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 v
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