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Heat transfer for falling film evaporation of industrially relevant fluids up to very high Prandtl numbers

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Abstract

In many industrial applications, falling film evaporation is an attractive technique for solvent removal due to high heat transfer and low residence times. Examples are the powder production in the dairy industry and in kraft pulp production process to remove water from so called black liquor. Common for both applications is that the fluids exhibit high viscosities in industrial practice. In this paper, results from experimental studies on both black liquor and a dairy product are reported for Prandtl numbers up to 800. The results are compared with several existing correlation in literature, and the need for a modified correlation is recognized especially to cover higher Prandtl-numbers. The following correlation for the turbulent flow region with 3 < Pr < 800 was derived from the data:

$${\text{Nu}}_{t} = 0.0085 \cdot \text{Re}^{0.2} \cdot {\text{Pr}^{0.65}}$$

The correlation has been compared to literature data from one additional study on two other fluids (propylene glycol and cyclohexanol) with fairly high Prandtl-numbers, from 40 to 58 and from 45 to 155 respectively and the agreement was within ±40 %.

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Abbreviations

A :

Area (m2)

c p :

Specific heat (J kg−1 K−1)

g :

Gravitational acceleration (m s−2)

h :

Heat transfer coefficient (W m−2 K−1)

k :

Thermal conductivity (W m−1 K−1)

K :

Constant in Nusselt correlations

K τ :

Consistency factor (Pa sn)

l :

Viscous length (m)

n :

Exponent in Nusselt correlations

n τ :

Flow behaviour index

P :

Parameter

Q tot :

Rate of heating (W)

q :

Heat flux (W m−2)

S :

Dry solids mass fraction (kg kg−1)

T :

Temperature (°C)

v :

Velocity (m s−1)

U :

Overall heat transfer coefficient (W m−2 K−1)

x :

Distance from liquid/gas interface (m)

\(\dot{\gamma }\) :

Shear rate (s−1)

Γ :

Specific mass flow rate (kg m−1 s−1)

δ :

Thickness (m)

ΔT :

Temperature difference (°C)

μ :

Dynamic viscosity (Pa s)

ν :

Kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

σ :

Surface tension (N m−1)

τ :

Shear stress (Pa)

Nu:

Nusselt number

Pr:

Prandtl number

Re:

Reynolds number

exp:

Experimental

film:

Falling film

i:

Inside

l:

Laminar flow

m:

Mean

model:

Model

o:

Outside

sat:

Saturation

steam:

Heating steam

t:

Turbulent flow

w:

Evaporator tube wall

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Acknowledgments

This work was co-funded by the Swedish Energy Agency, Metso Power AB, Tetra Pak Processing Systems, Troëdssons forskningsfond and Chalmers Energy Initiative.

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Authors and Affiliations

  1. Energy and Environment, Chalmers University of Technology, 412 96, Gothenburg, Sweden

    Mathias Gourdon, Erik Karlsson & Lennart Vamling

  2. Tetra Pak CPS, 8400, Heerenveen, The Netherlands

    Fredrik Innings & Alfred Jongsma

Authors
  1. Mathias Gourdon
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  2. Erik Karlsson
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  3. Fredrik Innings
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  4. Alfred Jongsma
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  5. Lennart Vamling
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Correspondence to Mathias Gourdon.

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Gourdon, M., Karlsson, E., Innings, F. et al. Heat transfer for falling film evaporation of industrially relevant fluids up to very high Prandtl numbers. Heat Mass Transfer 52, 379–391 (2016). https://doi.org/10.1007/s00231-015-1556-9

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