GATE ME 2014 Set 3 — Question 62
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Manufacturing Processes → Casting → Riser & Gating Design
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Question
A cylindrical blind riser with diameter and height , is placed on the top of the mold cavity of a closed type sand mold as shown in the figure. If the riser is of constant volume, then the rate of solidification in the riser is the least when the ratio is
Correct answer
(A) 1:2
Solution
According to Chvorinov's rule, the solidification time is given by , where is the volume and is the surface area. To minimize the rate of solidification (i.e., maximize solidification time) for a constant volume, we must minimize the surface area .For a top blind riser, the surface area through which heat is lost is the top surface and the curved surface (the bottom surface is in contact with the mold cavity and is not a cooling surface):
The volume is Substituting into the area equation:
To find the minimum area, differentiate with respect to and set to zero:
Substitute :
Thus, the ratio is 1:2.
The volume is Substituting into the area equation:
To find the minimum area, differentiate with respect to and set to zero:
Substitute :
Thus, the ratio is 1:2.
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