  This work examines the thermodynamics and hydrodynamics behaviors of a
five-dimensional black hole under the influence of an external magnetic field.
The solution is the gravity dual to the Anti-de Sitter/Boundary Conformal Field
Theory correspondence, enabling the study of properties within an anisotropic
fluid framework. Utilizing holographic renormalization, we compute the free
energy and the holographic stress tensor residing on the boundary denoted as
$Q$. Within the fluid/gravity correspondence framework, we have a class of
boundary extensions in $Q$, where the stress-energy tensor describes a
magnetizing conformal fluid. We discuss the characteristics of this special
solution as well as its thermodynamic properties, including the bulk and shear
viscosity, the square of the speed of sound, as well as the anisotropic effects
induced by the magnetic field in the magnetized conformal plasma.
