Transport phenomena bird stewart lightfoot 2ed

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Transport phenomena bird stewart lightfoot 2ed

Transport PhenomenaSecond EditionMicroscopicMolecularMacroscopicR. Byron Bird • Warren E. Stewart Edwin N. Lightfoot•••ALGEBRAIC OPERATIONS FOR VECTOR

Transport phenomena bird stewart lightfoot 2ed RS 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 sca

lars, those enclosed in brackets are vectors)(v • w) = vxwx IVyWy 4v,w, =(w v)[v X w]x — VyW.- V.lUy--[wX v]x|v X w|M = v.wx- VKW..=— [wX v]y|v X w|z Transport phenomena bird stewart lightfoot 2ed

= VxWy- VyW*=-[wX vljIt • v|r - T„px ♦T^Vy ♦[t • v]v = TyXVx t+ 7y,vz[t • v], -- T.^)x + T_yVy + raV,|v • Tlr = I PyTyr I V2T„[v • t]v = vx7xy + VyTyy

Transport phenomena bird stewart lightfoot 2ed

+ VZT^[v • t]2 =+VyTyz+V/raNote: The above operations may be generalized to cylindrical coordinates by replacing (x, y, z) by (r, t), z), and to sphe

Transport PhenomenaSecond EditionMicroscopicMolecularMacroscopicR. Byron Bird • Warren E. Stewart Edwin N. Lightfoot•••ALGEBRAIC OPERATIONS FOR VECTOR

Transport phenomena bird stewart lightfoot 2ed •DIFFERENTIAL OPERATIONS FOR SCALARS, VECTORS, AND TENSORS IN CARTESIAN COORDINATES(Vsb = IIvsl. = Ẽ■ "yrrr 1IV X vl._ =- -r-21dz dxrrr .1 _(vVS) = v,

g + ry^ + ĩ,g-* ỞXởVy.[Wv]y = vy-g +, d2Vx . d2Vx . Transport phenomena bird stewart lightfoot 2ed

+dx2 dy2 ởz2 iv-VvL = vx^ + v,,^ + vz% âvv âvu v^ + v^

Transport PhenomenaSecond EditionMicroscopicMolecularMacroscopicR. Byron Bird • Warren E. Stewart Edwin N. Lightfoot•••ALGEBRAIC OPERATIONS FOR VECTOR