THE EQUATION OF MOTION IN RECTANGULAR COORDINATES (x, y, z) In terms of T a-component +D 5tu,5+ux p a (++出)+ y-component (数+吗++) y a)+昭v(B) dt Z-component P5+vx2+U,2+U p au In terms of velocity gradients for a Newtonian fluid with constant p and u: A-component +mao+vato. du z +Pg(D) y-componenr(a+uaz+uy可+ ay dy P6, p z-component ar a2+ym+υ 十 2y+z2 +;(
The three fundamental equations of conservation EQUATION OF Locol change Change b I Chonge by Chonge by CONSERVATION OF convection diffusion production 0 Boundary condition ac MASS c at Moss transfer a km.△c ENERGY 0 Heot transfer=ha△r MOMENTUM :0 Sheor force Surfoce tension force= 7( CORRESPONDING Diffusive QUANTITIES Unit Production Boundary (per unit of volume) transport transfer MASS D km△c ENERGY cppr h△T MOMENTUM T or TE-I
System of dimensionless groups(numerics) RotiooftermsI: I N:I:I:TIN:IY:IK: x:mM:Y Mass " 如回四 L Dam kmt Sh IL Energy cppL CppT m回杀m图器网回酬 Momentum evL Rel l几 Well fa正 MEANING OF SYMBOLS NUMERICS(see Gen Ref) surface per unit of volume T= surfoce tension Bm Bingham c s concentration n= viscosity Bo Bodenstein specific heat 入= heat conductivity Da Damkohler p* density Fa s Fanning electric charge T= shear stress Fo Fourier E modulus of elasticity w= angular frequency Me a Merkel fe= electric field per unit of volume Ny s Nusselt g s gravitational acceleration reaction rate per unit of volume h s heat transfer coefficient first order r=kc Po s Poiseuille k r reaction rate constant second order rskc2 etc Re Reynolds moss transfer coefficient heat production rate per unit of volume Sh s Sherwood 7- length per unit of volume force per unit of volume St a Stonton L- characteristic length grovitotionot f=gP We s Weber pressure centrifugal f-的Lp pressure grodient f-A P/L elocity surface tension f= 7/22 length coordinate electric f* ofet
Couette. Care∽)clos Csimuplo sheariM c> 除“学](2) =C→LC=C,u+C2 z 认C→co,uC=→c 以C8 au 从 人 at teer aton:ag-A8=( 人
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