Stanton Number Calculator

At a glance:The Stanton number (symbol St) is a dimensionless number in convective heat transfer, defined as the ratio of the heat actually received by the fluid to the heat capacity the fluid can carry: St = Nu/(Re·Pr), where St is dimensionless, Nu is the Nusselt number (convective vs conductive heat transfer), Re is the Reynolds number (inertial vs viscous forces) and Pr is the Prandtl number (momentum vs thermal diffusivity). It can also be written St = h/(ρ·v·cp), with h the convective heat transfer coefficient (W·m⁻²·K⁻¹), ρ the fluid density, v the flow velocity and cp the specific heat. The numerator h represents the heat-transfer capacity per unit area per unit temperature difference; the denominator ρ·v·cp is the heat capacity the fluid carries as it flows past. Their ratio measures what fraction of the carryable heat is actually transferred to the fluid. For example, in internal forced convection with Nu=50, Re=10000, Pr=0.7: St = 50/(10000×0.7) = 0.007143. The most important use of the Stanton number is the Reynolds analogy: at Pr≈1, St ≈ f/8 (f the Darcy friction factor), which connects flow resistance to heat transfer; the more accurate Chilton–Colburn analogy is St·Pr^(2/3)=f/8. Applications: (1) dimensionless characterization of convective heat transfer intensity; (2) estimating the heat transfer coefficient from the friction factor via the Reynolds / Chilton–Colburn analogy (and vice versa); (3) the NTU method for heat exchangers and compact heat-exchanger design; (4) boundary-layer heat-transfer analysis.