Thermophotovoltaics (TPV) shows promise for direct heat-to-electricity conversion. Unlike solar cells that are powered by the Sun, TPV sources (concentrated sunlight heating, waste heat, power beaming), typically at 1000-2000 K, are closer, which yields radiation with significantly higher power densities (5-60 W/cm2 versus ~0.1 W/cm2 for solar) but below the bandgaps of many common semiconductors. This has drawn attention toward low-bandgap, CMOS-compatible materials (particularly group-IV semiconductors such as germanium (Ge) and germanium-tin alloys (GeSn). This work presents a comprehensive finite element model (FEM) of a TPV system employing a low-bandgap, direct-gap GeSn photovoltaic cell, accounting for indirect recombination, multilayer generation dynamics, and the thermal equilibrium between emitter and cell. It supports in-depth study of Ge-based materials under varying strain, composition, and temperature, providing insights for the design of future devices.