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Design and optimization of thermo-electrochemical cells

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Abstract

Thermo-electrochemical cells (or thermocells) convert thermal energy to electricity in continuous operation based on a balance of ion conduction and redox reactions at hot and cold electrodes. In this study, the fundamental governing equations for mass and heat transfer, fluid dynamics, and electrokinetics in thermocells are presented and solved numerically using COMSOL. A parametric study is performed to explore the limitations and optimal cell dimensions for maximum energy conversion efficiency in thermocells. Series-stacking designs are demonstrated to have the potential to increase conversion efficiency by 100 % compared to a single cell configuration. Natural convection is shown to significantly increase the conversion efficiency of thermocells with conventional aqueous electrolyte (0.4 M potassium ferri/ferrocyanide), by compressing the diffusive boundary layers. A flow cell thermocell design is also considered. Results reveal that the ohmic resistance of the electrolyte limits the energy conversion efficiency of this design.

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Abbreviations

A :

Electrode surface area (m2)

β T1 :

Temperature density change coefficient 1 (kg m−3)

β T2 :

Temperature density change coefficient 2 (kg m−3 K−1)

β T3 :

Temperature density change coefficient 3 (kg m−3 K−2)

C p :

Electrolyte heat capacity (J kg−1 K−1)

C i :

Ion concentration (mol m−3)

\(C_{\text{i}}^{ *}\) :

Initial ion concentration (mol m−3)

C O :

Oxidized concentration (mol m−3)

C R :

Reduced concentration (mol m−3)

C CI :

Counter-ion concentration (mol m−3)

D i :

Ion diffusion coefficient (m2 s−1)

D O :

Oxidized diffusion coefficient (m2 s−1)

D R :

Reduced diffusion coefficient (m2 s−1)

D CI :

Counter-ion diffusion coefficient (m2 s−1)

ρ :

Electrolyte density (kg m−3)

ρ o :

Electrolyte density reference at 300 K (kg m−3)

ε :

Dielectric constant (A2 s4 kg−1 m−3)

E :

Electrode potential (V)

E°:

Standard electrode potential (V)

E a :

Anode potential (V)

\(E_{\text{a}}^{\text{eq}}\) :

Anode equilibrium potential (V)

E c :

Cathode potential (V)

\(E_{\text{c}}^{\text{eq}}\) :

Cathode equilibrium potential (V)

\(E{x}_{\text{a}}\) :

Rate constant activation energy (J mol−1K−1)

F:

Faraday constant (C mol−1)

h e :

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

I o :

Optimum cell current (A)

j :

Electronic current density (A m−2)

j a :

Electronic current density at the anode (A m−2)

j c :

Electronic current density at the cathode (A m−2)

J sc :

Short-circuit current density (A m−2)

j wc :

Electronic current density without convection (W m−2)

k :

Electrochemical rate constant (m s−1)

k 0 :

Standard rate constant (m s−1)

κ s :

Electrolyte thermal conductivity (W m−1 K−1)

κ e :

Electrode thermal conductivity (W m−1 K−1)

\(\vec{N}_{\text{i}}\) :

Ion flux density (mol m−2 s−1)

\(\vec{N}_{\text{O}}\) :

Oxidized flux density (mol m−2 s−1)

\(\vec{N}_{\text{R}}\) :

Reduced flux density (mol m−2 s−1)

\(\vec{N}_{\text{CI}}\) :

Counter-ion flux density (mol m−2 s−1)

n :

Number of electrons transferred (−)

η :

Conversion efficiency (%)

η i :

Conversion efficiency of intermediate cell (%)

η r :

Relative efficiency (%)

ξ a :

Anode overpotential (V)

ξ c :

Cathode overpotential (V)

P e :

Electric power density (W m−2)

P i :

Electric power of intermediate cell (W)

P m :

Maximum electric power density (W m−2)

q :

Heat flux density (W m−2)

q wc :

Heat flux density without convection (W m−2)

Q CI :

Counter-ion heat of transport (J mol−1)

Q i :

Ion heat of transport (J mol−1)

Q O :

Oxidized heat of transport (J mol−1)

Q R :

Reduced heat of transport (J mol−1)

R :

Gas constant (J mol−1K−1)

\(\mathcal{R}_{T}\) :

Thermocell volume (m3)

S :

Heat generation sources (W m−3)

T :

Temperature (K)

T a :

Anode temperature (K)

T c :

Cathode temperature (K)

T H :

Temperature at the hot electrode (K)

T o :

Standard temperature (K)

U C :

Cold flow temperature (K)

U H :

Hot flow temperature (K)

u i :

Ion mobility (m2 s−1 V−1)

\(\vec{u}\) :

Bulk vector velocity (m s−1)

\({{\upupsilon}}\) :

Kinematic viscosity (m2 s−1)

V o :

Optimum cell voltage (V)

V oc :

Open-circuit cell voltage (V)

V T :

Cell voltage (V)

Z CI :

Counter-ion charge number (−)

Z i :

Ion charge number (−)

Z O :

Oxidized charge number (−)

Z R :

Reduced charge number (−)

ϕ :

Electrostatic potential (V)

θ :

Charge transfer coefficient (−)

∆ϕ s :

Solution ohmic drop (V)

\(\Updelta S_{{\text{rx}}}^{\circ}\) :

Standard electrochemical redox reaction entropy (J mol−1 K−1)

\(\Updelta H_{{\text{rx}}}^{\circ}\) :

Standard electrochemical redox reaction enthalpy (J mol−1)

\(\Updelta G_{{\text{rx}}}^{\circ}\) :

Standard electrochemical redox reaction free energy (J mol−1)

∫ a :

Integral at the anode surface

∫ c :

Integral at the cathode surface

∫ T :

Integral in the thermocell

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Acknowledgments

We are grateful for the financial support of National Science Foundation Award No. CBET 1055479.

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Authors and Affiliations

  1. George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Pablo F. Salazar, Satish Kumar & Baratunde A. Cola

  2. School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Baratunde A. Cola

Authors
  1. Pablo F. Salazar
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  2. Satish Kumar
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  3. Baratunde A. Cola
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Correspondence to Pablo F. Salazar.

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Salazar, P.F., Kumar, S. & Cola, B.A. Design and optimization of thermo-electrochemical cells. J Appl Electrochem 44, 325–336 (2014). https://doi.org/10.1007/s10800-013-0638-y

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