Modeling the dependency of radon concentration levels inside ancient Egyptian tombs on the ambient temperature variations

Radon concentration inside partially closed places like dwellings, caves and tombs, depends on many parameters. Some parameters are known quantitatively as radon exhalation rate for walls, decay constant, surface to volume ratio and outdoor concentration while other parameters as ventilation rate is in common known qualitatively due to useless of traditional methods (tracer gases) in many places as ancient Egyptian tombs. This work introduces a derived mathematical model to evaluate the sensitivity of radon concentration levels inside single sided opening places as ancient Egyptian tombs on the ambient temperature differences. The obtained formula for the natural ventilation rate depends on the indoor and outdoor temperature difference and the geometrical dimensions of the doorway. The effects of in and out flow mixing, air viscosity, streamline contraction, swirling flow and turbulence, were taken into consideration in terms of an empirical correction factor. According UNSCEAR reports, the exhalation rate Φ=Craλrn fρs(1-ε)L; Cra the effective radium content, λrn decay constant, f emanation fraction, ρs soil grain density, ε porosity and L diffusion length, these are approximately static parameters but the variability of ambient temperature introduces a source of energy of fluctuating strength to radon atoms in rocks which controls the flow rate and the ambient content of radon. Therefore, the change of outdoor and indoor temperature difference causes fluctuation of value and direction of volume flow rate in such places consequently causes the daily variation and on average the seasonal variation of radon concentration. Therefore according to the present model, the daily accurate expectation of radon concentrations inside ancient Egyptian tombs, require precise measurements of indoor and outdoor temperatures