Transport processes Part 5 Ron Zevenhoven bo Akademi University - - PDF document

▶
transport processes part 5
SMART_READER_LITE
LIVE PREVIEW

Transport processes Part 5 Ron Zevenhoven bo Akademi University - - PDF document

Jan 10, 2023 400 likes •616 views

Transport processes (TRP) Transport processes Part 5 Ron Zevenhoven bo Akademi University Thermal and Flow Engineering / Vrme- och strmningsteknik tel. 3223 ; ron.zevenhoven@abo.fi VST rz18 2/39 5 Transport processes (TRP) VST rz18

slide-1
SLIDE 1

Transport processes (TRP)

VST rz18

Ron Zevenhoven Åbo Akademi University Thermal and Flow Engineering / Värme- och strömningsteknik

  • tel. 3223 ; ron.zevenhoven@abo.fi

Transport processes – Part 5

Transport processes (TRP)

VST rz18 2/39 5

slide-2
SLIDE 2

Transport processes (TRP)

VST rz18 3/39 5

           V v

2 2

x T neglecting  

Steady state: ∂../∂t = 0

Transport processes (TRP)

VST rz18 4/39 5 Pr1/3 = thickness thermal boundary layer / hydraulic boundary layer Sc1/3 = thickness mass transfer boundary layer / hydraulic boundary layer

slide-3
SLIDE 3

Transport processes (TRP)

VST rz18 5/39 5

T0 (T-T0)/(T1-T0)

Transport processes (TRP)

VST rz18 6/39 5

λ (T1-T0) √ … T0 (T-T0)/(T1-T0)

slide-4
SLIDE 4

Transport processes (TRP)

VST rz18 7/39 5

(T1-T0)

Transport processes (TRP)

VST rz18 8/39 5

T0 T0 T - T0 = T(x, y=0) - T0 = q/(T(x,y=0) - T0) =

slide-5
SLIDE 5

Transport processes (TRP)

VST rz18 9/39 5

q/(T(x)-T0) =

0.89 ~ √(½π) 1.77 ~ 2√(½π)

Transport processes (TRP)

VST rz18 10/39 5 5.78 ~(2.405)2

slide-6
SLIDE 6

Transport processes (TRP)

VST rz18 11/39 5

T

  • f

instead used be can T  

against direction r : - → +

Transport processes (TRP)

VST rz18 12/39 5

slide-7
SLIDE 7

Transport processes (TRP)

VST rz18 13/39 5

x Ay V Blasius  : See section 5.1

Transport processes (TRP)

VST rz18

Lévêque problem

  • Lines of constant concentration in a Lévêque problem description
  • Note that the substitution of (5.45) into (5.41) requires that

which with m = 1 gives n = (ν-1)/(μ+2) &      ν μ n m

slide-8
SLIDE 8

Transport processes (TRP)

VST rz18 15/39 5

2 2 2 2 2 2 2 2 2 2 2 2 2

2 µ ) 1 ( 1 2 requires condition boundary the 2 µ ) 1 ( and 1 ) 1 (                                               c y y c c x x c µ n m n m c y m m c y m y c c x n x c

Transport processes (TRP)

VST rz18 16/39 5

2 1 2 1 1         µ x µ µ x

 

    

  

1 1

) ( ) , ( dt t e x dt t e p x

x t p x t

slide-9
SLIDE 9

Transport processes (TRP)

VST rz18 17/39 5

Transport processes (TRP)

VST rz18 18/39 5

slide-10
SLIDE 10

Transport processes (TRP)

VST rz18 19/39 5

See end of chapter 4

Transport processes (TRP)

VST rz18 20/39 5                          

2 2 2

) ( 2 2 ) 1 ( 1 2 ) ( 1 2 R y R y V R y V R y R V

slide-11
SLIDE 11

Transport processes (TRP)

VST rz18 21/39 5

41/3 = 1.59 1.59·0.539 = 0.855

Transport processes (TRP)

VST rz18 22/39 5

Gz corrects for entrance region growing boundary layer thickness

slide-12
SLIDE 12

Transport processes (TRP)

VST rz18 23/39 5

Ideal gas β ~1/T(K)

Transport processes (TRP)

VST rz18 24/39 5

difference with respect to average

slide-13
SLIDE 13

Transport processes (TRP)

VST rz18 25/39 5

Transport processes (TRP)

VST rz18 26/39 5 See also Bird Stewart & Lightfoot 1960 p. 297 - 300

slide-14
SLIDE 14

Transport processes (TRP)

VST rz18 27/39 5

Transport processes (TRP)

VST rz18 28/39 5

Energy balance Momentum balance

slide-15
SLIDE 15

Transport processes (TRP)

VST rz18 29/39 5 weight to due ) (

2

g z p T T g z p y v µ

z

               

T(y)

Transport processes (TRP)

VST rz18

Example Lévêque problem /1question

slide-16
SLIDE 16

Transport processes (TRP)

VST rz18

Example Lévêque problem /2question

Transport processes (TRP)

VST rz18

Example Lévêque problem /3answer

slide-17
SLIDE 17

Transport processes (TRP)

VST rz18

Example Lévêque problem /4answer

Transport processes (TRP)

VST rz18

Example Lévêque problem /5answer

slide-18
SLIDE 18

Transport processes (TRP)

VST rz18

Example Lévêque problem /6answer

110

Transport processes (TRP)

VST rz18

A classroom exercise - 6

  • Derive equation (5.21) in the course material:

differential equation (5.7) with boundary conditions (5.18, 5.19, 5.20).

  • Note that for the Laplace transform £ {τ} = p, and £

{T} = T the boundary condition (5.19) becomes .

  • And, what would be the result with T = T0 in

boundary conditions (5.18) and (5.20)?

36/39

p q dy T d   

slide-19
SLIDE 19

Transport processes (TRP)

VST rz18

Mass transfer, phase equilibrium

  • Note: For heat transfer problems the driving force is

a temperature gradient which is continuous at material boundaries or phase boundaries, and transport proceeds until thermal equilibrium is

  • reached. For mass transfer the driving force for

transfer across phase (or material) boundaries is the deviation from chemical - and phase equilibrium, and transport proceeds until the different concentrations reach this equilibrium.

  • Example:

Transport processes (TRP)

VST rz18 januari 2018

Mass transfer, phase equilibrium

Driving force = cequilibrium – c, saturation at c = cequilibrium

slide-20
SLIDE 20

Transport processes (TRP)

VST rz18

Sources used

(besides course book Hanjalić et al.)

  • Beek, W.J., Muttzall, K.M.K., van Heuven, J.W. ”Transport phenomena”

Wiley, 2nd edition (1999)

  • R.B. Bird, W.E. Stewart, E.N. Lightfoot ”Transport phenomena” Wiley,

New York (1960)

  • * C.J. Hoogendoorn ”Fysische Transportverschijnselen II”, TU Delft /

D.U.M., the Netherlands 2nd. ed. (1985)

  • * C.J. Hoogendoorn, T.H. van der Meer ”Fysische Transport-

verschijnselen II”, TU Delft /VSSD, the Netherlands 3nd. ed. (1991)

  • J.R. Welty, C.E. Wicks, R.E. Wilson. “Fundamentals of momentum,

heat and mass transfer” Wiley New York (1969) * Earlier versions of Hanjalić et al. book but in Dutch

39/39 5