73511 - Fluid Mechanics And Transport Phenomena M

Learning outcomes

The course addresses mainly the continuum-level analyses of non-equilibrium processes in fluids (e.g., fluid flow under applied force, energy or mass transfer in flowing fluids). Continuum-level balance laws for mass, energy and momentum are derived. These provide the basis for the fluid mechanical and heat or mass transfer analyses in engineering. The need for material-specific “constitutive laws” for the “conductive” fluxes of mass, energy and momentum is demonstrated. These are developed from continuum and thermodynamic principles with reference to key experimental tests. Applications of the continuum theory are discussed to define important classes of problems, to demonstrate analytical methods, and to derive quantities usually sought in engineering analyses.

Course contents

• Continuum View (multi-scale nature of transport analysis and the continuum view; notion of local volume averaging of key properties; material particles, material volume)
  

• Kinematics (material vs spacial descrptions of motion; displacement functions, deformation gradient, local velocity field; substantial derivative, velocity gradient, vorticity)
  

• Mass & Momentum Balances (developing a continuum field theory for isothermal systems, minimal local description;  Reynold's Transport Theorum (RTT); mass balance via RTT, spacial equation of continuity; linear momentum balance via RTT, pressure tensor, spacial eqns of motion; angular momentum balance)
  

• Simple Fluid Constitutive Laws (need for consitutive laws; mechanical definition of a simple fluid, viscous stress; material frame indifference, isotropic linear-response (Newtonian) fluid; incompressible Newtonian model, Navier-Stokes (NS) equations)
  

• Non-Newtonian Fluids (characterization of rheological properties of fluids; higher order constitutive equations for viscous fluid; basics of stress-strain relations in elastic solids; constitutive equations for viscoelastic materials)
  

• 1D and Nearly 1D Laminar Flows of Incompressible Newtonian Fluids (scaling and dimensional analysis of the NS equations, significance of the Reynold's number (Re), laminar vs turbulent flow; fully developed, steady 1D flows in cylindrical conduits; Hamel Flow; lubrication flows, order of magnitude analysis for lubrication flows, analysis of the boogie board)

• 2D Flows (general notion of the stream function for incompressible fluids; stream functions for plane and axisymmetric flows; NS eqns in terms of the stream function)
  

• Low Re Flows (low Re approximation, Stokes' equation; Hamel flow at low Re; a 2D flow: Stokes flow past a sphere, the sedimentation process; problems with Stokes' equation)

• High Re Flows (high Re approximation, Euler's equation,; Bernoulli's Eqn,; Hamel flow at high Re; problems with Euler's equation)
  

• Energy and Entropy Balance (developing a continuum field theory for non-isothermal systems, minimal local description; energy concepts, energy content, energy transduction (work and heat); energy balance via RTT, partial reduction to "temperature only" form; need for additional constitutive laws; entropy balance and the second law, thermodynamic constraints on constitutive laws; linearized constitutive laws, Fourier's law, the Navier-Stokes-Fourier (NSF) fluid)
  

• Heat Conduction (1D steady state heat conduction and generation in solids; 1D transient heat conduction problems in solids; heat transfer fin effectiveness)

• Forced Convection HT (forced vs free convection; dimensional analysis of nonisothermal incompressible NSF fluid dynamics, Peclet number (Pe); heat transfer coefficients and the Nusselt number (Nu); a 1D forced convection energy transport process; Graetz and Leveque forced convection heat transfer problems)

• Kinematics and Constitutive Equations for Mass Transport in Binary and Multicomponent Systems ( component velocities and diffusive fluxes in multicomponent systems; Fick's constitutive equation for diffusive flux in binary mixtures; Stefan-Maxwell relations for diffusive fluxes in multicomponent systems)
  

• Diffusion Dominated Problems in Binary Systems (1D steady state mass diffusion and generation in solids and fluid at rest; 1D transient mass diffusion problems for sorption and permeation processes; catalyst effectiveness factor)
  

• Mass Transfer with Fluid Flow (film theory for mass transfer coefficients, surface renewal theory for mass transfer coefficients, effect of homogeneous reaction on mass transfer coefficients in fluids)
  

Readings/Bibliography

Required Text: W.M. Deen, Analysis of Transport Phenomena, 2nd Ed. Oxford University Press, NY (2011)
Supplemental Text: R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd Edition, J. Wiley, NY (2002)

Assessment methods

Take home quizes on homeworks (approximately 4); midterms (2) and written final exam.
Grades based on quizes and exams or based on written final.

Office hours

See the website of Ferruccio Doghieri

See the website of Christopher Durning