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Research Papers: Melting and Solidification

# Modeling Frost Growth for Subcooled Tube-Array Configurations

[+] Author and Article Information

Department of Mechanical Engineering, The University of Auckland, Auckland 1142, New Zealandv.yadav@auckland.ac.nz

C. G. Moon

Department of Mechanical Engineering, The University of Auckland, Auckland 1142, New Zealandc.moon@auckland.ac.nz

K. Kant

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016, Indiakeshav@iitk.ac.in

1

Corresponding author.

J. Heat Transfer 131(6), 062301 (Mar 31, 2009) (12 pages) doi:10.1115/1.3082424 History: Received December 02, 2007; Revised December 06, 2008; Published March 31, 2009

## Abstract

Methodology for predicting frost growth trends on a subcooled cylindrical surface is developed and implemented for multitube array configuration. Extension of conventional analysis and a novel technique for understanding frost formation phenomenon on the cylindrical surfaces is proposed; later one takes into account the nonsteady temperature field, which affects the density and thermal conductivity at a local level in the growing frost mass, for more accurate prediction of thermal resistance. The influence of migration of liquid water due to tortuosity effect is also considered. The results due to new model are found to be in good agreement with the data in the open literature. Data for frost thickness ratio (FTR) versus time for a section of array with four (tube) rows in the airstream are presented and thoroughly analyzed. The trends of FTR noted are complex and considerably dependent on the tube location, temperature of subcooled surface $(Ts)$, airflow velocity $(Ua)$, and the relative humidity $(RHa)$ values. Approximate ranges for important parameters are $−30≤Ts≤−5.0°C$, $1.0≤Ua≤5.0 m/s$, and $0.20≤RHa≤0.80$. Presented analysis and the results are valuable in order to predict probable locations and precursors to partial or complete choking of airflow passages due to frost deposition in the evaporator coils.

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## Figures

Figure 1

Schematics for a conical needlelike portion

Figure 2

Schematics of internal control volume

Figure 3

Schematic of a tube-array section

Figure 4

Schematic of external control volume

Figure 5

Algorithm for implementing Model-1

Figure 6

Algorithm for implementing Model-2

Figure 7

Comparison of frost growth trends from Model-1 with literature

Figure 8

Comparison of frost growth trends from Model-2 with literature

Figure 9

Comparison of frost growth trends for initial period (from Model-2) with literature

Figure 10

Trends for frost layer development at leading-tube surfaces for flow velocity Ua=1.0 m/s

Figure 11

Trends for frost layer development at leading-tube surface for flow velocity Ua=5.0 m/s

Figure 12

Trends in frost thickness ratio for tubes in succession at Ua=1.0 m/s and Tr=−10.0°C for RHa values of (a) 0.40, (b) 0.60, and (c) 0.80

Figure 13

Trends in frost thickness ratio for tubes in succession at Ua=1.0 m/s and Tr=−30.0°C for RHa values of (a) 0.40, (b) 0.60, and (c) 0.80

Figure 14

Trends in frost thickness ratio for tubes in succession at Ua=5.0 m/s and Tr=−10.0°C for RHa values of (a) 0.40, (b) 0.60, and (c) 0.80

Figure 15

Trends in frost thickness ratio for tubes in succession at Ua=5.0 m/s and Tr=−30.0°C for RHa values of (a) 0.40, (b) 0.60, and (c) 0.80

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