Mathematical Modeling and Sensitivity Analysis of Enzymatic Biofuel Cells with

The mathematical model in this study advances prior research on enzymatic biofuel cells by applying the Rajendran–Joy method, which enables approximate analytical solutions of nonlinear reaction–diffusion equations incorporating Michaelis–Menten-type enzyme kinetics. Unlike many earlier models that primarily relied on numerical simulation or simplified linear assumptions, this study provides explicit analytical expressions for substrate concentration profiles and current–potential relationships for multiple electrode geometries (planar, cylindrical, spherical). The analytical approach delivers high accuracy validated against numerical simulations, allowing systematic parametric sensitivity analysis to reveal how critical parameters—such as the Thiele modulus, Michaelis–Menten constants for substrate and mediator, applied potential, and electrode geometry—govern biofuel cell performance. This enhances mechanistic understanding and design optimization, including evaluation of limiting cases, thereby offering new insights beyond previous methods that were either purely numerical or less comprehensive in addressing nonlinear kinetics and geometric effects.