Electromagnetic effects on the stability of anisotropic cylinder

This paper is devoted to analyzing the stability of charged anisotropic cylinder using the radial perturbation scheme. For this purpose, we consider the non-static cylindrically symmetric self-gravitating system and apply both Eulerian as well as Lagrangian approaches to establish a linearized perturbed form of dynamical equations. The conservation of baryon number is used to evaluate perturbed radial pressure in terms of an adiabatic index. A variational principle is developed to find a characteristic frequency which helps to examine the combined effect of charge and anisotropy on the stability of gaseous star. It is found that dynamical instability can be prevented until the radius of cylinder exceeds the limit [Formula: see text] and anisotropy increases the instability up to the limiting value of [Formula: see text]. Finally, we conclude that the system becomes more stable by increasing the definite amount of charge gradually.

Numerical Solution of Unsteady Conduction Heat Transfer in Anisotropic Cylinders

This paper investigates a numerical solution of 2D transient heat conduction in an anisotropic cylinder, subjected to a prescribed temperature over the two end sections and a convective boundary condition over the whole lateral surface. The analysis of this anisotropic heat conduction problem is tedious because the corresponding partial differential equation contains a mixed-derivative. In order to overcome this difficulty, a linear coordinate transformation is used to reduce the anisotropic cylinder heat conduction problem to an equivalent isotropic one, without complicating the boundary conditions but with a more complicated geometry. The alternating-direction implicit finite-difference method (ADI) is used to integrate the isotropic equation combined with boundary conditions. Inverse transformation provides profile temperature in the anisotropic cylinder for full-field configuration. The numerical code is validated by the analytical heat conduction solutions available in the literature such as transient isotropic solution and steady-state orthotropic solution. The aim of this paper is to study the effect of cross-conductivity on the temperature profile inside an axisymmetrical anisotropic cylinder versus time, radial Biot number (Bir), and principal conductivities. The results show that cross-conductivity promotes the effect of Bir according to the principal conductivities. Furthermore, the anisotropy increases the time required to achieve the steady-state heat conduction.