made up of a flexible wall. However, such forces are usually not strong enough to deform cylindrical wall of a metallic waveguide.

Conclusion {#Sec4}
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In this article, we have presented theoretical calculation on quantum Casimir force (and pressure) exerted by a self-interacting Bose-Einstein condensate confined to a circular-cylinder by applying zeta regularization technique introduce be Gosdzinsky and Romeo [@Gosdzinsky] for the leading order in condensate density, and dimensional regularization cum Chowla-Selberg lattice summation technique [@Milton2010] for the higher orders in condensate density. In this regard, we have approximately computed the (grandcanonical) self-energy of the confined condensate up-to the quadratic order in fluctuations. Both the inhomogeneity of the order parameter of the confined BEC and the vacuum fluctuations of the phonon field in the BEC contribute to the Casimir force.

Our analytic results, for the Casimir force, are valid only for the repulsive interaction ($a_s>0$). For $a_s<0$, the condensate becomes unstable beyond a critical number of particles [@Biswas2009]. The Casimir force exerted by the condensate would be minimum for $\tilde{\rho} = 3 \pi^2/4$. For high density, the Bose condensate inside the cylinder essentially becomes homogeneous, and the quantum fluctuation of the phonon field become important. For noninteracting case, there will 