Chvorinov's rule is an applied physics relationship first expressed by Czech engineer Nicolas Chvorinov in 1940, that relates the

solidification Freezing is a phase transition where a liquid turns into a solid when its temperature is lowered below its freezing point. In accordance with the internationally established definition, freezing means the solidification phase change of a liquid ...

time for a simple

casting Casting is a manufacturing process in which a liquid material is usually poured into a mold, which contains a hollow cavity of the desired shape, and then allowed to solidify. The solidified part is also known as a ''casting'', which is ejected ...

to the

volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Th ...

and surface area of the casting. 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 a large volume. The relationship can be written as: :

t = B \left( \frac \right)^n,

where is the solidification time, is the volume of the casting, is the surface area of the casting that contacts the

mold A mold () or mould () is one of the structures certain fungi can form. The dust-like, colored appearance of molds is due to the formation of spores containing fungal secondary metabolites. The spores are the dispersal units of the fungi. Not ...

, is a constant, and is the mold constant. The ratio of the casting's volume to its surface area is the modulus : :

M = \left( \frac \right).

The mold constant depends on the properties of the metal, such as density,

heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity ...

heat of fusion In thermodynamics, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a s ...

and superheat, and the mold, such as initial temperature, density,

thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...

, heat capacity and wall thickness. The S.I. units of the mold constant are . According to Askeland, the constant is usually 2, however Degarmo claims it is between 1.5 and 2. The mold constant of Chvorinov's rule, , can be calculated using the following formula: :

B = \left \frac \right 2 \left \frac \right \left 1 + \left(\frac \right)^2 \right

where : = melting or freezing temperature of the liquid (in

kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and phy ...

s), : = initial temperature of the mold (in kelvins), : = superheat (in kelvins), : = latent heat of fusion (in ), : = thermal conductivity of the mold (in ), : = density of the mold (in ), : = specific heat of the mold (in ), : = density of the metal (in ), : = specific heat of the metal (in ). It is most useful in determining if a riser will solidify before the casting, because if the riser solidifies first then defects like shrinkage or porosity can form.

References

{{reflist Casting (manufacturing) Metallurgy