  The basic entity of nonlinear interaction in Navier-Stokes and the
Magnetohydrodynamic (MHD) equations is a wavenumber triad ({\bf k,p,q})
satisfying ${\bf k+p+q=0}$. The expression for the combined energy transfer
from two of these wavenumbers to the third wavenumber is known. In this paper
we introduce the idea of an effective energy transfer between a pair of modes
by the mediation of the third mode, and find an expression for it. Then we
apply this formalism to compute the energy transfer in the quasi-steady-state
of two-dimensional MHD turbulence with large-scale kinetic forcing. The
computation of energy fluxes and the energy transfer between different
wavenumber shells is done using the data generated by the pseudo-spectral
direct numerical simulation. The picture of energy flux that emerges is quite
complex---there is a forward cascade of magnetic energy, an inverse cascade of
kinetic energy, a flux of energy from the kinetic to the magnetic field, and a
reverse flux which transfers the energy back to the kinetic from the magnetic.
The energy transfer between different wavenumber shells is also complex---local
and nonlocal transfers often possess opposing features, i.e., energy transfer
between some wavenumber shells occurs from kinetic to magnetic, and between
other wavenumber shells this transfer is reversed. The net transfer of energy
is from kinetic to magnetic. The results obtained from the studies of flux and
shell-to-shell energy transfer are consistent with each other.
