Some tilted Bianchi type IX dust fluid cosmological model is investigated. To get a deterministic model we assume that

Bianchi type IX cosmological models are interesting because these models allow not only expansion but also rotation and shear, and in general these are anisotropic. Many relativists have taken keen interest in studying Bianchi type IX universe because familiar solutions like Robertson-Walker universe, the de Sitter universe, the Taub-Nut solutions, and so forth are of Bianchi type IX space-times. Bianchi type IX universe includes closed FRW models. The homogeneous and isotropic FRW cosmological models, which are used to describe standard cosmological models, are particular cases of Bianchi type I, V and IX space-times according to the constant curvature of the physical three-space,

There has been a considerable interest in spatially homogeneous and anisotropic cosmological models in which the fluid flow is not normal to the hypersurface of homogeneity. These are called tilted universes. The general dynamics of tilted cosmological models have been studied by King and Ellis [

In general relativity, a dust solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a perfect fluid which has positive mass energy density but vanishing pressure. Concerning the tilted perfect fluid models, Bradley [

Motivated by the situations discussed above, in this paper we shall focus on the problem tilted Bianchi type IX cosmological models with dust fluid, and we investigated dust cosmological model. To get the deterministic model, we have assumed supplementary condition

We consider the homogeneous anisotropic Bianchi type IX metric in the following form:

The energy-momentum tensor for perfect fluid distribution with heat conduction is given by Ellis [

Here

The fluid flow vector

The Einstein’s field equation

Equations from (

Firstly we assume that the model is filled with dust of perfect fluid which leads to

Secondly, we assumed relation between metric potentials as

Equations (

Equation (

The metric (

The density for the model (

Here

The rates of expansion

To find model in terms of

Then metric (

The density for the model (

The tilt angle

The nonvanishing components of shear tensor

The rates of expansion

The model (

In the model (

For particularly at

_{0}electric type cosmological models in general relativity with stiff fluid and heat conduction