Convection

Convection is heat transfer between a surface and a moving fluid. Learn Newton's law of cooling, heat-transfer coefficients, natural vs forced convection, Nusselt, Reynolds and Prandtl numbers, and common correlations.

Blowing on hot soup cools it faster; a car radiator uses a fan; a CPU cooler has a fan pushing air through fins. In each case moving fluid carries heat away from a surface — convection.

Everything about convection is packed into one number, the heat-transfer coefficient h, which depends on fluid, velocity and geometry.

An analogy

Standing in wind feels colder than still air at the same temperature (wind chill): moving air sweeps away the warm layer next to your skin, raising h.

Natural and forced convection

Natural (free) convection: fluid moves because warm fluid is lighter and rises — radiators, hot pipes in still air (h ≈ 2–25 W/m²K for air). Forced convection: a fan or pump drives flow (air 25–250, water 100–20 000 W/m²K). Boiling and condensation reach 2 500–100 000.

Dimensionless correlations

h is found from Nu = f(Re, Pr) for forced convection or Nu = f(Ra, Pr) for natural convection, based on experiments. Pick the correlation that matches geometry (pipe, plate, cylinder, tube bank) and regime (laminar/turbulent).

Thermal boundary layer

Heat passes through a thin layer of slow fluid near the wall. Thinner boundary layers (faster flow, turbulence) mean higher h. Pr compares momentum and thermal diffusion: air ≈ 0.7, water ≈ 7, oils ≈ 100–1000.

Enhancement and phase change

Fins, turbulators, dimples, jet impingement and microchannels raise h·A. Boiling curves show nucleate boiling (very high h) up to critical heat flux, beyond which a vapour film forms and surface temperature jumps — a key limit in nuclear reactors and electronics two-phase cooling.

Formulas

• Newton's law of cooling: Q̇ = h A (T_s − T_∞)
• Dittus–Boelter (turbulent pipe): Nu = 0.023 Re^0.8 Pr^n (n = 0.4 heating, 0.3 cooling)
• Laminar pipe (fully developed): Nu = 3.66 (const T) or 4.36 (const q″)
• Natural convection: Nu = C Ra^m, Ra = gβΔT L³/(να)

Worked example: Cooling a hot plate

Given: A = 2 m², T_s = 80 °C, T∞ = 20 °C; h = 25 W/m²·K (light forced air)

Find: Heat loss.

• Q̇ = 25 × 2 × 60 = 3000 W

Answer: 3 kW

Worked example: Water in a tube

Given: Re = 50 000, Pr = 7, D = 25 mm; k = 0.6 W/m·K, being heated

Find: h.

• Nu = 0.023 × 50 000^0.8 × 7^0.4 = 288
• h = 288 × 0.6/0.025 = 6900 W/m²·K

Answer: ≈ 6.9 kW/m²·K

Common mistakes

• Wrong: Using a turbulent correlation for laminar flow. — Right: Check Re first — laminar pipe Nu ≈ 3.66–4.36.
• Wrong: Evaluating fluid properties at the wrong temperature. — Right: Use the film or bulk mean temperature as the correlation specifies.

Applications

• Electronics cooling: Fan-cooled heat sinks, liquid cold plates and immersion cooling for data centres.
• Engines & radiators: Coolant and air-side convection set radiator size.
• HVAC: Coil and duct heat transfer; building surface coefficients in U-value calculations.

Key takeaways

• Q̇ = hA(T_s − T∞).
• Forced ≫ natural; phase change highest.
• Nu = f(Re, Pr) or f(Ra, Pr) correlations.
• Enhancements trade h against pressure drop.

Going further

• Reynolds analogy: Friction and heat transfer are linked: St·Pr^⅔ ≈ f/8 (Chilton–Colburn), so enhancing heat transfer usually costs pressure drop.
• Conjugate heat transfer: CFD couples conduction in solids with convection in fluids — standard in electronics and turbine blade design.
• Nanofluids & two-phase cooling: Heat pipes and vapour chambers move heat with evaporation/condensation at very low ΔT.