Modeling Heat Transfer through Concentric Cylindrical Layers for Controlled Thermal Regulation of a Commercial Research Cryostat

Abstract The thermal characteristics of a variable temperature, flowing vapor cryostat are theoretically modeled, taking into account specific geometrical and material constraints, temperature-varying heat transfer coefficients, and thermal conductivities for conductive, convective, and radiative heat transfer. The temperature within the cryostat is controlled by an internal heater and is monitored at both the heater and the sample stage. The modeled system consists of multiple coaxial, cylindrical layers of stainless steel containing various fluids (light vacuum, helium gas, nitrogen gas; the liquid cryogen is nitrogen or helium). The calculated Prandtl and Grashof numbers for the fluid layers suggest that the Churchill-Chu form of the Nusselt equation be used for heat transfer analysis of this system. Developing a model that predicts heat flows throughout the cryostat allows for appropriate articulation of the heater so that the sample quickly reaches the desired temperature without overshooting. Transient and steady-state models are investigated for predictive ability and consistency with the system's experimentally collected heating and cooling behavior.