  In this work, we analyze the long time behavior of 2D as well as 3D
convective Brinkman-Forchheimer (CBF) equations and its stochastic counter part
with non-autonomous deterministic forcing term in $\mathbb{R}^d$ $ (d=2, 3)$:
  $$\frac{\partial\boldsymbol{u}}{\partial t}-\mu
\Delta\boldsymbol{u}+(\boldsymbol{u}\cdot\nabla)\boldsymbol{u}+\alpha\boldsymbol{u}+\beta|\boldsymbol{u}|^{r-1}\boldsymbol{u}+\nabla
p=\boldsymbol{f},\quad \nabla\cdot\boldsymbol{u}=0,$$ where $r\geq1$. We prove
the existence of a unique global pullback attractor for non-autonomous CBF
equations, for $d=2$ with $r\geq1$, $d=3$ with $r>3$ and $d=r=3$ with
$2\beta\mu\geq1$. For the same cases, we show the existence of a unique random
pullback attractor for non-autonomous stochastic CBF equations with
multiplicative white noise. Finally, we establish the upper semicontinuity of
the random pullback attractor, that is, the random pullback attractor converges
towards the global pullback attractor when the noise intensity approaches to
zero. Since we do not have compact Sobolev embeddings on unbounded domains, the
pullback asymptotic compactness of the solution is proved by the method of
energy equations given by Ball. For the case of Navier-Stokes equations defined
on $\mathbb{R}^d$, such results are not available and the presence of Darcy
term $\alpha\boldsymbol{u}$ helps us to establish the above mentioned results
for CBF equations.
