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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