Heat and Mass Transfer in the Melting of Frost

The impact of frost formation on refrigeration performance is described, and several current methods for frost removal are discussed. Defrost efficiency is generally defined for use at either the system or surface levels. An example of the economic impact of defrost is given for U.S. transportation refrigeration units.

The majority of the research conducted over the past five decades has concentrated on the description of frost formation and growth. The prevailing ambient environment greatly influences frost morphology. Several models have been proposed to describe time-variant physical properties and growth of the frost layer, and several researchers have developed frosted fin models to predict the thermal performance of heat exchangers. Experiments have visualized the growth of frost on simple and finned surfaces, as well as, quantified the degradation of the system performance and efficiency under frosted conditions. Recently, studies have been completed to experimentally determine the heat load imposed on the refrigeration system during defrosting and recovery cycles. There have been relatively few models proposed to predict the heat transfer in defrost, with very little analysis of mass transfer. In this chapter we examine several relevant modeling efforts on frost formation and defrost.

A comprehensive one-dimensional model is developed for heat and mass transfer in each stage of the defrost process. The model describes sublimation, vapor transport, liquid melting and evaporation on a heated vertical surface in each of three distinct stages of the defrost process: diffusion, melting-permeation and dry out. Dimensionless forms of the governing differential equations yield the Lewis, Stefan, and Biot numbers as the key parameters. These parameters for each stage of defrost are slightly different owning to the difference in the dominate heat and mass transfer mechanisms. By analyzing the magnitude of the dimensionless groups, it is possible to determine the relative weight of each term in the governing equation. From such an analysis, the effect of mass transfer due to sublimation in the first and second stages of the defrost process can be neglected. The effects of several limiting cases on the governing equations are evaluated, with simplified equation sets developed for them.

This chapter provides a description of an experimental apparatus constructed to permit real time measurement of frost thickness and planar morphology during growth and melting, as well as heat transfer rates. Quantitative data are obtained via digital reduction of normal and in plane images of the frosted test surface. Data reduction is described, and measurement uncertainties are summarized.

Quantitative and visual data on defrost are presented. The data base comprises normal and in plane images of the defrost process over a range of ambient temperature, dew point, and surface temperature. Twelve frost layers are created at prescribed surface temperature, dew point, and ambient temperature. Melting is initiated by application of heating on the frosted surface. Predictions of the multistage defrost model developed in Chap. 3 are compared to the reduced data where possible, and empirically based relations for heat and mass transfer are developed. Assumptions used to simplify the differential equations for coupled heat and mass transfer in Chap. 3 are validated by the measurements. Overall defrost efficiency is proportional to initial frost thickness.

The differential equations describing heat and mass transfer during each stage of defrost are solved, and results are compared to measurement. Numerical solutions for defrost Stages I and II are obtained, while an analytical solution for Stage III is possible. For Stage I, the duration of the stage is predicted and validated by experiment. For Stage II, melt front and duration of the stage are predicted and in good agreement with measurement. For Stage III, the solution under predicts defrost time but generally simulating the general trends for duration seen in the experiments. We conclude with a graphical summary that indicates that further research is needed for measurements with greater super saturation and subcooling.