Chap.1      HEAT FLOW IN SOLIDFICATION
1-3 A large slab of aluminum,25cm thick,is poured in a sand mold with no superheat.
solidity(a) How long will it take for the slab to solidify?(Assume negligible resistance to heat flow at the mold-metal interface and within the solidity metal)
(b) Show schematically cooling curves for a thermocouple 6.25 cm form the surface and one at the center of the casting .(Remember,the solidified portion of the casting remains very close to until the casting is completely solid)
1-10 (a) A slab of iron,25 cm thick,is poured with no superheat into an iron mold.Calculate the solidification time assuming no mold-metal interface .
(b) How much longer is required for solidification of the slab in a sand mold ? Neglect resistance to flow within the solidified metal and at the mold-metal interface.
(c)What percentage error did you introduce in (b) by neglecting resistance to heat flow within the solidified metal?
1-14 You are to help design a vertical continuous-casting machine to make 8-in-thick low-carbon steel slabs.Casting speed to be aimed for is 100in/min.What is the minimum-height casting tower you must plan to build?
Chap.2 PLANE FRONT SOLIDIFICATION OF SINGLE-PHASE ALLOYS
2-1 A Ge-Ga ingot containing 10 ppm Ga is solidified at R=8*cm/s with negligible convection.Show schematically,the composition along the length of the fully solidified ingot,giving the initial composition and lengths of the initial and final transient.Assume =5*/s,k=0.1.
2-5 An Al-1%Cu alloy is normally solidified with =k.The phase diagram for this alloy is schematically as in Fig.2-3 with =33%Cu,=5.65%Cu,=660℃，and =548℃.
(a) How much eutectic will be present in the finally solidified bar assuming no solid diffusion?
(b) At a solidification velocity of cm/s,do you expect significant diffusion in the solid?[Note:=0.29*/s;R=1.99 cal/(mol)(°K).]
Chap.3 CELLULAR SOLIDIFICATION
3-2 An Al-1%Cu alloy is grown by normal freezing at 3*cm/s with convection completely suppressed.(The phase diagram for this alloy is as shown schematically in Fig.2-3,=33%Cu,=5.65%Cu,=660℃,=548℃,and constant k and ;=3*/s.)
3-3 What thermal gradient would be required to maintain the plane front in Prob.3-2,according to the Mullins and Sekerka interface stability criterion?(Assume the thermal conductivity of the solid is half that of the liquid;σ=1.2*cal/.The volumetric heat of fusion can be calculated from Appendix B.)
3-4 An Al-1%Cu ingot is solidified with no convection at 3*cm/s,with a thermal gradient of 300℃/cm.Solidification is cellular.(See the data in Prob.3-2).
(a) What is the approximate liquid composition at the cell tips？The solid composition?
(b) What is the temperature of the cell tips?
(c) What is the distance from the cell tips to the cell roots?
(d) How far does characteristic distance of the diffusion boundary layer extend in front of the cell tips?
Chap.5 PLANE FRONT SOLIDIFICATION OF POLYPHASE ALLOYS
4-1 A tin-lead eutectic alloy(==26.1 at%Pb) is directionally solidified at R=cm/s.Use the experimentally determined value of λ(Fig.4-8) to calculate and .What is the liquid composition at the center of the β lamella?Assume =6.7* /s and the densities of the tin-rich and lead-rich phase are 7.3 and 11.5 g/.
4-2 At what distance in front of the eutectic interface does the deviation of the liquid composition from in Prob.4-1 become negligible? Show that this is small compared with /R.

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