inverse method. The equation that governs the two-dimen- sional transient heat conduction was solved inversely using InverseSolver software for estimating the heat flux boundary condition. The mathematical details of the inverse method are given in references 16 and 17.
Equation 1 results and discussion
Figure 2 shows the typical thermal history inside the chill and the solidifying casting. TC1 is the temperature of the solidifying alloy at a distance of 5mm from the chill surface. TC2, TC3 and TC4 are the chill temperatures at locations 2mm, 14mm and 26mm from the interface. The difference between the temperatures at near and far locations from the casting/chill interface is larger for graphite than for alumi- num chill. This is due to the difference in thermal conductiv- ities of chill materials. The higher the thermal conductivity of the chill material, the lower the tem- perature gradient is. Figure 3 shows the typical thermal field in the chill at differ- ent time steps. Figure 3 clearly indicates the gradual heating of the chill during the initial stage. The heat transfer within the chill at this stage was one-dimensional. The two-dimensional temperature distri- bution is observed after a time interval of about 200 seconds. The heat transfer again became one-dimensional in the fi- nal stage. It is found that, the heat flow changes from one-dimensional to two- dimensional, at the time of occurrence of peak temperature in the chill. This also corresponds to the start of the solidifica- tion process. The transformation from one to two-dimensional heat transfer is due to the chill reaching its saturation tempera- ture early when the chill is no longer capa- ble of extracting the heat from the source. In the case of aluminum chill, there was no one-dimensional to two-dimensional heat transfer transformation, because the heat diffusivity of the aluminum chill is higher compared to that of the graph- ite chill (Figure 4). The thermophysical properties of chill materials are given in Table 1. The peak cooling rate of the alloy was higher by about 23% with aluminum chill than with graphite chill, although the thermal diffusivities of both chill materi- als are of similar magnitude. However, the ability of the aluminum chill to absorb heat is better compared to that of graphite.
International Journal of Metalcasting/Fall 2011
Heat flux transients were measured from the thermal histo- ry and thermophysical properties of chill material by using the inverse method. Figure 5 shows the heat flux transients at the interface estimated during downward solidification of the alloy against chills. For all experiments, the heat flux shows a maximum shortly after pouring and then drops off rapidly. The heat flux increases rapidly and reaches a peak value after about 10 seconds and then decreases gradually. Liquid metal first establishes contact with the surface of the chill resulting in the rapid increase of heat flux. As the thickness of the solidified shell increases with time, the casting skin contracts away from the chill, leading to non- conforming contact at the interface. Heat flux drastically decreases due to transformation of casting/chill interfacial condition, from conforming contact to nonconforming con- tact. The heat flux transients were normalized with respect to the peak flux, and the chill surface temperature were nor- malized with respect to the peak chill temperature. Figure 6 show the plots of q/qmax
against graphite chill. The peak in the heat flux transients occurs when chill temperature reaches about 50% of satu- ration temperature of the chill.
Vs T/Tmax for the alloy solidifying
Figure 3. Thermal plot of graphite chill at different time interval during solidification of A413 casting.
65
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80