[@Biswas2010]. Now, it is easy to obtain the mean-field Casimir force, $f_R^{(\text{mf})}=F_R^{(\text{mf})}-F_\infty^{(\text{mf})}$, from Eqs. -, and it is given by $$\label{eqn:47}
f_R^{(\text{mf})}=-\frac{2\pi\hbar^2N_0LR|a|^2}{3Mb}\left[\frac{1}{4}-\eta(1-\eta)\right].$$ We can rewrite the mean-field force in Eq.  in terms of the dimensionless density ($\tilde{\rho}(R,g\bar{n})=\frac{g\bar{n}2MR^2}{\hbar^2}$) and substituting the original expressions of $a$ ($=\frac{2Mg\bar{n}}{\hbar^2}$), $b$ ($=\frac{2MgN_0}{\hbar^2}$) and the coupling constant g ($=\frac{4\pi\hbar^2a_s}{M}$), as $$\begin{aligned}
\label{eqn:72}
f_R^{(\text{mf})}=-\frac{1}{48}\frac{\hbar^2L}{MR^4}\frac{R}{a_s}\tilde{\rho}^2~\text{sech}^4\bigg(\frac{\sqrt{\frac{4\tilde{\rho}}{3}-\pi^2}}{2\sqrt{2}}\bigg).\end{aligned}$$

Total Casimir force 
--------------------

The total Casimir force is now simply given by the sum of the terms on the RHS of Eq.  and Eq. , as $$\begin{aligned}
\label{eqn:73}
f_R=f_R^{(\text{mf})}+f_R^{(\text{qf})}~.\end{aligned}$$ We emphasis that the mean-field part of the Casimir force is a direct consequence of the inhomogeneity of the condensate, and it dominates over the phononic contribution for low densities. For high densities, the condensate inside the cylinder becomes essentially homogeneous, and the phononic contribution to the Casimir force dominate the mean-field part of the Casimir force for typical values of the parameters. We plot this force in units of $\frac{\hbar^2L}{MR^4}$ in Fig. \[fig2\], for different values of interaction strength - $a_s/R$.

While the Casimir-Polder force between a cigar shaped BEC and a flat surface has been observed to be attractive [@Harber], the Casimir effect for a BEC inside a circular-cylinder although has 