Convection Coefficient Calculator
Calculate the convective heat transfer coefficient α for forced pipe flow from the fluid properties, the velocity and the inner diameter. The tool determines the Reynolds, Prandtl and Nusselt number, selects the correlation (Dittus-Boelter as default, Gnielinski as accuracy option, laminar Nu = 3.66) and returns α as well as the heat flow Q = α·A·ΔT, live with every input.
Calculation
Model: forced, fully developed pipe flow of a single-phase fluid. Empirical Nu correlations (Dittus-Boelter, Gnielinski) with typical scatter of a few percent; use fluid properties at the mean fluid temperature. The tool provides the fluid-side heat transfer, not a full heat transmission (k-value) and no heat exchanger design.
Results
Calculating …
Calculation in your browser, inputs go to our server only when you export or save.
Formulas and fundamentals
Heat transfer coefficient and Nusselt number
The heat transfer between a wall and a flowing fluid is described by the heat transfer coefficient α; the heat flow is:
with the contact area A and the temperature difference ΔT between wall and fluid. α is not a material constant but depends on the flow and geometry. In dimensionless form α is expressed through the Nusselt number:
where λ is the thermal conductivity of the fluid and d the characteristic length (for pipe flow the inner diameter).
Reynolds and Prandtl number, Dittus-Boelter
The Nusselt number follows from two dimensionless groups: the Reynolds number, which describes the ratio of inertial to viscous forces and thus the flow regime, and the Prandtl number, a pure fluid property:
For turbulent pipe flow the widely used standard correlation is Dittus-Boelter:
with n = 0.4 when heating and n = 0.3 when cooling the fluid. It applies approximately for Re > 10⁴, 0.6 < Pr < 160 and L/d > 10.
Gnielinski correlation and laminar flow
For higher accuracy the Gnielinski correlation is available, which includes the friction factor and is more reliable in the transitional and lower turbulent range:
In laminar, fully developed pipe flow (Re < 2300) the Nusselt number at constant wall temperature is constant and thus independent of Re and Pr:
From the chosen Nu the heat transfer coefficient follows directly as:
Worked example
Air at about 1 bar flows at c = 20 m/s through a pipe with d = 25 mm. With ν = 18.25·10⁻⁶ m²/s the Reynolds number is Re = c·d/ν = 20·0.025/18.25·10⁻⁶ = 27,397 - the flow is clearly turbulent. The Prandtl number of air is Pr ≈ 0.71.
With λ = 0.0279 W/(m·K) the Gnielinski correlation gives a Nusselt number of order Nu ≈ 64 and thus α = Nu·λ/d ≈ 71 W/(m²·K). This lies in the typical band of forced convection of gases (roughly 10 to 300 W/(m²·K)).
Dittus-Boelter yields a slightly higher Nu for the same case; the empirical correlations scatter by a few percent depending on the source. For a reliable design the fluid properties should be taken at the mean fluid temperature and manufacturer data observed.
Frequently asked questions
What does the heat transfer coefficient α mean?
α (in W/(m²·K)) describes how much heat is transferred per area and kelvin of temperature difference between wall and fluid: Q = α·A·ΔT. Unlike the thermal conductivity λ, α is not a material constant but depends on the flow, geometry and fluid properties.
When to use Dittus-Boelter, when Gnielinski?
Dittus-Boelter is the widely used, robust standard correlation for smooth pipes at Re > 10⁴. Gnielinski is more accurate and also usable in the lower turbulent and transitional range. Both agree to within a few percent at moderate Reynolds numbers; the tool shows both values for comparison.
Why is Nu constant 3.66 in laminar flow?
For fully developed laminar pipe flow at constant wall temperature a fixed temperature profile establishes, so that Nu = α·d/λ = 3.66 becomes independent of Re and Pr. α then decreases with increasing diameter, not with velocity.
What order of magnitude does α have?
Rough guide values: free convection of gases 3 to 20, forced convection of gases 10 to 300, water (forced) 500 to 10,000 and condensing steam 5,000 to 30,000 W/(m²·K). The tool places the result into these bands.
Does the tool replace a full heat exchanger design?
No. It provides the fluid-side heat transfer coefficient of forced pipe flow. For the overall heat transmission both fluid sides, the wall conduction and possibly fins and fouling must be considered via the k-value.
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