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In this paper we have investigated an LRS Bianchi I anisotropic cosmological model of the universe by taking time varying and in the presence of bulk viscous fluid source described by full causal non-equilibrium thermodynamics. We obtain a cosmological constant as a decreasing function of time and for , the value of cosmological ``constant’’ for this model is found to be small and positive which is supported by the results from recent supernovae observations.

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