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A model-based analysis of heat transport in electrolytic reactors

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Abstract

Thermal behaviour and heat transport phenomena occurring in electrolytic reactors are analysed via the governing equations of appropriate models. Applications of the continuous-flow stirred tank electrochemical reactor (CSTER) and plug-flow electrochemical reactor (PFER) models to estimate temperature profiles in electrolysers are discussed.

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Abbreviations

a, b :

regression parameters for (ΔH w,T)

a s :

specific investment cost

A E :

electrode area

A j :

the area of thejth heat transfer surface

A s :

electrolyte surface area

b s :

specific cost of electric energy

c :

electrolyte concentration

C H :

specific cost of thermal energy

C i :

specific cost of thermal insulation

C k :

concentration of thekth ionic species

c 0 :

solvent concentration

C p :

specific heat of the electrolyte

c T :

total solution concentration

C T :

composite cost

d i :

insulation thickness

D :

electrolyte diffusivity (based on a thermodynamic driving force)

D/Dt :

substantive differential operator

F :

Faraday's constant

G :

mass flow rate of electrolyte

\(\bar H_k \) :

partial molar enthalpy of thekth ionic species

h s :

surface-to-air heat transfer coefficient

I :

electric current

i :

electric current density

k i :

thermal conductivity of insulation

L :

characteristic length

\(\bar m\) :

average rate of evaporation

M :

heat capacity of electrolyte mass in reactor

n k :

mole fraction of thekth component

N k :

substance flux of thekth ionic component

P :

pressure

P w :

vapour pressure of water at the evaporating surface

P ∞ :

vapour pressure of the ambient water vapour

q:

heat flux vector

Q L :

rate of heat losses

R e :

electrolyte resistance

R k :

rate of homogeneous production in chemical reaction of thekth ionic species, per unit are

S :

separation distance of electrolyser walls parallel to plug flow direction

S 1,S 2 :

dimensions of the horizontal section of a rectangular electrolyser

T :

temperature

T A :

ambient temperature

t :

time

U :

overall heat transfer coefficient;U j pertains to thejth heat transfer surface insulation volume

V i :

insulation volume

υk :

velocity of thekth ionic component

V:

velocity vector

w :

electrode area per unit reactor length

α 1 :

lumped parameter (U/Sϱc p)

α 2 :

lumped parameter (i 2m /ϱcp σm)

α 4 β 4 :

regression parameters for (σ,T)

β 1 :

lumped parameter (U/V x Sϱc p)

β 2 :

lumped parameter (l/V xϱc p)

β 3 :

lumped parameter (ΔH R/V x Sϱc p zF)

ΔH R :

heat of the overall electrolytic cell reaction

ΔH w :

latent heat of vapourization (of water);\(\Delta \hat H_w \) its estimated value by regression

ν:

dissociation number (number of ion moles produced by the dissociation of one mole of electrolyte)

νi :

ionic dissociation number (number of moles of thekth ionic species produced by the dissociation of one mole of electrolyte)

ϱ:

electrolyte density

σ:

electrolyte conductivity

σS :

Soret coefficient

τ:

PFER time constant

τ:

stress tensor

ωe :

mass fraction of the electrolyte

m:

average

L:

at exit site

S:

steady state

x:

along the principal direction of axial flow

References

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Thomas Z. Fahidy

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  1. Thomas Z. Fahidy
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Fahidy, T.Z. A model-based analysis of heat transport in electrolytic reactors. J Appl Electrochem 16, 250–258 (1986). https://doi.org/10.1007/BF01093357

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  • DOI: https://doi.org/10.1007/BF01093357

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