# Transport Phenomena 2020

An introduction to transport phenomena, course given to 3rd year students in the engineering curriculum at ESPCI Paris. This course is a part of the Advanced Fluid Mechanics module.

### Lecture Notes

#### General laws for transport of heat and mass

This first document describes a general framework for the transport of heat and mass. The diffusion equations (Fourier and Fick’s laws) are extended to take into account transport by convection (here convection refers to the macroscopic motion of a fluid).

#### Steady state one dimensional diffusion problems

This second document shows how to solve one dimensional steady state diffusion problems, in particular with source terms. It introduces the notion of effective transfer coefficient at an interface and thermal resistance. As an example, the concepts described are used to derive the bioheat equation modeling heat transfer in living tissues.

This document describes the characteristics of the electromagnetic radiation emitted by a body at finite temperature. It shows how one can compute the exchange of energy by radiation between two bodies. The derivation of the detailed formula for the black-body radiation is here only for reference. The ideas to memorize are listed in the summary of the document.

#### Transfer by convection. Coupling diffusion/convection.

This document describes the interplay between convection and diffusion when the Peclet number is large. It introduces the crucial concept of transport boundary layer and analyses situations in which transport is controled by the thickness of this boundary layer.

#### Thermal convection

This document describes the bases of thermal convection and introduces the relevant dimensionless numbers. These concepts are also applicable to flows driven by concentration gradients : Erosion of dissolvable bodies by convection-driven flows. A paper by M.S. Davies-Wykes et al.

### Presentations in class and problems

#### Presentation on January 8

course introduction and « coffee cup » problem : pdf document

#### Drop freezing problem

Problem definition and physical parameters : pdf document. Solution of the Stefan’s problem: pdf document.

#### Finger freezing problem (1D diffusion with source term)

Problem definition and solution: pdf document.

Problem definition and physical parameters : pdf document.

#### Oxygen transfer in fish gills (Convection and diffusion together)

Problem definition and physical parameters : pdf document.

#### Pigeon cooling (heat transfer by coupled convection and diffusion)

Problem definition and physical parameters : pdf document

#### Chupa chup dissolution (convection driven by density gradients)

Problem definition and physical parameters : pdf document

#### Solar heater (heat transfer by natural convection)

Problem definition and physical parameters : pdf document.

### Bibliography for the course

• Bird, Stewart, Lightfoot, « Transport Phenomena », Wiley (1960). An old but very comprehensive reference book on momentum, heat and mass transfer.
• F. Incropera, D. Dewitt, T. Bergman & A. Lavine, « Principles of heat and mass transfer ». Wiley (2013). A good reference book on transport.
• F. Kreith, R.M. Manglik, M.S. Bohn, « Principles of heat transfer » Cengage Learning (2011). A reference book on heat transfer.
• H.S. Carslaw, J.C. Jaeger « Conduction of heat in solids », Oxford Clarendon Press (1959). Describes in detail the solutions of the diffusion equation with different mathematical methods, in many different situations.
• B. Levich, « Physico chemical hydrodynamics », Prentice Hall (1962). As the title suggests, it is a fluid mechanics book, but it deals with transport of mass, heat and electrical charges in fluids. Rather advanced.
• R. Probstein « Physico-chemical hydrodynamics », Butterworths (1989). Deals only with laminar flows. Much easier to read than Levich’s book, but more limited in scope.
• C. Kittel, « Physique de l’état solide » Dunod (1983). For the calculation of transport coefficients in solids.
• F. Reif « Fundamentals of statistical and thermal physics », Mc Graw Hill (1965). Diffusion and Brownian motion. Black body radiation.
• R. Borghi et M. Destriau, La combustion et les flammes, Technip (1995). An introduction to the physico-chemistry of flames.

Bases of fluid mechanics are required to follow this course. Appropriate reference textbooks are : E. Guyon, J.P. Hulin, L. Petit « Hydrodynamique Physique », CNRS Editions (2001) and G.K. Batchelor, « An Introduction to Fluid Mechanics », Cambridge University Press (1967).