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We use a recently-developed, turbulence-informed physics-based model to study frost buildup over a flat plate subjected to turbulent flow. The plate temperature is held fixed but varied across simulations in the range −10◦C ≤ T∗ p ≤ −5◦C. Similarly, the free-stream temperature and humidity ratio are also held fixed but varied across simulations in the range 0◦C ≤ T∗∞ ≤ 20◦C and 3.77 × 10−3 ≤ ew∞ ≤ 1.47×10−2, respectively. We find the Nusselt and Sherwood numbers, when scaled by the frost surface to free stream temperature and humidity ratio difference, respectively, to become independent of free-stream temperature and humidity ratio as well as plate temperature. The scaling can be used in conjunction with the frost layer conservation equations of mass and energy to provide an estimate for the temporal evolution of the frost layer under turbulent flow conditions for a range of plate temperatures as well as free-stream temperatures and humidity ratios. For an initial shear Reynolds number of Re = 180, we find the heat and mass transfer rates to be enhanced by about a factor of three compared to laminar flow conditions. We additionally conduct a sensitivity analysis on the frost layer density and thermal conductivity empirical correlations, as well as the frost layer Schmidt number. The latter parameterizes lateral frost diffusion and must be obtained from experiments. For the cases considered, we find the frost buildup to be only sensitive to the frost density correlation.


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International Journal of Heat and Mass Transfer



Available for download on Saturday, February 17, 2024