  We have investigated shear viscosity of quark matter in presence of a strong
uniform magnetic field background where Nambu-Jona-Lasinio model has been
considered to describe the magneto-thermodynamical properties of the medium. In
presence of magnetic field, shear viscosity coefficient gets split into
different components because of anisotropy in tangential stress of the fluid.
Four different components can be merged to two components in limit of strong
field, where collisional width of quark becomes much lower than its synchrotron
frequency. A simplified contact diagram of quark-quark interaction can estimate
a small collisional width, where strong field limit expressions are exactly
applicable. Although, for RHIC or LHC matter, one can expect a large thermal
width, for which generalized four components viscosities are necessary. We have
explored these all different possible cases in the thermodynamical framework of
Nambu-Jona-Lasinio model.
