Abstract
A mathematical model is introduced for thermoelectrochemical phenomena in an electrolysis cell, and its qualitative analysis is focused on existence of solutions. The model consists of a system of nonlinear parabolic PDEs in conservation form expressing conservation of energy, mass and charge. On the other hand, an integral form of Newton’s law is used to describe heat exchange at the electrolyte/electrode interface, a nonlinear radiation condition is enforced on the heat flux at the wall and a nonlinear boundary condition is considered for the electrochemical flux in order to account for Butler–Volmer kinetics. The main objective is the nonconstant character of each parameter, that is, the coefficients are assumed to be dependent on the spatial variable and the temperature. Making recourse of known estimates of solutions for some auxiliary elliptic and parabolic problems, which are explicitly determined by the Gehring–Giaquinta–Modica theory, we find sufficient smallness conditions on the data to guarantee the existence of the original solutions via the Schauder fixed point argument. These conditions may provide useful information for numerical as well as real applications. We conclude with an example of application, namely the electrolysis of molten sodium chloride.
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Consiglieri, L. Sufficient conditions for the existence of solutions for a thermoelectrochemical problem. J. Fixed Point Theory Appl. 17, 669–692 (2015). https://doi.org/10.1007/s11784-015-0255-y
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DOI: https://doi.org/10.1007/s11784-015-0255-y