Skip to main content
SpringerLink
Log in

The impact of viscosity on the combined heat, mass and momentum transfer in laminar liquid falling films

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

In this article we present a model describing a laminar film flow over a vertical isothermal plate whilst heat and mass transfer is occurring. We focus on a formulation where most common assumptions, such as constant property data and constant film thickness, have been cancelled. The hydrodynamic model results in longitudinal and transversal velocity components and their evolution in the entrance region. Heat and mass transfer occurs simultaneously and is modelled with respect to release of differential heat of solution as well as heat flow due to interdiffusion. The numerical solution is obtained by utilising a Newton-Raphson method to solve the finite difference formulation of the governing equations. Mass transfer across the film affects the development of both longitudinal and transversal velocity components. The hydrodynamics are modelled using a boundary layer approximation of the Navier-Stokes equations. The significance of simplifications on the hydrodynamic model are illustrated and discussed using a fully developed velocity profile (Nusselt flow) and a plug flow at the inlet for comparison. Even if a Nusselt profile is assumed, it develops further since mass is absorbed or desorbed. It is found that the onset of absorption occurs at shorter flow length when applying a plug flow at the inlet. If the film is initially in equilibrium, this results in a 9.3% increase in absorbed mass over a length of 0.03 m as compared with the Nusselt flow. A fluid with a viscosity five times the one of lithium bromide solution but sharing comparable properties apart from that, leads to lower overall heat and mass transfer rates. If the respective fluids are saturated at the inlet, the accumulated mass flux absorbed by lithium bromide solution is 2.2 times higher than the one absorbed by a high viscous fluid. However, when a plug flow is applied and the fluid is sub-cooled, ab initio the absorbed mass flux is slightly higher for a high viscous fluid. Assuming a sub-cooling of 3 K at the inlet, lithium bromide solution now only performs around 11% better as compared with a high viscous fluid over the considered length of 0.03 m. The code may be downloaded from: https://github.com/mittermaier/hmt.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29

Similar content being viewed by others

Abbreviations

c p Specific heat capacity:

J/(k g ⋅ K)

D Mass diffusivity:

m 2/s

g Gravitational acceleration:

m/s 2

h Enthalpy:

J/k g

\(\overline {h}\) Partial massive enthalpy:

J/k g

L e Lewis-Number = λ/(D ⋅ c p ⋅ ρ):

-

\(\dot {m}\) Mass flux:

k g/(m 2 ⋅ s)

p Pressure:

P a

\(\dot {q}\) Heat flux:

W/m 2

T Temperature:

K

u Longitudinal velocity:

m/s

v Transversal velocity:

m/s

x Longitudinal coordinate, streamwise:

m

y Transversal coordinate:

m

\(\dot {\Gamma }\) Mass flow per unit length:

k g/(m ⋅ s)

\(\overline {\Delta y}\) :

Abbreviation, please see Eq. 24

\({\Delta } \overline {h}\) :

Abbreviation, please see Eq. 27

Δh s o r Heat of sorption:

J/k g

δ Film thickness:

m

λ Thermal conductivity:

W/(m ⋅ K)

μ Dynamic viscosity:

P a ⋅ s

ξ Mass fraction:

k g/k g

ρ Density:

k g/m 3

0 :

Inlet condition

a v g :

Average

A :

Absorbate e.g. water in liquid state

e q :

Equilibrium

if :

Interface

i :

node index in longitudinal direction (x)

j :

node index in transversal direction (y)

S :

Solution of absorbent e.g. L i B r − H 2 O

V :

Vapour e.g. steam

w :

Wall

References

  1. Aminyavari M, Aprile M, Toppi T, Garone S, Motta M (2017) A detailed study on simultaneous heat and mass transfer in an in-tube vertical falling film absorber. Int J Refrig 80:37–51

    Article  Google Scholar 

  2. Andberg JW, Vliet GC (1983) Nonisothermal absorption of gases into falling liquid films. ASME-JSME Therm Eng Joint Conf Proc 2:423–431

    Google Scholar 

  3. Brauner N (1991) Non-isothermal vapour absorption into falling film. Int J Heat Mass Tran 34:767–784

    Article  MATH  Google Scholar 

  4. Cerro RL, Whitaker S (1971) Entrance region flows with a free surface: the falling liquid film. Chem Eng Sci 26:785–798

    Article  Google Scholar 

  5. Conlisk A (1995) Analytical solutions for the heat and mass transfer in a falling film absorber. Chem Eng Sci 50:651–660

    Article  Google Scholar 

  6. Gao D, Morley N, Dhir V (2003) Numerical simulation of wavy falling film flow using vof method. J Comput Phys 192:624–642

    Article  MATH  Google Scholar 

  7. Grossman G (1983) Simultaneous heat and mass transfer in film absorption under laminar flow. Int J Heat Mass Tran 26:357–371

    Article  Google Scholar 

  8. Grossman G (1987) Analysis of interdiffusion in film absorption. Int J Heat Mass Tran 30:205–208

    Article  Google Scholar 

  9. Hosseinnia SM, Naghashzadegan M, Kouhikamali R (2017) Numerical study of falling film absorption process in a vertical tube absorber including soret and dufour effects. Int J Therm Sci 114:123–138

    Article  Google Scholar 

  10. Islam MA, Miyarab A, Setoguchib T (2009) Numerical investigation of steam absorption in falling film of libr aqueous solution with solitary waves. Int J Refrig 32:1597–1603

    Article  Google Scholar 

  11. Jernqvist A, Kockum H (1996) Simulation of falling film absorbers and generators. In: Ab-Sorption, vol 96

  12. Kabova Y, Kuznetsov V, Kabov O (2012) Temperature dependent viscosity and surface tension effects on deformations of non-isothermal falling liquid film. Int J Heat Mass Tran 55(4):1271–1278

    Article  MATH  Google Scholar 

  13. Karami S, Farhanieh B (2011) Numerical modeling of incline plate libr absorber. Heat Mass Transf 47:259–267

    Article  Google Scholar 

  14. Kharangate CR, Lee H, Mudawar I (2015) Computational modeling of turbulent evaporating falling films. Int J Heat Mass Transf 81:52–62

    Article  Google Scholar 

  15. Killion JD, Garimella S (2001) A critical review of models of coupled heat and mass transfer in falling-film absorption. Int J Refrig 24:755–797

    Article  Google Scholar 

  16. Killion JD, Garimella S (2004) Simulation of pendant droplets and falling films in horizontal tube absorbers. J Heat Trans-T ASME 126:1003–1013

    Article  Google Scholar 

  17. Kim DS, Infante Ferreira CA (2009) Analytic modelling of a falling film absorber and experimental determination of transfer coefficients. Int J Heat Mass Tran 52:4757–4765

    Article  MATH  Google Scholar 

  18. Kim KJ (1992) Heat and mass transfer enhancement in absorption cooling. Ph.D. thesis, Arizona State University

  19. Löwer H (1960) Thermodynamische und physikalische Eigenschaften der wässrigen Lithiumbromid-Lösung. Ph.D. thesis, Karlsruhe

  20. McKee S, Tom M, Ferreira V, Cuminato J, Castelo A, Sousa F, Mangiavacchi N (2008) The mac method. Comput Fluids 37:907–930

    Article  MathSciNet  MATH  Google Scholar 

  21. Meyer T (2014) Improvement of the exact analytical solutions for combined heat and mass transfer problems obtained with the fourier method. Int J Refrig 43:133–142

    Article  Google Scholar 

  22. Meyer T (2015) Analytical solution for combined heat and mass transfer in laminar falling film absorption with uniform film velocity - diabatic wall boundary. Int J Heat Mass Transf 80:802–811

    Article  Google Scholar 

  23. Min JK, Park IS (2011) Numerical study for laminar wavy motions of liquid film flow on vertical wall. Int J Heat Mass Tran 54:3256–3266

    Article  MATH  Google Scholar 

  24. Mirzabeygi P, Zhang C (2015) Three-dimensional numerical model for the two-phase flow and heat transfer in condensers. Int J Heat Mass Transf 81:618–637

    Article  Google Scholar 

  25. Mittermaier M, Schulze P, Ziegler F (2014) A numerical model for combined heat and mass transfer in a laminar liquid falling film with simplified hydrodynamics. Int J Heat Mass Tran 70:990–1002

    Article  Google Scholar 

  26. Nakoryakov V, Grigoryeva N, Bartashevich M (2011) Heat and mass transfer in the entrance region of the falling film: Absorption, desorption, condensation and evaporation. Int J Heat Mass Tran 54:4485–4490

    Article  MATH  Google Scholar 

  27. Nakoryakov VE, Grigor’eva NI (1977) Combined heat and mass transfer during absorption in drops and films. JEPT 32:243–247

    Google Scholar 

  28. Park IS (2010) Numerical analysis for flow, heat and mass transfer in film flow along a vertical fluted tube. Int J Heat Mass Tran 53:309–319

    Article  MATH  Google Scholar 

  29. Schlichting H, Gersten K (2006) Grenzschicht-Theorie. Springer, Berlin

    MATH  Google Scholar 

  30. Wu Y (2016) Simultaneous heat and mass transfer in laminar falling film on the outside of a circular tube. Int J Heat Mass Transf 93:1089–1099

    Article  Google Scholar 

  31. Yang R, Wood BD (1992) A numerical modeling of an absorption process on a liquid falling film. Sol Energy 48:195–198

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut fuer Energietechnik, Technische Universitaet Berlin, Sekretariat KT 2, Marchstrasse 18, 10587, Berlin, Germany

    M. Mittermaier & F. Ziegler

Authors
  1. M. Mittermaier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Ziegler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Mittermaier.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mittermaier, M., Ziegler, F. The impact of viscosity on the combined heat, mass and momentum transfer in laminar liquid falling films. Heat Mass Transfer 54, 1199–1215 (2018). https://doi.org/10.1007/s00231-017-2219-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-017-2219-9

Keywords

Search

Navigation