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Unsteady-State Heating and Cooling of Solid Objects

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Engineering Flow and Heat Exchange

Abstract

If a hot object is plunged into cold water, it cools, but not instantaneously. Two factors govern the cooling rate of the object:

$$ \frac{\partial {T}_s}{\partial t}=\alpha \left(\frac{\partial^2{T}_s}{\partial {x}^2}+\frac{\partial^2{T}_s}{\partial {y}^2}+\frac{\partial^2{T}_s}{\partial {z}^2}\right) $$

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References and Notes

  • L.M.K. Boelter, V.H. Cherry, H.A. Johnson, R.C. Martinelli, Heat Transfer Notes (McGraw-Hill, New York, 1956). Gives detailed derivations of the many equations for unsteady state conduction used in this chapter

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  • H.P. Gurney, J. Lurie, Charts for estimating temperature distributions in heating and cooling solid shapes. Ind. Eng. Chem. 15, 1170 (1923)

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Levenspiel, O. (2014). Unsteady-State Heating and Cooling of Solid Objects. In: Engineering Flow and Heat Exchange. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7454-9_11

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