Transport Phenomena PDF
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l ALGEBRAIC OPERATIONS FOR VECTORS AND 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], = - - - [ V x v ] =--- Y d z dx [V x v], = ax - - d y d z aY dv, dvy dv, ( V . v ) = - + - + - dx d y d z d2vz d2v, d2vZ [V2v], = [V Vv], = - +- ax2 + 3 az2 dvx dvx dvx [v Vv], = vx - + v - + v, -- dx Y dy dz dvz dv, dvz [v ' Vv], = vx - + v - + v, - dx Y dy dz ~(v,v,) a(vyvx) d(v,vX) [V vv], = - + ------ + - dx dy dz a(vXvy) a(vYvy) ~(v,v,) [V . vv], = - +-+- dx dy dz a(vXvz) d(vyvz) ~(v,v,) [V vv], = ---- +-+- dx dy d z dvx dux dux (T : Vv) = rxx - + r - + rxz - 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 Left Blank This Page Intentionally Left Blank Transport Phenomena Second Edition R. Byron Bird Warren E. Stewart Edwin N. Lightfoot Chemical Engineering Department University of Wisconsin-Madison John Wiley & 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 & 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 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (508)750-8400, fax (508)750-4470. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 605 Third Avenue, New York, NY 10158-0012, (212)850-6011, fax (212)850-6008, E-Mail:
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