Natural Convection

With no fan or pump, heat transfer is set by buoyancy — and by geometry and orientation far more than intuition suggests. These six tools cover the natural-convection cases that dominate enclosure design, passive cooling and heat-loss estimation.

What's in this suite

• Vertical Plate — Isothermal — free-convection boundary layer on a vertical face, one-sided exchange.
• Horizontal Plate, Heated Up — buoyant fluid escapes freely upward; the stronger of the two horizontal orientations.
• Horizontal Plate, Heated Down — warm fluid trapped under the plate drains only at the edges; leading coefficient 0.27 versus 0.54 for the heated-up case.
• Horizontal Cylinder — Isothermal — Churchill–Chu single-cylinder correlation across the full laminar-to-turbulent range.
• Vertical Channel — Isothermal — symmetric parallel-plate chimney flow; the Bar-Cohen & Rohsenow composite bridges the Elenbaas fully-developed limit and the isolated-plate limit.
• Concentric Cylinders — Raithby–Hollands effective-conductivity method for the annular gap between two cylinders.

Method

Every tool starts from the Rayleigh number, with properties at the film temperature $T_f=(T_s+T_{\infty })/2$:

The characteristic length $L_c$ depends on geometry — plate height for a vertical plate, diameter for a cylinder, area-to-perimeter ratio $A/P$ for horizontal plates, plate spacing for a channel, radial gap for an annulus. A geometry-specific correlation (Churchill–Chu, McAdams, Bar-Cohen & Rohsenow, Raithby–Hollands) then gives $Nu$, and $h=Nu\cdot k/L_c$, $Q=hA\Delta T$.

Assumptions

Quiescent surroundings (no imposed flow), uniform surface temperature, air-like Prandtl-range fluids from the property database. Radiation is not included — at natural-convection coefficients of 2–10 W/m²·K, radiation is often the same order, so add it separately (see the Thermal Radiation suite).