  In this study we report numerical results of turbulent transport of heat $Nu$
and angular momentum $\nu_{t}/\nu$ in Taylor-Couette (TC) flows subjected to a
radial temperature gradient. Direct numerical simulations are performed in a TC
cell with a radius ratio $\eta=0.5$ and an aspect ratio $\Gamma=8$ for two
Rayleigh numbers ($Ra=10^5$, $10^6$) and two Prandtl numbers ($Pr=0.7$,
$4.38$), while the Reynolds number $Re$ varies in the range of $0 \le Re \le
15000$. With increasing $Re$, the flows undergo two distinct transitions: the
first transition being from the convection-dominated regime to the transitional
regime, with the large-scale meridional circulation evolving into spiral
vortices; the second transition occurring in the rotation-dominated regime when
Taylor vortices turn from a weakly non-linear state into a turbulent state. In
particular, when the flows are governed by turbulent Taylor vortices, we find
that both transport processes exhibit power-law scaling: $Nu\sim
Re^{0.619\pm0.015}$ for $Pr=4.38$, $Nu\sim Re^{0.590\pm0.025}$ for $Pr=0.7$ and
$\nu_{t}/\nu\sim Re^{0.588\pm0.036}$ for both $Pr$.These scaling exponents
suggest an analogous mechanism for the radial transport of heat and angular
momentum, which is further evidenced by the fact that the ratio of turbulent
viscosity to diffusivity is independent of $Re$. To illustrate the underlying
mechanism of turbulent transport, we extract the coherent structures by
analyzing the spatial distributions of heat and momentum flux densities. Our
results reveal mutual turbulent structures through which both heat and angular
momentum are transported efficiently.
