  In this paper we employ non equilibrium thermodynamics of fluxes and forces
to describe magnetization and heat transport. By the theory we are able to
identify the thermodynamic driving force of the magnetization current as the
gradient of the effective field $\nabla H^*$. This definition permits to define
the spin Seebeck coefficient $\epsilon_M$ which relates $\nabla H^*$ and the
temperature gradient $\nabla T$. By applying the theory to the geometry of the
longitudinal spin Seebeck effect we are able to obtain the optimal conditions
for generating large magnetization currents. Furthermore, by using the results
of recent experiments, we obtain an order of magnitude for the value of
$\epsilon_{M} \sim 10^{-2}$ TK$^{-1}$ for yttrium iron garnet
(Y$_3$Fe$_5$O$_{12}$).
