Slowly rotating cosmological viscous fluid Universe

The perturbation by a spherical rotating shell is investigated in a homogeneous and isotropic cosmological model of viscous fluid distribution to first order in angular velocity (r, t) of matter and the metric rotation function (r, t) which is uniform and non-uniform the exact solutions for (r, t) are obtained for all cosmological models. The physical properties of these solutions are discussed.     

Free convection effects on the flow past a moving vertical infinite porous plate

An analysis of the effects of free convection currents on the flow field of an incompressible viscous fluid past an infinite porous plate, which is uniformly accelerated upwards in its own plane, is presented, when the fluid is subjected to a variable suction (or injection) velocity. It is assumed that this normal velocity at the porous plate varies att^–1/2, wheret denotes time. The equations governing the flow are solved numerically, using two-point boundary value shooting techniques.     

Orbits of fluid elements accreting onto a black hole

An exact analysis of the unsteady free and forced convection flow of an incompressible viscous fluid is presented in the presence of thermal diffusion effect. The Laplace transform technique is used to obtain the expressions for velocity, leading edge effects, and skin-friction. During the course of the discussion, the effects ofS (thermal diffusion parameter), Pr (Prandtl number), andt (time parameter) on velocity, leading edge, and skin-friction are extensively discussed.     

Slowly rotating cosmological viscous fluid universe in Brans-Dicke theory

The Brans-Dicke field equations for a viscous distribution representing slowly rotating fluid spheres are investigated. Exact solutions are obtained for differential rotation by imposing physical restrictions on the matter rotation (r,t). The physical properties are discussed fork=±1.     

Cosmological models with viscous fluid and time- dependent equation of state in Wesson’s theory

Assuming the time-dependent equation of state p=λ(t)ρ, five dimensional cosmological models with viscous fluid for an open universe (k=−1) and flat universe (k=0) are presented. Exact solutions in the context of the rest mass varying theory of gravity proposed by Wesson (Astron. Astrophys. 119, 145, 1983) are obtained. It is found that the phenomenon of isotropisation takes place in this theory, i.e. the mass scale factor A(t) which characterizes the rest mass of a typical particle is evolving with cosmic time just as the spatial scale factor R(t). It is further found that rest mass is approximately constant in the present universe.     

Rate of change of vorticity covariance in turbulence

The present paper deals with the turbulent flow of an incompressible viscous fluid which is isotropic and spatially homogeneous. The expression for the rate of change of vorticity covariance is derived. The derived result shows that the defining scalars (r, t) and (r,t) of the rate of change of vorticity covariance solely depend upon the defining scalarQ of the two-point velocity correlation.     

Some magnetized bulk viscous string cosmological models in?General Relativity

Some Bianchi type-I viscous fluid string cosmological models with magnetic field are investigated. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density ξ(t)=ξ ₀ ρ ^m , where ξ ₀ and m are constants. To get a determinate model, we assume conditions ρ=(1+ω)λ, where ρ is rest energy density, ω a positive constant and λ the string tension density and expansion θ is proportional to eigen value σ ₁¹ of the shear tensor σ _j ⁱ . The behaviour of the models from physical and geometrical aspects in presence and absence of magnetic field is discussed.      

Full Causal Bulk Viscous LRS Bianchi I With Time Varying Constants

In this paper we study the evolution of a LRS Bianchi I Universe, filled with a bulk viscous cosmological fluid in the presence of time varying constants “but” taking into account the effects of a c-variable into the curvature tensor. We find that the only physical models are those which “constants” G and c are growing functions on time t, while the cosmological constant Λ is a negative decreasing function. In such solutions the energy density obeys the ultrastiff matter equation of state i.e. ω = 1.     

Scalar field cosmology with polytropic and causal viscous fluids

In this paper, we have considered a model for FRW space-time in the presence of coupled scalar field φ and potential V(φ) with causal viscous fluid and polytropic fluid. We have shown that irrespective of fluid the causality theory provides late time acceleration of the universe. In all cases, the potential always decreases due to evolution of the universe.     

Non-vacuum solutions of Bianchi type VI0 universe in f(R) gravity

In this paper, we solve the field equations in metric f(R) gravity for Bianchi type VI ₀ spacetime and discuss evolution of the expanding universe. We find two types of non-vacuum solutions by taking isotropic and anisotropic fluids as the source of matter and dark energy. The physical behavior of these solutions is analyzed and compared in the future evolution with the help of some physical and geometrical parameters. It is concluded that in the presence of isotropic fluid, the model has singularity at [(t)\tilde]=0\tilde{t}=0 and represents continuously expanding shearing universe currently entering into phantom phase. In anisotropic fluid, the model has no initial singularity and exhibits the uniform accelerating expansion. However, the spacetime does not achieve isotropy as t→∞ in both of these solutions.     

The skin friction in the unsteady free-convection flow past an accelerated plate

In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU ₀ t ⁿ wheret is time,U ₀ a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=², the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania.     

Bianchi Type-III String Cosmological Model with Bulk Viscous Fluid in General Relativity

A Bianchi type-III string cosmological model with bulk viscous fluid for massive string is investigated. To get a determinate solution, a supplementary condition B=C ⁿ, between metric potentials, is used whereB and C are function of time alone. The behaviour of the model in presence and absence of bulk viscosity, is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

An inhomogeneous stiff fluid universe with electromagnetic field in general relativity

An inhomogeneous cylindrically symmetric cosmological model for stiff perfect fluid distribution with electromagnetic field is obtained.F ₁₂ is the non-vanishing component of electromagnetic field tensor. The metric potentials are functions ofx andt both. The behaviour of the electromagnetic field tensor together with geometrical and physical aspects of the model are also examined.     

Bianchi type – IX string cosmological models with bulk viscous fluid in general relativity

Some Bianchi Type IX string cosmological models with bulk viscous fluid for massive string is investigated. To get a determinate solution, a supplementary condition a=b ⁿ, between metric potentials, is used wherea and b are function of time alone. A particular solution for n=0 is also discussed. The behaviour of the model in presence and absence of bulk viscosity, is discussed. The physical and implications of the model is also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bianchi type I two-fluid cosmological models with a variable G and Λ

This paper presents anisotropic, homogeneous two-fluid cosmological models in a Bianchi type I space–time with a variable gravitational constant G and cosmological constant Λ. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the CMB radiation. We find a variety of solutions in which the cosmological parameter varies inversely with time t. We also discuss in detail the behavior of associated fluid parameters and kinematical parameters. This paper pictures cosmic history when the radiation and matter content of the universe are in an interactive phase. Here, Ω is closing to 1 throughout the cosmic evolution.      

Bianchi type-III universe with perfect fluid

We study Bianchi type-III cosmological model filled with perfect fluid in the presence of cosmological constant Λ(t). The Hubble law utilised yields a constant value of deceleration parameter. Physical and Kinematical properties of the model have also studied.      

Inhomogeneous imperfect fluid spherical models without big-bang singularity

So far all known singularity-free cosmological models are cylindrically symmetric. Here we present a new family of spherically symmetric non-singular models filled with imperfect fluid and radial heat flow, and satisfying all the energy conditions. For larget anisotropy in pressure and heat flux tend to vanish leading to a perfect fluid. There is a free function of time in the model, which can be suitably chosen for non-singular behaviour and there exist multiplicity of such choices.     

Bulk viscous fluid hypersurface–homogeneous cosmological models with time varying G and Λ

Hypersurface–homogeneous cosmological models containing a bulk viscous fluid with time varying G and Λ have been presented. We have shown that the field equations are solvable for any arbitrary cosmic scale function. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of the energy density. Exact solutions of Einstein’s field equations are obtained which represent an expanding, shearing and accelerating/decelerating models of the universe. The physical and kinematical behaviours of the models are also discussed.     

Nonlinear spinor field in Bianchi type-I Universe filled with viscous fluid: numerical solutions

We consider a system of nonlinear spinor and a Bianchi type I gravitational fields in presence of viscous fluid. The nonlinear term in the spinor field Lagrangian is chosen to be λ F, with λ being a self-coupling constant and F being a function of the invariants I an J constructed from bilinear spinor forms S and P. Self-consistent solutions to the spinor and BI gravitational field equations are obtained in terms of τ, where τ is the volume scale of BI universe. System of equations for τ and ε, where ε is the energy of the viscous fluid, is deduced. This system is solved numerically for some special cases.