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In this paper, we calculate the stress-energy tensor for a quantized masslessconformally coupled scalar field in the background of a conformally flatbrane-world geometries, where the scalar field satisfying Robin boundaryconditions on two parallel plates. In the general case of Robin boundaryconditions formula are derived for the vacuum expectation values of theenergy-momentum tensor. Further the surface energy per unit area are obtained .As an application of the general formula we have considered the importantspecial case of the AdS$_{4+1}$ bulk, moreover application to theRandall-Sundrum scenario is discused. In this specific example for a certainchoice of Robin coefficients, one could make the effective cosmologicalconstant vanish.Comment: 10 pages,LaTeX,no figure,references added, typos corrected,clarifying  comments added, has been accepted for the publication in Eur.Phys.J.

Stress-energy tensor for parallel plate on background of conformally flat brane-world geometries and cosmological constant problem