Coupled Heat and Mass Transfer on a Chilled Beer Bottle: Experimental Nu–Ra Correlation, Caputo Fractional‐Order Modeling, and Monte Carlo Uncertainty Quantification

ABSTRACT

This study investigates coupled natural convection and vapor condensation on a chilled glass beer bottle exposed to warm humid air. A 600‐mL bottle initially at −1.5°C was monitored during warming at 19°C and 68% relative humidity. Experimentally derived temperature and condensate histories were used to estimate effective heat‐ and mass‐transfer coefficients and to obtain an empirical Nu–Ra relationship for the tested configuration. The resulting correlation, Nu = 11,717·Ra ^−0.371 (R ²  = 0.989), is restricted to the investigated transient cooled, humid, condensation‐active conditions. Classical and Caputo fractional‐order reduced models were compared to evaluate whether memory effects improved the description of the measured transients. The optimized fractional orders remained close to unity, and AIC favored the classical integer‐order model. Monte Carlo simulations showed low parametric uncertainty relative to measurement resolution. The framework provides experimentally grounded reduced‐order tools for analyzing coupled heat and mass transfer on chilled cylindrical surfaces while explicitly distinguishing parametric uncertainty from structural model limitations.