The Graetz number, Gz, is a nondimensional group applicable mainly to transient heat conduction in laminar pipe flow. It is defined as

where U is the velocity of the fluid, D the diameter of the pipe, κ the fluid thermal diffusivity (λ/ρc_{p}) and x the axial distance along the pipe.

Gz represents the ratio of the time taken by heat to diffuse radially into the fluid by conduction (sometimes called the "relaxation time"), D^{2}/κ, to the time taken for the fluid to reach distance x, x/U, i.e.,

For small values of Gz (Gz < 20) radial temperature profiles are fully developed, but for larger values thermal boundary layer development has to be taken into account.

Note that

and Gz^{−1} is often used as a nondimensional form of axial distance in the representation of entrance effects on laminar flow heat transfer.

Graetz number is the reciprocal of Fourier number with time replaced by x/U, and many of the equations for transient heat conduction in laminar pipe flow are analogous to those of transient heat conduction in cylinders.

#### REFERENCES

Hewitt, G. F, Shires, G. L. and Bott, T. R. (1994) *Process Heat Transfer*, CRC Press, Boca Raton, FL, USA.