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| '''Chvorinov's Rule''' is a mathematical relationship first expressed by [[Nicolas Chvorinov]] in 1940,<ref>"Theory of the Solidification of Castings", ''Giesserei'', 1940, Vol 27, p 177-186</ref> that relates the [[solidification]] time for a simple [[casting]] to the [[volume]] 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:<ref name="askeland">Askeland.</ref>
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| :<math>t = B \left ( \frac{V}{A} \right )^n</math>
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| Where ''t'' is the solidification time, ''V'' is the volume of the casting, ''A'' is the surface area of the casting that contacts the [[molding (process)|mold]], ''n'' is a constant, and ''B'' is the mold constant. The mold constant '''B''' depends on the properties of the metal, such as density, [[heat capacity]], [[heat of fusion]] and superheat, and the mold, such as initial temperature, density, [[thermal conductivity]], heat capacity and wall thickness. The metric units of the mold constant B are <math>min/cm^2</math>.<ref>Groover, Mikell P. ''Fundamentals of Modern Manufacturing: Materials, Processes, and Systems''. John Wiley & Sons, Inc. Hoboken, NJ: 2010, p. 223.</ref> According to Askeland, the constant ''n'' is usually 2, however Degarmo claims it is between 1.5 and 2.<ref name="askeland"/><ref name="degarmo"/> The mold constant of Chvorinov's rule, ''B'', can be calculated using the following formula:
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| :<math>B = \left[ \frac{\rho_m L}{ \left( T _m-T_o \right )} \right ]^2 \left[ \frac{\pi }{4 k \rho c} \right] \left[ 1 + \left( \frac{c_m \Delta T_s}{L} \right)^2 \right] \left(\frac{1 min}{60 sec}\right) \left(\frac{1 m^2}{10,000 cm^2}\right)</math>
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| Where
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| :T<sub>m</sub> = melting or freezing temperature of the liquid (in Kelvin) | |
| :T<sub>o</sub> = initial temperature of the mold (in Kelvin)
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| :ΔT<sub>s</sub> = T<sub>pour</sub> − T<sub>m</sub> = superheat (in Kelvin)
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| :L = latent heat of fusion (in [J.Kg<sup>-1</sup>])
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| :k = thermal conductivity of the mold (in [W.m<sup>-1</sup>.K<sup>-1</sup>)])
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| :ρ = density of the mold (in [Kg.m<sup>-3</sup>])
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| :c = specific heat of the mold (in [J.Kg<sup>-1</sup>.K<sup>-1</sup>])
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| :ρ<sub>m</sub> = density of the metal (in [Kg.m<sup>-3</sup>])
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| :c<sub>m</sub> = specific heat of the metal (in [J.Kg<sup>-1</sup>.K<sup>-1</sup>])
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| It is most useful in determining if a [[riser (casting)|riser]] will solidify before the casting, because if the riser solidifies first then it is worthless.<ref name="degarmo">Degarmo, p. 282.</ref>
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| ==References==
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| ===Notes===
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| {{reflist}}
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| ===Bibliography===
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| *Askeland, Donald R., and Phule, Pradeep P. ''Essentials of Materials Science and Engineering''. Thomson, Ontario, Canada: 2004.
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| *{{Citation | last = Degarmo | first = E. Paul | last2 = Black | first2 = J T. | last3 = Kohser | first3 = Ronald A. | title = Materials and Processes in Manufacturing | publisher = Wiley | year = 2003 | edition = 9th | isbn = 0-471-65653-4}}.
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| [[Category:Casting (manufacturing)]]
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| [[Category:Metallurgy]]
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Hello and welcome. My title is Irwin and I completely dig that title. North Dakota is her beginning place but she will have to transfer 1 working day or an additional. Body developing is what my family and I appreciate. Bookkeeping is what I do.
Stop by my site - std testing at home; get redirected here,