Heat Transfer

Convective Heat Transfer Coefficient

Internal pipe flow heat transfer calculator for water and Therminol 66 — computes Reynolds number, Prandtl number, and Nusselt number (Gnielinski correlation) to solve for the convective film coefficient (h) at a given average bulk temperature.

Inputs

Fluid properties at average temperature

Bulk mean of inlet/outlet temperature — properties are evaluated at this single point.
From the flow-through-pipe calculator: V = Q / A.
Only used when Re < 2,300. Ignored once flow is transitional/turbulent.
Enables the Sieder-Tate viscosity-ratio correction (µ/µ_wall)^0.14 — heating vs. cooling is captured automatically through this ratio.
Switches from Petukhov's smooth-tube friction factor to Colebrook–Haaland once Re ≥ 2,300. Ignored in laminar flow.
⚠ Reynolds number is in the transitional band (2,300–3,000). The Gnielinski correlation is formally valid for Re ≥ 3,000; the result below is shown for reference only.
⚠ Average temperature is outside the fitted property range — results are extrapolated and less reliable.

Results

Reynolds number (Re)

—

dimensionless

Prandtl number (Pr)

—

dimensionless

Nusselt number (Nu)

—

dimensionless

Friction factor (f)—

Film coefficient (h)

—

W/(m²·K)

—kW/(m²·K)
—Btu/(hr·ft²·°F)

Gnielinski Correlation & Related Equations

Re = ρ V d / µ     Pr = cₚ µ / k Re < 2,300 (laminar): Nu = 3.66 (const. T_wall) or 4.36 (const. q") Re ≥ 2,300, smooth: f = (0.79·ln(Re) − 1.64)⁻²   [Petukhov] Re ≥ 2,300, rough: 1/√f = −1.8·log₁₀[(ε/D / 3.7)^1.11 + 6.9/Re]   [Colebrook–Haaland] Nu = (f/8)(Re − 1000)Pr  /  [1 + 12.7(f/8)^0.5 (Pr^(2/3) − 1)] Nu_corrected = Nu · (µ / µ_wall)^0.14   [Sieder-Tate viscosity ratio, if T_wall given] h = Nu · k / d
Re = Reynolds number Pr = Prandtl number Nu = Nusselt number f = Darcy friction factor (Petukhov) h = convective film coefficient ρ, µ, k, cₚ = fluid density, dynamic viscosity, thermal conductivity, specific heat at T µ_wall = fluid viscosity evaluated at T_wall ε/D = relative pipe roughness d = pipe inner diameter V = mean flow velocity

Gnielinski correlation valid ~3,000 ≤ Re ≤ 5×10⁶, 0.5 ≤ Pr ≤ 2,000, fully developed flow. Bulk properties (ρ, k, cₚ, Pr) are always evaluated at the average temperature; if a wall temperature is entered, only the viscosity ratio (µ/µ_wall)^0.14 is applied as a Sieder-Tate correction to Nu — this is a mild, empirical correction meant for cases with a substantial wall-to-bulk ΔT, not a full property re-evaluation. Friction factor defaults to Petukhov's smooth-tube correlation; selecting a pipe material switches to the Colebrook–Haaland explicit approximation (typically within ~1.5% of the implicit Colebrook equation, valid for 4,000 ≤ Re ≤ 10⁸ and ε/D ≤ 0.05). Water properties fit (4th–6th order regression, T = 0–300 °C) to Cengel & Ghajar, Heat and Mass Transfer, Table A-3 (saturated liquid). Therminol 66 properties fit (4th–6th order regression, T = −3–340 °C) to the Eastman Therminol 66 heat transfer fluid technical data sheet (SI liquid properties table).