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Each of the exciting new technologies blossoming around us is governed, at the detailed level of interest, by the conservation laws and flux expressions, together with information on the transport coefficients. Adapting the problem formulations and solution techniques for these new areas will undoubtedly keep engineers busy for a long time, and we can only hope that we have provided a useful base from which to start. | ALGEBRAIC OPERATIONS FOR VECTORS AND l TENSORS IN CARTESIAN COORDINATES s is a scalar v and w are vectors T is a tensor dot or cross operations enclosed within parentheses are scalars those enclosed in brackets are vectors Note The above operations may be generalized to cylindrical coordinates by replacing x y z by r 6 z and to spherical coordinates by replacing x y z by r 6 4 . Descriptions of curvilinear coordinates are given in Figures 1.2-2 A.6-1 A.8-1 and A.8-2. .DIFFERENTIAL OPERATIONS FOR SCALARS VECTORS AND TENSORS IN CARTESIAN COORDINATES dv dvy dv dvZ dvy dux V x v - dy - dz V x v - Y dz dx V x v ax - aY dv dvy dv V.v - - - dx dy dz d2vz d2v d2vZ V2v V Vv - ax2 -az2 3 dvx dvx dvx dx vY - v Vv vx - dy v - dz- dvz v Vv vx- v dv - v dvz - dx Y dy dz v v a vyvx d v vX V vv - dy - dx - dz a vXvy a vYvy v v V .vv - dx - -dy dz a vXvz d vyvz v v V vv - - - dx dy dz T V v dvx r - rxx- dux rxz- dux dx dy dz Note the differential operations may not be simply generalized to curvilinear coordi- nates see Tables A.7-2 and A.7-3. This Page Intentionally Intentionally Left Left Blank Transport Phenomena Second Edition R. Byron Bird Warren E. Stewart Edwin N. Lightfoot Chemical Engineering Department University of Wisconsin-Madison John Wiley amp Sons Inc. New York Chichester Weinheim Brisbane Singapore Toronto Acquisitions Editor Wayne Anderson Marketing Manager Katherine Hepburn Senior Production Editor Petrina Kulek Director Design Madelyn Lesure Illustration Coodinator Gene Aiello This book was set in Palatino by UG GGS Information Services Inc. and printed and bound by Hamilton Printing. The cover was printed by Phoenix. This book is printed on acid free paper. a Copyright O 2002 John Wiley amp Sons Inc. All rights reserved. No part of this publication may be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording scanning or otherwise except as permitted under Sections 107 or 108 of the 1976 .
