  Fully resolved simulations are used to quantify the effects of heat transfer
in the presence of buoyancy on the drag of a spatially fixed heated spherical
particle at low Reynolds numbers ($Re$) in the range $10^{-3} \le Re \le 10$ in
a variable property fluid. The amount of heat addition from the sphere
encompasses both, the heating regime where the Boussinesq approximation holds
and the regime where it breaks down. The particle is assumed to have a low Biot
number which means that the particle is uniformly at the same temperature and
has no internal temperature gradients. Scaling buoyancy with inertial and
viscous forces yields two related non-dimensional quantities, called Buoyancy
Induced Viscous Reynolds Number ($Re_{BV}$) and Buoyancy Induced Inertial
Reynolds Number ($Re_{BI}$). For ideal gases, $Re_{BV}$ is analogous to the
Grashof number ($Gr$). No assumptions are made on the magnitude of $Re_{BI}$
(or equivalently $Re_{BV}$). The effects of the orientation of gravity relative
to the free-stream velocity are examined. Large deviations in the value of the
drag coefficient are observed when the Froude number ($Fr$) decreases and/or
the temperature of the sphere increases. Under appropriate constraints on
$Re_{BI}$ and $Re$, the total drag on a heated sphere in a low $Re$ flow in the
presence of buoyancy (mixed convection) is shown to be, within 10% error, the
linear superposition of the drag computed in two canonical setups: one being
the drag on a steadily moving heated sphere in the absence of buoyancy (forced
convection) and the other being natural convection. However, the effect of
temperature variation on the drag of a sphere in both, forced and natural
convection, is significant.
