Dome Geometry + Radiative Coating: Combined Performance Evidence

The Only Direct Study: Glazed Tiles on Domes (Faghih & Bahadori, 2011)

Authors: Ahmadreza K. Faghih (Yazd University) and Mehdi N. Bahadori (Sharif University of Technology). World Renewable Energy Congress 2011.

Modeled the School of Theology dome in Yazd, Iran. Thermal network method with 18 nodes for dome, 12 for flat roof.

Results — Maximum Indoor Air Temperature (August, Yazd)

Configuration	Max Indoor Temp	Time
Flat roof, ordinary material (α=0.8)	37.30°C	16:43
Dome roof, ordinary material (α=0.8)	37.09°C	17:35
Dome roof, glazed tiles (α=0.4)	36.04°C	17:35

The coating multiplied the dome’s advantage by 6×: uncoated dome gains 0.21°C over flat roof, but coated dome gains 1.26°C.

Key Physics Insight

Domes absorb ~20% more beam radiation and ~30% more total radiation than flat roofs of same base area (Tang et al. 2003). BUT despite greater solar absorption, domes perform better due to:

• Higher convection (wind accelerates over curved surfaces)
• Greater radiative emission area

The dome’s larger surface area is a double-edged sword: absorbs MORE solar radiation but provides MORE area for radiative emission and convective cooling. A reflective coating suppresses the absorption penalty while retaining the emission advantage.

Sky View Factor

The study models radiative heat transfer with sky using Stefan-Boltzmann equation with (1+cos β)/2 view factor term accounting for dome curvature. Each point on a curved dome has different sky view factor — most dome surface has excellent sky view, maximizing radiative emission effectiveness.

LBNL Steady-State Framework (Akbari & Konopacki)

The foundational equation for roof surface temperature:

(1-a)I = ε·σ·(T_s⁴ - T_sky⁴) + h_c·(T_s - T_a) + U·(T_s - T_in)

For a dome, the radiative term is modified by view factor at each surface element, and the convective term increases due to wind acceleration over the curve. This framework has never been applied to domed geometries with modern radiative coatings.

Flat Roof Performance Data

• Cooling savings from reflective coatings: 10-50% in real buildings
• National scale: light-colored US roofing could save $0.75B annually, 10 TWh/yr, 7 GW peak demand
• Phoenix residential: 314 kWh annual cooling savings per 100 m² roof area
• Albedo degradation: most occurs in first year (0.15 decrease); washing restores 90-100%

The Untested Combination

No study has combined modern radiative cooling coatings (BaSO4 ultrawhite: 98.1% reflectance, ε=0.95) with geodesic dome geometry. The predicted combined effect:

1. Dome increases radiative emission area by 30% over box equivalent
2. High-emissivity coating (ε=0.95 vs typical 0.85) maximizes radiative channel through enlarged area
3. High-reflectivity suppresses dome’s absorption penalty (20-30% more solar radiation absorbed)
4. Combined effect should be multiplicative: coating per-unit-area benefit × dome’s larger surface area, while addressing dome’s main thermal weakness