This paper presents a nonlinear reaction–diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both solid and fluid phases, we proceed to an analysis of well-posedness, considering a broad class of right-hand side terms. The system involves parameters such as heat conductivity, kinematic viscosity, and electrical conductivity, all of which exhibit nonlinearity contingent upon the temperature variable. The mathematical analysis extends to establishing the existence of a global solution, employing the Faedo–Galerkin method in a three-dimensional space. To enhance the practical applicability of our theoretical results, we complement our study with a series of numerical experiments. We implement the discrete system using the finite element method for spatial discretization and an Euler scheme for temporal discretization. Nonlinear parameters are linearized through decoupling systems, as introduced in our continuous analysis. These experiments are conducted to demonstrate and validate the theoretical findings we have established. • Proposition of a new coupled electro-thermo radiofrequency model of cardiac tissue. • Establishment of the existence of a global solution, employing the Faedo–Galerkin method in a three-dimensional space. • Proof of the existence of a discrete solution to the discrete problem. • Indication of the main steps of the convergence proof of the finite element solution generated by the discrete problem. • Provide numerical results to illustrate the influence of electric potential in the cardiac tissue, saline viscosity, and external forces. [ABSTRACT FROM AUTHOR]