Page 17 - Modelling in Transport Phenomena A Conceptual Approach

xiv CONTENTS

9 Steady-State Microscopic Balances With Generation 325
9.1 MOMENTUM TRANSPORT ...................... 325

9.1.1 Flow Between Parallel Plates .................. 326
9.1.2 Falling Film on a Vertical Plate ................. 330
9.1.3 Flow in a Circular Tube ..................... 334
9.1.4 Axial Flow in an Annulus .................... 337
9.1.5 Physical Significance of the Reynolds Number ......... 341
9.2 ENERGY TRANSPORT WITHOUT CONVECTION ........ 342
9.2.1 Conduction in Rectangular Coordinates ............ 342
9.2.2 Conduction in Cylindrical Coordinates ............. 347
9.2.3 Conduction in Spherical Coordinates .............. 354
9.3 HEAT TRANSFER WITH CONVECTION .............. 360
9.3.1 Laminar Flow Forced Convection in a Pipe .......... 360
9.3.2 Viscous Heating in a Couette Flow ............... 372
9.4 MASS TRANSFER WITHOUT CONVECTION ........... 377
9.4.1 Diffusion in a Liquid With Homogeneous Reaction ...... 377
9.4.2 Diffusion in a Spherical Particle With Homogeneous Reaction 381
9.5 MASS TRANSFER WITH CONVECTION .............. 384
9.5.1 Laminar Forced Convection in a Pipe ............. 384
9.5.2 Diffusion Into a Falling Liquid Film .............. 398
9.5.3 Analysis of a Plug Flow Reactor ................ 406

10 Unsteady-State Microscopic Balances Without Generation 429
10.1 MOMENTUM TRANSPORT ...................... 429
10.1.1 Solution for Short Times ..................... 435
10.2 ENERGY TRANSPORT ........................ 436
10.2.1 Heating of a Rectangular Slab ................. 436
10.2.2 Heating of a Rectangular Slab: Revisited ........... 446
10.2.3 Heating of a Spherical Particle ................. 450
10.3 MASS TRANSPORT .......................... 457

10.3.1 Mass Transfer Into a Rectangular Slab ............. 458
10.3.2 Gas Absorption Into a Spherical Droplet ............ 464

11 Unsteady-State Microscopic Balances With Generation 473
11.1 UNSTEADY LAMINAR FLOW IN A TUBE ............. 473
11.1.1 Exact Solution .......................... 475
11.1.2 Approximate Solution by the Area Averaging
Technique ............................. 479
11.2 UNSTEADY CONDUCTION WITH HEAT GENERATION .... 480
11.3 ABSORPTION WITH REACTION .................. 485