RSR
Platinum Member
It's not quite that simple. Convection is a function of the temperature change (delta T), given by q" = h(T_surf - T_air), where h is the convection coefficient, which can easily reach values of 10-100 W/(m^2 K).Of course radiation is more effective than convection so moving air in the amounts that could be practically done would likely just increase the available moisture to the underside of the roof without raising it's temperature significantly. The heat radiated to the underside of the roof from the slab is more effective but it is just passed through and radiated to space. It would be like keeping the metal roof of your car cool while parked in the sun by running the vent fan. The sun is obviously more radiant gain than the radiant loss to space but the same principles apply.
Radiation is a function of temperature to the 4th power given as (under some approximations) q"=eps*sigma* (T_surface^4 - T_surrounding^4), with eps being the emissivity of the surface, which varies between about 0.3 - 0.8 for painted metal. (For highly polished metal it's <0.1, hence my earlier comment).
While this would suggest radiation is more important, sigma is the Stefan- Boltzmann's constant, which is 5.67 x 10^-8 W/(m^2 K^4) (very very small). In practical use, radiation is only more important than convection if there are large temperature differences.
It wouldn't take much of a fan to move enough air across the underside of a roof to offset the radiative heat losses and avoid condensation. The question is how practical it would be to access power, etc. and set it up.