Contents

Preface xi

Part 1. Transport processes: the basic prototypes

Chapter 1. Convection 3

Material volumes and transport theorem 3

Problem 1.1: Convection along a one-dimensional line 5

Problem 1.2: Jacobian of flow map 6

Problem 1.3: Transport theorem by change of variable 8

Problem 1.4: Time derivative of integral over a changing region 9

The convection PDE 10

Problem 1.5: Density carried by incompressible flow 10

Problem 1.6: Transformation of velocities as a flow map 11

Convective flux and boundary conditions 12

Elastic rebounds from a moving wall 13

Problem 1.7: Adiabatic expansion of particles in a box I 15

Problem 1.8: Adiabatic expansion of particles in a box II 15

Problem 1.9: Adiabatic expansion of particles in a box III 16

Problem 1.10: Adiabatic expansion of particles in a box IV 17

Convective derivative 18

Convected scalars 19

Problem 1.11: A convected scalar 19

Gradient of a convected scalar 20

Problem 1.12: Flows that preserve gradients 22

Problem 1.13: Vector analog of a convected scalar 24

Problem 1.14: Vector analogs of a convected density 25

Geometric postscript 29

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