A possible discrepancy found between the determination of mass of the intra
cluster medium (ICM) from gravitational lensing data and that from X-ray ob
servations has been much discussed in recent years. For instance, Miralda-E
scude & Babul found that the mass estimate derived from gravitational lensi
ng can be as much as a factor of 2-2.5 larger than the mass estimate derive
d from analysis of the X-ray observations. Another important discrepancy re
lated to these data is that X-ray imaging, with some spectral resolution, s
uggests that the mass distribution of the gravitating matter, mostly dark m
atter, has a central cusp, or at least that the dark matter is more central
ly condensed than the X-ray-emitting gas, and also with respect to the gala
xy distribution (Eyles et al.), at variance with what is expected from the
most accepted models of formation of large-scale structure. Could these dis
crepancies be a consequence of the standard description of the ICM, in whic
h hydrostatic equilibrium maintained by thermal pressure is assumed? In ana
logy to the interstellar medium of the Galaxy, a non-thermal term of pressu
re is expected, which contains contributions of magnetic fields, turbulence
and cosmic rays. We follow the evolution of the ICM, considering a term of
magnetic pressure, aiming at answering the question of whether or not thes
e discrepancies can be explained via non-thermal terms of pressure. Our res
ults suggest that the magnetic pressure could only affect the dynamics of t
he ICM on scales as small as less than or similar to 1 kpc. Our models are
constrained by the observations of large- and small-scale fields, and we ar
e successful at reproducing available data, for both Faraday rotation limit
s and inverse Compton limits for the magnetic fields. In our calculations,
the radius (from the cluster centre) in which magnetic pressure reaches equ
ipartition is smaller than radii derived in previous works. The crucial dif
ference in our models is our more realistic treatment of the magnetic field
geometry, and the consideration of a sink term in the cooling flow which r
educes the amplification of the field strength during the inflow. In additi
on, the magnetic field calculations are changed after the cooling flow has
been formed.