Page 16 - Modelling in Transport Phenomena A Conceptual Approach

CONTENTS xiii

6 Steady-State Macroscopic Balances 149
6.1 CONSERVATION OF CHEMICAL SPECIES ............. 150
6.2 CONSERVATION OF MASS ...................... 152
6.3 CONSERVATION OF ENERGY .................... 156
6.3.1 Energy Equation Without Chemical Reaction ......... 159
6.3.2 Energy Equation With Chemical Reaction ........... 166

7 Unsteady-State Macroscopic Balances 181
7.1 APPROXIMATIONS USED IN UNSTEADY PROCESSES ..... 182
7.1.1 Pseudo-Steady-State Approximation .............. 182
7.1.2 No Variation of Dependent Variable Within the
Phase of Interest ......................... 183
7.2 CONSERVATION OF CHEMICAL SPECIES ............. 185
7.3 CONSERVATION OF TOTAL MASS ................. 186
7.4 CONSERVATION OF MOMENTUM ................. 194
7.5 CONSERVATION OF ENERGY .................... 198
7.5.1 Unsteady-State Energy Balance Around a
Continuous Stirred Tank Reactor ................ 208
7.6 DESIGN OF A SPRAY TOWER .................... 211
7.6.1 Determination of Tower Diameter ............... 212
7.6.2 Determination of Tower Height ................. 213

8 Steady-State Microscopic Balances Without Generation 237
8.1 MOMENTUM TRANSPORT ...................... 238
8.1.1 Plane Couette Flow ....................... 238
8.1.2 Annular Couette Flow ...................... 241
8.2 ENERGY TRANSPORT WITHOUT CONVECTION ........ 245
8.2.1 Conduction in Rectangular Coordinates ............ 245
8.2.2 Conduction in Cylindrical Coordinates ............. 260
8.2.3 Conduction in Spherical Coordinates .............. 269
8.2.4 Conduction in a Fin ....................... 276
8.3 ENERGY TRANSPORT WITH CONVECTION ........... 283
8.4 MASS TRANSPORT WITHOUT CONVECTION .......... 284
8.4.1 Diffusion in Rectangular Coordinates .............. 286
8.4.2 Diffusion in Cylindrical Coordinates .............. 291
8.4.3 Diffusion in Spherical Coordinates ............... 293
8.4.4 Diffusion and Reaction in a Catalyst Pore ........... 295
8.5 MASS TRANSPORT WITH CONVECTION ............. 301
8.5.1 Diffusion Through a Stagnant Gas ............... 302
8.5.2 Diffusion Through a Stagnant Liquid .............. 311
8.5.3 Diffusion With Heterogeneous Chemical Reaction ....... 315