Chvorinov's rule

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Chvorinov's Rule is a mathematical relationship first expressed by Nicolas Chvorinov in 1940, that relates the solidification time for a simple casting is related to the volume and surface area of the casting. The relationship can be written as:

$t = B\times\left(\frac{V}{A}\right)^n.$

Where t is the solidification time, V is the volume of the casting, A is the surface area of the casting that contacts the mold, n is a constant, and B is the mold constant.

The mold constant B depends on the properties of the metal and mold and their initial temperatures. The constant n is usually 2.

In simple terms the rule establishes that under otherwise identical conditions, the casting with large surface area and small volume will cool more rapidly than a casting with small surface area and large volumes.

For example, two castings are of identical volume and weight:

Casting A has a length of 8 units, a width of 1 unit and height of 1 unit. It's volume is 8 cubic units and it's surface area is 34 square units.

Casting B has a length of 2 units, a width of 2 units and a height of 2 units. It's volume is 8 cubic units and it's surface area is 24 square units.

Alhtough both castings are of identical volume and mass, and might be expected to solidify at the same time interval, Casting A will solidify more quickly than Casting B because Casting A has more surface area to allow heat to transfer from the molten liquid into the mold material.

The constant n is 2 for insulating molds and 1 for conducting molds.^{[citation needed]}