Gas convection requires a gas heat-transfer path, while thermal radiation also crosses empty space. [1] In a vacuum oven, compare those heat paths for the actual pressure. A wall thermostat cannot establish equal radiative input to every coil: the load geometry determines which surfaces see the heated wall.
Map heated walls, exposed coil faces and obstructed regions. View factor Fij is the fraction of diffuse radiation leaving surface i that reaches surface j. It is dimensionless and depends on geometry, not heater power.
Build the radiation network
| Surface pair | Geometry input | Property input |
|---|---|---|
| Wall → exposed coil | Distance, orientation and unobstructed view | Wall and coil emissivity |
| Wall → shielded insulation | Occlusion by adjacent active part or fixture | Actual visible surface state |
| Coil → coil | Mutual view and load spacing | Temperatures and surface properties |
| Fixture → insulation | Contact and radiation paths | Fixture temperature and finish |
Keep absolute temperatures in the heat calculation
Radiative exchange follows a fourth-power absolute-temperature relation. For ideal black surfaces, the pair contribution is σAF(Ti⁴ − Tj⁴), with σ in W/(m² K⁴), A in m², dimensionless view factor F and temperatures in kelvin to obtain watts. Real gray surfaces require emissivities and the appropriate exchange network. [1]
Using degrees Celsius inside the fourth powers is incorrect. Using one emissivity for bare metal, insulation and altered surface condition may also misrepresent the load.
Drying calculations require the material temperature history. An equal wall setpoint cannot substitute for that input when load geometry changes the material’s heat supply. [2]
Compare exposed and shadowed radiation input
Assumptions: a black 1 m² coil region is initially at 300 K; the heated black wall is at 400 K and all other visible surfaces are at 300 K. Using σ = 5.670374419×10⁻⁸ W/(m² K⁴), wall view factors of 0.8 and 0.2 give 793.9 W and 198.5 W net input. Against an assumed minimum initial radiative input of 600 W, the shadowed position is deficient by 401.5 W. Hold that load arrangement pending a validated thermal history. Real emissivities and all exchange paths must replace these black-surface assumptions. [1]
References
- U.S. Department of Energy, DOE-HDBK-1012/2-92, Thermodynamics, Heat Transfer, and Fluid Flow, Volume 2, 1992.
- Y. Brahami, A. Betie, F. Meghnefi, I. Fofana and Z. Yeo, Development of a Comprehensive Model for Drying Optimization and Moisture Management in Power Transformer Manufacturing, Energies 18, 789, 2025. DOI: 10.3390/en18040789.