Slow flow past a cylinder and sphere. Nonuniformity of the twodimensional approximation; Oseen's equation. Flow around corners and eddies. Lubrication theory: bearings, squeeze films, thin films; HeleShaw cell and SaffmanTaylor instability. 
Programme availability: 
MA40255 is Optional on the following programmes:Department of Mathematical Sciences

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