ABSTRACT:

We present a unified framework for the analysis and simulation of a coupled nonlinear PDE–ODE system with nonlinear boundary conditions arising in bioheat transfer. The PDE extends a linear elliptic bioheat transfer model derived using homogenization by Deuflhard and Hochmuth; we extend this model to a nonlinear parabolic setting, incorporating dynamic coupling between local tissue temperature and core body temperature, which is modeled by an ODE. Our main result is an a priori error estimate for a fully discrete backward-Euler-Galerkin scheme, supported by stability bounds. We also present numerical evidence validating the parabolic extension of the Deuflhard/Hochmuth model, and we present simulations demonstrating model sensitivity and its effectiveness in capturing physiologically realistic core-to-extremity energy exchange.