Numerical modelling of frost formation

Frost formation is a common phenomenon occurring especially in refrigeration industry and causes efficiency problems in systems. In this work, frost formation on a flat plate in 2-D is investigated by numerical modelling to predict frost thickness and frost surface temperatures and analysis outcomes are compared to experimental data stated in literature. Finite differences method is used for solving differential equations, a transient approach is applied and convective terms are discretized by using second order upwinding method and governing equations are solved by means of a self written MATLAB code. Proposed mathematical model is tested initially with 12 experimental data and then another 19 experimental data to see the accuracy of model. Outcomes showed that, model predicts frost thickness accurately for air temperatures between 2 °C and 25 °C, air inlet velocity between 0.6 m/s and 2.5 m/s and wall surface temperatures between -20.5 °C and -4 °C for conditions of inlet air with humidity ratio between 0.01 kg/kg and 0.00298 kg/kg. Conditions in which humidity ratio is between 0.01 kg/kg and 0.01596 kg/kg model is found to be valid under air inlet temperatures between 21.85 °C and 25 °C, air inlet velocities between 0.7 m/s and 2.92 m/s and wall surface temperatures between -28.15 °C and -5 °C. Surface temperature values are also compared to first 12 experimental data. Outcomes showed that, proposed model predicts frost surface temperatures with a maximum difference of 1.9 °C; but mainly this difference band for most conditions can be regarded as ±1 °C.