This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MED 3300 Biotransport BMED 3300 Biotransport Lecture 3 ugust 29 2011 August 29, 2011. Professor Julie Babensee Differential Equation For Mass Transfer y y A differential control volume x y z x z x z Net rate of mass Net rate of accum Mass balance of species A for control volume Rate of chemical efflux of A from control volume ulation of A within control volume production of A within control volume =0 { } { { } } + WWWR 25.1 Net rate of mass efflux from the control volume may be evaluated by onsidering e ass ansferred cross ontrol urfaces or xample considering the mass transferred across control surfaces. For example, the mass of A transferred across the area y z at x will be A v A,x y z x in terms of the flux vector n A = A v A , it would be n A,x y z x . The net rate of efflux of constituent A will be z y n z x n x z y x A n x x z y x A n + : direction y in the , , : direction x in the z y x z A n z z y x z A n y y A y y y A + + , , : direction z in the , , he rate of accumulation of A in the control volume is The rate of accumulation of A in the control volume is z y x t A p A is produced within the control volume by a chemical reaction at a rate r If A is produced within the control volume by a chemical reaction at a rate r A , where r A has the units (mass of A produced)/(volume)(time), the rate of production of A is z y x A r Substituting each term into equation WWWR 25.1, we obtain , , , , , , = + + + + + + z y x A r z y x t A p z y x z A n z z y x z A n y z y y A n y y z x y A n x z y x A n x x z y x A n WWWR25.2 Dividing through by the control volume x y z and canceling terms, we have , , , , , , + + + A p z z A n z z z A n y y A n y y y A n x x A n x x x A n + + + A r t z y x WWWR 25.3 Evaluated in the limit as x, y, and z approach zero, this yields,...
View
Full
Document
This note was uploaded on 09/07/2011 for the course BME 3300 taught by Professor Babensee during the Spring '11 term at Georgia Institute of Technology.
 Spring '11
 Babensee

Click to edit the document details