  We study the magnetocaloric effect (MCE) in spin clusters of six spins with
site spins $s=1$, $3/2$ and $2$ for different exchange anisotropies. We also
study MCE in an assembly of spin clusters, on a chain, a 2-D square lattice and
3-D cubic lattice with spin-dipolar interactions using a Monte Carlo method in
spin-1 systems. We compute the magnetic Gr\"uneisen parameter $\Gamma_H$, and
study its dependence on exchange anisotropy and spin-dipolar interaction. With
increase of exchange anisotropy the maxima in $\Gamma_H$, shifts to higher
magnetic fields and becomes a sharp singularity. The first maximum in
$\Gamma_H$ shifts to lower fields as we increase spin-dipolar interaction. The
behaviour of $\Gamma_H$ on applied magnetic field is also reflected in the
magnetic entropy of the systems. The first maximum in $\Gamma_H$ also shifts to
lower magnetic field strength as the magnitude of the site spin increases. We
also show the dependence of $\Gamma_H$ on dimensionality of the lattice for a
fixed lattice constant.
