  This study aims to develop second-order relativistic viscous
magnetohydrodynamics (MHD) derived from kinetic theory within an extended
relaxation time approximation (momentum/energy dependent) for the collision
kernel. The investigation involves a detailed examination of shear stress
tensor evolution equations and associated transport coefficients. The Boltzmann
equation is solved using a Chapman-Enskog-like gradient expansion for a
charge-conserved conformal system, incorporating a momentum-dependent
relaxation time. The derived relativistic non-resistive, viscous second-order
MHD equations for the shear stress tensor reveal significant modifications in
the coupling with dissipative charge current and magnetic field due to the
momentum dependence of the relaxation time. By utilizing a power law
parametrization to quantify the momentum dependence of the relaxation time, the
anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes
limit have been investigated. The resulting viscous coefficients are seen to be
sensitive to the momentum dependence of the relaxation time.
