Calculating special relativistic viscous stress and heat flux tensors.

Document Type : Research Paper

Author

Science department,Faculty member, Kosar University of Bojnord, Iran

Abstract

‎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.

Keywords


[1] Duez, M. D., Liu, Y. T., Shapiro, S. L., & Stephens, B. C. 2004, Phys. Rev. D, 69, 104030
[2] Eckart, C. 1940, Phys. Rev., 58, 919
[3] Landau, L. D., & Lifshitz, E. M. 1959, Fluid Mechanics
[4] Mihalas, D., & Mihalas, B. W., 1984, Foundations of Radiation Hydrodynamics, Oxford University Press
[5] Misner, C. W., Thorne, K. S., & Wheeler, J. A. 1973, Gravitation, Freeman, San Fran-cisco
[6] Moeen, M. arXiv:1712.02493 [astro-ph.HE]
[7] Moeen, M. 2017, IJAA, 4, 205
[8] Muronga, A. 2007, Phys. Rev., 76, 014910
[9] Pimentel, O. M., Lora-Clavijo, F. D., & Gonzlez, G. A. 2016, Gen Relativ. Gravit., 48,124
[10] Weinberg, S. 1972, Gravitation and Cosmology, John Wiley & Sons