Page 512 - Modelling in Transport Phenomena A Conceptual Approach

492 APPENDIX A. h4ATHt3MATICAL PRELIMINARIES

The application of Eq. (1.3-1) to determine the rate of a quantity requires the
integration of the flux of a quantity over a differential area. The differential areas
in the cylindrical and spherical coordinate systems are given as follows:

Rd0dz flux is in the T - direction
drdz flux is in the 0 - direction (A.l-8)
r drd0 flux is in the z - direction

R2 sin 0 dedd, flux is in the r - direction
r sin 0 drdqb flux is in the 0 - direction (A.l-9)
r drd0 flux is in the d, - direction

I

Figure A.l The cylindrical and spherical coordinate systems.