  This work addresses the conjugate heat transfer of a simplified PTT fluid
flowing past an unbounded sphere in the Stokes regime ($Re = 0.01$). The
problem is numerically solved with the finite-volume method assuming axial
symmetry, absence of natural convection and constant physical properties. The
sphere generates heat at a constant and uniform rate, and the analysis is
conducted for a range of Deborah ($0 \leq De \leq 100$), Prandtl ($10^0 \leq Pr
\leq 10^5$), Brinkman ($0 \leq Br \leq 100$) and conductivity ratios ($0.1 \leq
\kappa \leq 10$), in the presence or absence of thermal contact resistance at
the solid-fluid interface. The drag coefficient shows a monotonic decrease with
$De$, whereas the stresses on the sphere surface and in the wake first increase
and then decrease with $De$. A negative wake was observed for the two solvent
viscosity ratios tested ($\beta$ = 0.1 and 0.5), being more intense for the
more elastic fluid. In the absence of viscous dissipation, the average Nusselt
number starts to decrease with $De$ after an initial increase. Heat transfer
enhancement relative to an equivalent Newtonian fluid was observed for the
whole range of conditions tested. The temperature of the sphere decreases and
becomes more homogeneous when its thermal conductivity increases in relation to
the conductivity of the fluid, although small changes are observed in the
Nusselt number. The thermal contact resistance at the interface increases the
average temperature of the sphere, without affecting significantly the shape of
the temperature profiles inside the sphere. When viscous dissipation is
considered, significant changes are observed in the heat transfer process as
$Br$ increases. Overall, a simplified PTT fluid can enhance heat transfer
compared to a Newtonian fluid, but increasing $De$ does not necessarily improve
heat exchange.
