1 / 18

SURROUNDING

MASS BALANCE: WHY MASS FLOWS?. SURROUNDING. Phase a T a , P a , m i a. Phase b T b , P b , m i b. NO. NO. ISOLATED. SYSTEM. WORK. HEAT. Ideal fixed permeable membrane. a i = i th species activity. T a = T b P a = P b m i a = m i a. EQUILIBRIUM CONDITIONS

hall-cobb
Download Presentation

SURROUNDING

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MASS BALANCE: WHY MASS FLOWS? SURROUNDING Phase a Ta, Pa, mia Phase b Tb, Pb, mib NO NO ISOLATED SYSTEM WORK HEAT Ideal fixed permeable membrane ai = ith species activity Ta = TbPa= Pb mia = mia EQUILIBRIUM CONDITIONS dU=dUa+dUb = 0

  2. MASS BALANCE: EQ.CON. ALTERATION 1 Pa increase (>Pb) [Ta = Tb; mia = mib] Phase a T, Pa, mi Phase b T, Pb, mi MASS TRASPORT (CONVECTION) permeable membrane

  3. mia>mib [Ta = Tb; Pa = Pb] 2 Phase a T, P, mia Phase b T, P, mib permeable membrane MASS TRASPORT (DIFFUSION) Mass transport represents a possible way the system has to get new equilibrium conditions once the original ones have been altered.

  4. MASS BALANCE Z X Y DZ DX (X+DX, Y+ DY, Z+ DZ) G (X, Y, Z) DY (X, Y+ DY, Z) (X+DX, Y+ DY, Z)

  5. MASS BALANCE: EXPRESSION DX DZ (X, Y, Z) G DY Ci = f(X, Y, Z, t)

  6. DX DZ (X, Y, Z) G DY DIVIDING FOR DV

  7. FLUXES EXPRESSIONS Ideal solution Diffusion Diffusion Diffusion Convection Convection Convection Bi = mobility of the diffusing components

  8. Remembering that:

  9. MASS BALANCE EQUATION FOR ith SPECIES where: Remembering the definition of the NABLA operator:

  10. As: … the summation of ith mass balance over all the r components yields to the well known continuity equation:

  11. MASS BALANCE: CYLINDRICAL COORDINATES Jir+dr Jir+dr Jiz Jiz+dz Jir Jir Jir Jiz Jiz+dz Jir+dr r dr dz TWO DIMENSIONS r z

  12. Ci = f(z, r, t) r dr dz Dividing by 2prdrdz

  13. Constant diffusion coefficient D Remembering the derivativedefinition

  14. MOMENTUM BALANCE Incoming sand Escaping sand Sand containing vessel Sliding vessel motion direction Inclinate plane Friction Gravity NO Yes

  15. DZ DX (X+DX, Y+ DY, Z+ DZ) (X, Y, Z) DY (X, Y+ DY, Z) (X+DX, Y+ DY, Z) Body forces: gravitational, electro-magnetic fields Surface forces: viscous drag and pressure

  16. Surface forces gravitational field Incoming and exiting mass

  17. ENERGY BALANCE Conduction Expansion Viscous heating

More Related