Thermal management of heating elements in vacuum

Thermal management of heating elements placed in a vacuum must be handled carefully due to the lack of convective cooling and the difficulty of replacing components. This study investigates the thermal dissipation of a one-dimensional heating element placed in a vacuum, where the only cooling can occur through conduction through the wires and radiation. We model the heat in the element using a heat diffusion equation with Joule heating and radiative loss. We analytically and numerically analyze the equation and determine key parameters such as the critical current density and cycle rate. This study establishes a basis for the refinement of thermal management strategies in applied settings, ensuring both efficiency and reliability in high-vacuum environments.