Chvorinov's rule is a physical relationship that relates the

solidification Freezing is a phase transition in which a liquid turns into a solid when its temperature is lowered below its freezing point. For most substances, the melting and freezing points are the same temperature; however, certain substances possess dif ...

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 or ...

to the

volume Volume is a measure of regions in 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) ...

and

surface area The surface area (symbol ''A'') of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the d ...

of the casting. It was first expressed by Czech engineer Nicolas Chvorinov in 1940.

Description

According to the rule, a casting with a larger surface area and smaller volume will cool more quickly than a casting with a smaller surface area and a larger volume under otherwise comparable conditions. The relationship can be mathematically expressed 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 that certain fungus, fungi can form. The dust-like, colored appearance of molds is due to the formation of Spore#Fungi, spores containing Secondary metabolite#Fungal secondary metabolites, fungal ...

, is a constant, and is the mold constant. This relationship can be expressed more simply as: :

t = BM^n

Where the modulus is the ratio of the casting's volume to its surface area: :

M = \frac

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 is a ...

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 heat conduction, conduct heat. It is commonly denoted by k, \lambda, or \kappa and is measured in W·m−1·K−1. Heat transfer occurs at a lower rate in materials of low ...

, heat capacity and wall thickness.

Mold Constant

The S.I. unit for the mold constant is seconds per metre squared (). According to Askeland, the constant is usually 2, however Degarmo claims it is between 1.5 and 2. The mold constant 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 base unit for temperature in the International System of Units (SI). The Kelvin scale is an absolute temperature scale that starts at the lowest possible temperature (absolute zero), taken to be 0 K. By de ...

s), : = initial temperature of the mold (in kelvins), : = superheat (in kelvins), : =

latent heat Latent heat (also known as latent energy or heat of transformation) is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process—usually a first-order phase transition, like melting or condensation. ...

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 Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...

can form.

References

{{reflist Casting (manufacturing) Metallurgy