  As shown in earlier work (Ahlers et al., J. Fluid Mech. 569, p.409 (2006)),
non-Oberbeck Boussinesq (NOB) corrections to the center temperature in
turbulent Rayleigh-Benard convection in water and also in glycerol are governed
by the temperature dependences of the kinematic viscosity and the thermal
diffusion coefficient. If the working fluid is ethane close to the critical
point the origin of non-Oberbeck-Boussinesq corrections is very different, as
will be shown in the present paper. Namely, the main origin of NOB corrections
then lies in the strong temperature dependence of the isobaric thermal
expansion coefficient \beta(T). More precisely, it is the nonlinear
T-dependence of the density \rho(T) in the buoyancy force which causes another
type of NOB effect. We demonstrate that through a combination of experimental,
numerical, and theoretical work, the latter in the framework of the extended
Prandtl-Blasius boundary layer theory developed in Ahlers et al., J. Fluid
Mech. 569, p.409 (2006). The latter comes to its limits, if the temperature
dependence of the thermal expension coefficient \beta(T) is significant.
