BMED+3300+Lecture+3+Slides+082911

BMED+3300+Lecture+3+Slides+082911 - MED 3300 Biotransport...

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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,...
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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.

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BMED+3300+Lecture+3+Slides+082911 - MED 3300 Biotransport...

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