Modelling of Frost Formation and Growth on Microstuctured Surface 11th International Conference on Mechanical Engineering (18-20 December, 2015) Dhaka, Bangladesh Modelling of Frost Formation and Growth on Microstuctured Surface Md. Ali Muntaha Md. Mushfique Haider Md. Ashiqur Rahman Department of Mechanical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000 Bangladesh University of Engineering and Technology, BUET Paper ID: 542

Background Frost is a deposit of small white ice crystals Paper ID: 542 Background Frost is a deposit of small white ice crystals Formed on the various simple and complex geometrical surfaces when the temperature falls below freezing Application: Refrigeration, Cryogenics, Heat Pump, Air Conditioning etc. Effect of frost formation Nawaf F. (2006)

Background and Motivation Paper ID: 542 Background and Motivation The Modelling of frost formation is essential as because performance of a heat exchanger under frosting condition is characterized by frost properties. Modelling enables to predict the frost properties Frost properties are known to be affected by temperature and moisture content of air cold plate temperature , air velocity and surface wettability Hoke et al. (2004)

Motivation Paper ID: 542 The ability of a liquid to maintain contact with a solid surface is the surface wettability Modelling incorporating wettability effect on flat surfaces Wettability effect on micro-structured surfaces Importance of micro-structure surface No study could be located in available literature Rahman and Jacobi (2013,2015) Micro-groove Flat

Paper ID: 542 Research Objective To model the frost properties for various flat and micro-grooved metal surfaces having different geometries To incorporate the effects of wettability on frost formation and frost properties Validate the findings with experimental results [Rahman and Jacobi (2013)] Comparison of frost properties on flat and micro-grooved metal surfaces

Paper ID: 542 Numerical Method The total mass flux transferred from the moist air to the frost surface can be subdivided into two parts The equation can be written as The frost growth rate equation is obtained The heat transfer through the frost surface by conduction

Numerical Method Boundary Condition at t=0 Paper ID: 542 Boundary Condition at t=0 The temperature at the frost surface corresponding to x = 𝑥 𝑠 can be obtained from An empirical correlation by O’Neal and Tree(1985) Different initial thickness and density for different geometries

Results Paper ID: 542 Error 14% for DG = 122 µm Error 17% for Wp = 80 µm Initial density = 75 kg/m3 Initial density = 85 kg/m3 Wp = 110 µm WG = 130 µm DG = 67 µm WG = 130 µm

Results Paper ID: 542 Error 7% for Wp = 80 µm Initial Thickness = 2.65mm Error 7% for DG = 122 µm Initial Thickness = 2.2mm Wp = 110 µm WG = 130 µm DG = 67 µm WG = 130 µm

Paper ID: 542 Results Tao & Jia (Critical review,2004) Operating conditions: Ta = 22±2°C, Tw = -18°C, t = 0 to 225 min, RH = 30-70% Operating conditions: Ta = 25°C, Tw = -15°C, t=0 to 120 min, W = 0.007 kga/kgw.

Frost density is predicted quite accurately with respect to time Paper ID: 542 Results Wp = 110 µm DG = 67 µm Frost density is predicted quite accurately with respect to time Thermal Conductivity is predicted quite accurately with respect to density

Results Initial thickness and density calculation by image analysis Paper ID: 542 Results Droplet Distribution Label Area Perim. 1 0.005 0.331 2 0.032 2.551 3 0.092 4.182 4 0.427 7.06 5 0.009 0.562 6 0.02 0.951 7 1.256 8 0.147 8.172 9 0.04 3.082 10 0.008 0.793 11 0.01 0.698 12 0.034 1.778 13 0.801 43.142 14 0.671 15 0.815 16 0.015 1.389 17 18 Mean 0.099 4.603 Initial thickness and density calculation by image analysis Volume calculation Frost mass Density Calculation Amne El Cheikh (2013) Droplet Distribution (Top View) Image Analysis

Summary A model incorporating the wettability effect is developed Paper ID: 542 Summary A model incorporating the wettability effect is developed Incorporating initial thickness and density values from experimental results, a model is developed for different flat and micro-grooved geometries for a specific operating condition. Our model can satisfactorily predict the frost properties Maximum error of 7% for frost thickness and of 17% for frost density We are continuing our work for obtaining the initial frost thickness and density values directly form droplet image analysis

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