A non-iterative solution for frost growth on flat surfaces

An algebraic, first-principles solution for frost growth on horizontal flat surfaces is derived. To avoid dependence on the frost surface temperature, the proposed solution uses a generic, power-law frost density expression. This yields a new class of non-iterative, fully-algebraic solutions to the problem of frost growth and densification on flat surfaces that are based explicitly on time and heat transfer characteristics. Closure of the derived solution is reached via semi-empirical frost property expressions. With three frost density expressions selected from literature, the predictive accuracy of the proposed frost thickness solution for each density expression is compared to flat plate and parallel plate frost thickness databases. The proposed solution is shown to accurately predict frost thickness, with 73.2% and 81.5% of the predictions falling within +/- 20% proportional error bands for the flat and parallel plate geometries respectively. Moreover, the proposed solution is shown to be comparably accurate to other predictive methods. The proposed approach is particularly useful in applications that require a non-iterative implementation, or those interested in decreasing computational effort in frost predictions.