The same stack-effect formula, applied to a passively ventilated office building in the spirit of the Eastgate Centre in Harare. The 3D view moves to the building while this tab is open. It shares the clock and the outside weather with the mound.
Live
One day, 5-day steady cycle
Air changes per hour against stack height for three indoor–outdoor temperature differences; the dot is the building as set now.
Educational one-zone model with a lumped thermal mass. Published savings for the real Eastgate Centre vary widely between sources (from roughly a third to nearly 90 % lower energy than comparable buildings) and have not all been independently verified; this page does not reproduce or endorse any of them.
Temperatures over the last day: outside air, the outer wall, the fungus combs, the chimney air and the surface flutes. The comb temperature stays within a few degrees although the outside swings by tens of degrees.
Thermosiphon flow in the chimney–flute loop. Above zero the air rises in the chimney and sinks in the flutes; below zero it reverses. It switches sign when the lagging wall warms or cools the flutes relative to the chimney.
Temperature through the solid mud wall (outer surface at the left) on the sunny and the shaded sides. Dashed: the daily-wave envelope mean ± A·e−z/δ with δ = √(2α/ω).
The science
What is being modelled. African fungus-growing termites (Macrotermes) keep a fungus garden near 30 °C and 90 %+ humidity inside a mud mound while the air outside swings by tens of degrees between day and night. The colony and its fungus consume O₂ and release CO₂ and heat, so the mound must also breathe. The mound here is a stylised cross-section with a central chimney, surface flutes, a nest of fungus-comb galleries, a cellar and a royal cell. Sizes, flows and metabolic rates are order-of-magnitude values from the literature, not measurements of one mound.
The mechanism is debated. Early work described a chimney-and-flute thermosiphon (Lüscher 1961; Turner 2001 argued the mound works more like a lung, with wind and daily temperature changes pumping gas through its thin porous skin). King, Ocko and Mahadevan (2015) showed that the daily temperature cycle alone can drive a reversing flow in surface conduits, and Ocko et al. (2017) tested solar power for ventilation in field mounds. CT-scan work (Singh et al. 2019) describes the tunnel network as a combined ventilation and drainage system. This page lets you switch each mechanism on and off; it does not claim to settle the question.
1. Stack effect (buoyancy-driven flow)
Warm air is lighter, so a column of height H at temperature Ti next to one at To gives a pressure difference at its top:
Δp = (ρ_o − ρ_i) g H ≈ ρ g H ΔT / T (T in kelvin)
Q = C_d A √(2 g H |ΔT| / T) (Bernoulli with a loss coefficient)
momentum check: ρ L dv/dt = Δp − ½ ρ K v|v|, C_d = 1/√K
In the loop the temperature difference is chimney air minus flute air, H is the length of the flutes, and C_d ≈ 0.05 stands for the long, narrow, bendy passages. The pressure difference is only about a pascal, so velocities are centimetres per second: the flow is slow, which is why the arrows on screen are exaggerated (×30).
Through the porous wall, flow is laminar (Darcy) instead: Q = (κ A / μ L) Δp, with permeability κ from a Kozeny–Carman scaling in the porosity. A combined law a·Q + b·Q|Q| = Δp covers both.
2. Heat conduction and the daily thermal wave
ρ c ∂T/∂t = ∇·(k ∇T) + q (solved in 2-D, finite volumes, implicit)
−k ∂T/∂n = h (T − T_sol-air) (outer faces)
T_sol-air = T_out + α I(t) cosφ / h − sky cooling at night
A surface that oscillates as A cos ωt (ω = 2π/day) sends a damped, delayed wave into a wall of diffusivity α = k/ρc:
T(z,t) = A e^(−z/δ) cos(ωt − z/δ), δ = √(2α/ω)
For mud with 35 % porosity δ is about 11 cm: a few decimetres of wall remove most of the daily swing and delay the rest by about 6 hours per 11 cm of depth. Hot, dry savanna gives outside swings up to about 40 K; the fungus garden sees only a small fraction. Air in the channels has a tiny heat capacity, so its conductivity is raised by the measured circulation, keff = kair + ρ cp u ℓ, a mixing-length stand-in for advection. Metabolic heat (default 45 W) is spread over the comb cells.
The solver is checked against the exact decay of a Fourier mode, the penetration depth and the energy balance of a closed box (see the Checks tab). The cross-section is planar, whereas a real mound is closer to a cone; the slice is stretched to the height and base-radius sliders.
3. Gas exchange and the CO₂ budget
D_eff = D₀ φ^1.5, D₀(CO₂ in air) = 1.6×10⁻⁵ m²/s (Fick, porous wall)
Q_D = D_eff A_skin / L (equivalent exchange volume flow)
t ~ L² / D_eff (diffusion time through a wall of thickness L)
Q_W = ε · 0.8 · (κ A / μ L) · ρ C u² I (wind gusts: pulsating Darcy flow, efficiency ε)
Q_vent = 0.6 A_vent √(2 g H ΔT / T) (pin-holes near the top)
V dc/dt = S − Q_ex (c − c_out), c_ss = c_out + S / Q_ex
S is the CO₂ production, taken from the colony power P with a respiratory quotient of about 1 (21 kJ per litre of O₂ ⇒ S = P / 2.1×10⁷ m³/s). The wall exchange is placed in series with the internal transport |Qloop| + a small baseline mixing flow, so the exchange is weakest when the circulation reverses (CO₂ creeps up at those moments). The wind-pumping efficiency ε is an adjustable guess, not a measured number. The page also shows the vent area that would keep the daily mean below your CO₂ limit. The stress limit is illustrative; fungus and termites tolerate a few percent CO₂ in nature.
4. Biomimicry: a passively ventilated building
A_eff = A_in A_out / √(A_in² + A_out²), Q = C_d A_eff √(2 g H ΔT / T)
ACH = 3600 Q / V
C_b dT_b/dt = gains + UA (T_out − T_b) − ρ c_p Q (T_b − T_out) − P_chiller
The Eastgate Centre in Harare (architect Mick Pearce with Arup, opened 1996) is the famous example of a building that borrows the idea: cool night air is drawn in at the bottom, rises through atria and brick chimneys, and cools the concrete mass, which in turn smooths the day. Here a one-zone building with a thermal mass is run for five identical days; the chiller switches on only when the mass would exceed 26 °C and uses a COP of 3.5. The ratio of chiller electricity with and without the natural ventilation is the "saving". Neither humidity, wind, fan energy of the reference building, occupancy patterns nor the detailed floor-by-floor stack are modelled.
5. Numbers, simplifications, sources
- Termites are drawn about 10× life size (workers about 6–8 mm, soldiers a little larger) so you can see them; they are an animation and do not feed back into the model. The queen in the royal cell is drawn schematically; all biological numbers are approximate.
- One lumped air node for the CO₂ (no gas concentration field); a planar 2-D slice for heat; quasi-steady loop flow; fixed 6 flutes in the 3D model; no moisture, no digging, no fungus kinetics.
- Sources (read these for the real picture): Turner (2001) Physiol. Biochem. Zool. 74; Korb (2003) Naturwissenschaften 90; Turner & Soar (2008) living-building conference paper; King, Ocko & Mahadevan (2015) PNAS 112; Ocko et al. (2017) J. Exp. Biol. 220; Singh et al. (2019) Science Advances 5.
- Not affiliated with any building, architect or engineering firm named here. The building is generic.