  We study the problem of magnetization and heat currents and their associated
thermodynamic forces in a magnetic system by focusing on the magnetization
transport in ferromagnetic insulators like YIG. The resulting theory is applied
to the longitudinal spin Seebeck and the spin Peltier effects. By focusing on
the specific geometry with one YIG layer and one Pt layer, we obtain the
optimal conditions for generating large magnetization currents into Pt or large
temperature effects in YIG. The theoretical predictions are compared with
experiments from the literature permitting to derive the values of the
thermomagnetic coefficients of YIG: the magnetization diffusion length $l_M
\sim 0.4 \, \mu$m and the absolute thermomagnetic power coefficient $\epsilon_M
\sim 10^{-2}$ TK$^{-1}$.
