Calculating special relativistic viscous stress and heat flux tensors

The study of the thermodynamics of relativistic fluid is important in astrophysics and modern physics‎. ‎In this paper‎, ‎we calculate two important parameters of the special relativistic fluids which are the viscous stress and heat flux tensors in the Cartesian coordinate system‎. ‎We calculated the explicit relations of viscous stress tensor with velocity‎, ‎spatial and time derivative of velocity‎. ‎Also‎, ‎the relation of heat flux tensor is derived with velocity‎, ‎temperature and spatial and time derivatives of them‎. ‎The components of viscous stress and heat flux tensors in the other coordinates can be derived by the transformation matrix‎. ‎We use the relativistic method for deriving the non-relativistic viscous stress and heat flux tensors in the limit of the relativistic method‎. ‎So‎, ‎to improve the accuracy of non-relativistic studies of shear rate‎, ‎viscous stress tensor‎, ‎heat flux vector‎, ‎and heat flux tensor‎, ‎especially in the fast fluids‎, ‎the special relativistic corrections can be used‎.