Convection Coefficient Simulator: Forced & Natural Heat Transfer

simulator intermediate ~12 min
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h = 18.7 W/(m²·K) — forced convection in air

Air at 5 m/s flowing over a 0.3 m plate yields h ≈ 18.7 W/(m²·K) — typical for moderate forced convection cooling in air.

Formula

q = h × (T_surface − T_fluid) (Newton’s law of cooling)
Nu = h × L / k_fluid (Nusselt number definition)
Re = U × L / ν (Reynolds number)

The Boundary Layer Controls Everything

When fluid flows over a heated surface, a thin boundary layer forms where velocity and temperature transition from surface values to free-stream conditions. The thickness of this thermal boundary layer directly determines the heat transfer coefficient: thinner layers mean steeper temperature gradients and faster heat removal. This simulation visualizes the boundary layer and shows how flow velocity reshapes the temperature field in real time.

Dimensionless Numbers Tell the Story

Engineers use the Reynolds number (Re = UL/ν) to characterize flow regime, the Prandtl number (Pr = ν/α) to relate momentum and thermal diffusion, and the Nusselt number (Nu = hL/k) to express the heat transfer enhancement over pure conduction. Empirical correlations like the Dittus-Boelter equation or Churchill-Bernstein correlation connect these numbers, enabling engineers to predict h without solving the full Navier-Stokes equations.

Laminar Versus Turbulent

The transition from laminar to turbulent flow dramatically increases heat transfer. For a flat plate, transition occurs near Re = 500,000. In turbulent flow, eddies mix hot and cold fluid vigorously, thinning the effective boundary layer. The average Nusselt number can increase by a factor of 3–5 when flow transitions to turbulence. This simulator shows the boundary layer transition and its effect on the local heat transfer coefficient.

Practical Cooling Design

Electronics cooling, HVAC system design, and industrial process engineering all depend on accurate convection coefficients. A CPU heat sink uses forced air at 2–5 m/s to achieve h around 30–50 W/(m²·K). Liquid cooling with water can boost h by two orders of magnitude, which is why data centers increasingly adopt liquid cooling loops. This simulation helps engineers explore the parameter space and select appropriate cooling strategies.

FAQ

What is Newton's law of cooling?

Newton's law of cooling states q = h(T_s - T_f), where h is the convective heat transfer coefficient, T_s is the surface temperature, and T_f is the fluid temperature. Despite its simplicity, this law accurately describes convective heat transfer when h is properly determined from correlations or experiments.

What determines the convective heat transfer coefficient?

The coefficient h depends on fluid properties (viscosity, conductivity, Prandtl number), flow conditions (velocity, turbulence level), and geometry (flat plate, cylinder, channel). Dimensionless correlations like Nu = f(Re, Pr) encode these dependencies compactly.

What is the difference between forced and natural convection?

In forced convection, an external source (fan, pump) drives the fluid motion. In natural (free) convection, buoyancy from temperature-induced density differences drives the flow. Forced convection typically yields much higher heat transfer coefficients.

What is a typical value of h?

For natural convection in air: 5-25 W/(m²·K). Forced convection in air: 25-250. Forced convection in water: 100-20,000. Boiling water: 2,500-100,000. The wide range reflects the enormous influence of fluid properties and flow regime.

Sources

Embed

<iframe src="https://homo-deus.com/lab/heat-transfer/convection-coefficient/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub