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MMath&Phys Mathematics and Physics / Course details
Year of entry: 2023
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Course unit details:
|Unit level||Level 4|
|Teaching period(s)||Semester 2|
|Offered by||Department of Mathematics|
|Available as a free choice unit?||No|
|Unit title||Unit code||Requirement type||Description|
|Viscous Fluid Flow||MATH35001||Pre-Requisite||Recommended|
|Partial Differential Equations and Vector Calculus A||MATH20401||Pre-Requisite||Compulsory|
|Partial Differential Equations and Vector Calculus B||MATH20411||Pre-Requisite||Compulsory|
- Introduction : Vectors, tensors, co- and contra-variant transformation laws, invariance concepts, metric tensor, tensor calculus, divergence theorem.
- Kinematics : Deformation maps, Lagrangean and Eulerian viewpoints, displacement, velocity and acceleration, material derivative, strain measures, strain invariants, deformation rates, Reynolds transport theorem.
- Forces, momentum & stress : The continuum hypothesis, linear and angular momenta, stress tensors, equations of equilibrium.
- Conservation and Balance Laws & Thermodynamics : Conservation of mass and energy, balance of linear and angular momenta, work conjugacy, temperature and heat, first and second laws of thermodynamics, Clausius--Duhem inequality.
- Constitutive Modelling : Introduction to constitutive relationships, axiom of objectivity, objective deformation rates, constitutive modelling for an ideal gas.
- Elasticity : Constitutive modelling for thermoelastic materials, Hyperelastic materials, strain energy function, homogeneous, isotropic materials, incompressibility constraints, example analytic solutions, boundary conditions, linear thermoelasticity and reduction to Navier--Lame equations.
- Fluid Mechanics : Constitutive modelling for fluids, isotropic fluids, Newtonian and Reiner--Rivlin fluids, example analytic solutions, boundary conditions, reduction to Navier--Stokes equations.
- Coursework - 20%: two assignments, each worth 10%; each should take aprox 7 hours.
- End of semester examination: weighting 80%
- Spencer, A.J.M, Continuum Mechanics, Dover
- Gonzalez, O. and Stuart, A.M., A first course in continuum mechanics, CUP
- Irgens, F., Continuum Mechanics, Springer
|Scheduled activity hours|
|Independent study hours|
|John Gray||Unit coordinator|
The independent study hours will normally comprise the following. During each week of the taught part of the semester:
· You will normally have approximately 75-120 minutes of video content. Normally you would spend approximately 2.5-4 hrs per week studying this content independently
· You will normally have exercise or problem sheets, on which you might spend approximately 2-2.5hrs per week
· There may be other tasks assigned to you on Blackboard, for example short quizzes, short-answer formative exercises or directed reading
· In some weeks you may be preparing coursework or revising for mid-semester tests
Together with the timetabled classes, you should be spending approximately 9 hours per week on this course unit.
The remaining independent study time comprises revision for and taking the end-of-semester assessment.
The above times are indicative only and may vary depending on the week and the course unit. More information can be found on the course unit’s Blackboard page.