# Transport Phenomena

An introduction to transport phenomena, course given to 3rd year students in the engineering curriculum at ESPCI Paris

This course will give the basis to answer all kinds of questions and problems ranging from : why is my coffee cold way before it is sweetened by sugar ? and : how long can I stand on top of Everest without gloves ? to : how to a design a microchip to capture biomolecules ? how many showers can I take with a 10 meter square solar heater ? what do cetaceans and solar heaters have in common ? why mixing in turbulent flows is so efficient ?

### 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. Kreith, R.M. Manglik, M.S. Bohn, « Principles of heat transfer » Cengage Learning (2011). A reference book on heat transfer.
- F. Incropera, D. Dewitt, T. Bergman & A. Lavine, « Principles of heat and mass transfer ». Wiley (2013). Another good reference book on transport.
- 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.

### 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). Click here to download the document in pdf format.

### 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.

### Radiative heat transfer

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.

### List of problems

This document contains the definition of the problems we have considered so far in class : mass and heat transfer in the coffee cup, water solar heater, cooling a microprocessor, bioheat equation, flux of water vapor through a porous membrane.

### Combined convection and diffusion

This document analyses the interplay between convection and diffusion in situations when the Peclet number is large and when thin transport boundary layers control the flux of heat or mass.

In class, we are solving (partially) the problem of the efficiency of a surface-based biosensor. This problem is discussed in detail in a paper by T. Squires, R. Messinger and S. Manalis, « Making it stick: convection, reaction and diffusion in surface based biosensors », Nature Biotechnology, 26, 417 (2008). The supplementary material of the paper describes the transport equations involved in more detail.

A computer program to solve numerically the problem in the limit of fast chemical reaction. This code is written for the finite element software FreeFem++.

### Thermal convection

This document describes the basis of thermal convection and introduces the relevant dimensionless numbers through the analysis of a simple case.

### Heat exchangers

This document analyses the flow of heat within a counter curent heat exchanger, with application to heat transfer in fins of marine mammals.

### Presentations done in class

A copy in pdf format of the presentations done in class: March 22, March 28, March 29, March 31, April 04, April 05, April07 .

### Exam

The exam was based on two publications by S. Ward et al. on heat transfer from starlings : « Heat transfer from starlings sturnus vulgaris during flight » and « Metabolic power of European starlings sturnus vulgaris during flight in a wind tunnel, estimated from heat transfer modelling, doubly labelled water and mask respirometry« .