Classical thermodynamics, heat transfer Definition

Stefan number

Builds on Dimensionless numbers in fluid mechanics Heat capacity Latent heat

Definition

Let a material melt or freeze at temperature $T_m$ , with latent heat $L > 0$ per unit mass. Let $c_p > 0$ be the specific heat capacity of the relevant phase. Let $\Delta T > 0$ be a characteristic temperature difference, such as $\abs{T_b - T_m}$ for a boundary temperature $T_b$ . The Stefan number is the dimensionless number $\mathrm{Ste} = \frac{c_p \, \Delta T}{L}.$

Remarks

Example: for liquid water, $c_p \approx 4.2$ kilojoules per kilogram per kelvin and $L \approx 334$ kilojoules per kilogram. A boundary held $20$ kelvin above $0$ degrees Celsius gives $\mathrm{Ste} \approx 4.2 \cdot 20 / 334 \approx 0.25$ .

Non-example: the ratio $L / (c_p \, \Delta T)$ is the reciprocal of the Stefan number, not the Stefan number; some authors use it, so the convention should be checked.

With the latent heat per unit volume $\rho L$ , the same number reads $\rho c_p \Delta T / (\rho L)$ .

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Dimensionless numbers in fluid mechanics concept
Heat capacity concept
Latent heat concept
Stefan number definition

Tag	`KMEGHZDC3B`
URI	`m2://KMEGHZDC3B`
Kind	definition
Writing	W0 stub
MSC	80A22, 80A19
Defines	Stefan number
Uses	Dimensionless numbers in fluid mechanics, Heat capacity, Latent heat
Changed	3 November 2026

Stefan number

Definition

Remarks

Reading path

Further reading

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