🔥 Convection Heat Transfer Calculator

Convection Heat Transfer Calculator

Inputs

Fluid Type

Custom Fluid Properties

Flow Velocity

Characteristic Length

Results

Convection Coefficient (h)-BTU/hr·ft²·°F

Reynolds Number (Re)-

Nusselt Number (Nu)-

Flow Regime-

Calculator Description

The convection heat transfer coefficient (h) quantifies heat transfer between a fluid and a solid surface. By Newton's law of cooling, heat flux is q = h × (T_s − T_∞), varying with velocity, fluid properties, and geometry.

What this calculator finds

It calculates Reynolds number (Re), Prandtl number (Pr), selects the appropriate correlation (Nusselt number relationship), and computes the convection heat transfer coefficient h for various geometries such as flat plates, cylinders, and spheres.

Why it matters

Key factor in determining the overall heat transfer coefficient (U) in heat exchanger design
Essential for performance evaluation of cooling systems (engine cooling, electronics cooling, etc.)
Used for predicting heating/cooling time of process equipment

Formula

Newton's Law of Cooling

The fundamental formula for convection, expressing heat flux proportional to the temperature difference between fluid and surface.

q = h\left(T_s - T_{\infty}\right)

q — Heat flux [W/m²]
h — Convection heat transfer coefficient [W/(m²·K)]
T_s — Surface temperature [°C or K]
T_∞ — Fluid temperature (free stream) [°C or K]

Nusselt number correlations

The Nusselt number (Nu) is the dimensionless heat transfer coefficient, expressed as a function of Re and Pr. Select the appropriate correlation based on geometry and flow conditions.

Flat plate turbulent

Nu = 0.037\,Re^{0.8} Pr^{1/3}

Circular tube turbulent

Nu = 0.023\,Re^{0.8} Pr^{n}

Sphere

Nu = 2 + 0.6\,Re^{1/2} Pr^{1/3}

Derivation of convection coefficient h

h = \dfrac{Nu\,k}{L}

Nu — Nusselt number (dimensionless)
k — Thermal conductivity of fluid [W/(m·K)]
L — Characteristic length [m] (tube: diameter, plate: length)

Dimensionless number formulas

Re = \dfrac{\rho v L}{\mu}

Pr = \dfrac{\mu c_p}{k}

Re — Reynolds number: ratio of inertial to viscous forces (Re > 2300: transition, Re > 10⁴: turbulent)
Pr — Prandtl number: ratio of momentum to thermal diffusivity (air ≈ 0.71, water ≈ 7.0)
μ — Dynamic viscosity [Pa·s]
v — Velocity [m/s]

Useful Tips

Practical tips

Typical h ranges: air natural convection 5–25, forced convection 25–250, liquids 100–20,000 W/(m²·K)
Increasing velocity raises h but also increases erosion and noise
Using fins or turbulence promoters can significantly increase h by enhancing turbulence

Limitations & cautions

Correlations are derived for specific geometries/flow ranges; always verify applicability before use
Mixed convection (combined natural and forced) requires separate correlations
Transient convection heat transfer is not covered by this calculator and requires time-dependent analysis