We study the effects of heat flows and velocity shear on the parallel firehose instability in weakly collisional plasma flow. For this purpose we apply an anisotropic 16-moments MHD fluid closure model that takes into account the pressure and temperature anisotropy, as well as the effect of anisotropic heat flux. The linear stability analysis of the firehose modes is carried out in the incompressible limit, where the MHD flow is parallel to the background magnetic field, while the velocity is sheared in the direction transverse to the flow direction. It seems that an increase of the velocity shear parameter leads to higher growth rates of the firehose instability. The increase of the instability growth rate is most profound for perturbations with oblique wave-numbers $k_{perp}/k_{parallel} < 1$. The heat flux parameter introduces an asymmetry of the instability growth in the shear plane: perturbations with wave-vectors with a component in the direction of the velocity shear grow significantly stronger as compared to those with components in the opposite direction. We discuss the implications of the presented study on the observable features of the solar wind and possible measurements of local parameters of the solar wind based on the stability constraints set by the firehose instability.
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