Time-fractional effect on pressure waves propagating through a fluid filled circular long elastic tube

Dedicated to Prof. S. A. El-Wakil for his Diamond Birthday.

PACS: 47.53. + n; 05.30.Pr; 83.50.-v.

Figures & data

Fig. 1 The pressure wave with position and time for $R_0=0.38cm$, $H=0.02cm$, $\mu =0.4$, $r_f=0.75cm$, ${\rho }_0=1.03gm/c{m}^3$, ${\rho }_f=1.05gm/c{m}^3$, $a_1=78.692$, $b_1=296.105$, $b_2=991.496$, ${\lambda }_z={\lambda }_r=1.6$, $v=8cm/s$ and $\alpha =0.8$.

Fig. 2 The pressure wave with position at different values of $\alpha$ for $R_0=0.38cm$, $H=0.02cm$, $\mu =0.4$, $r_f=0.75cm$, ${\rho }_0=1.03gm/c{m}^3$, ${\rho }_f=1.05gm/c{m}^3$, $a_1=78.692$, $b_1=296.105$, $b_2=991.496$, ${\lambda }_z={\lambda }_r=1.6$ and $v=8cm/s$.

Fig. 3 The pressure wave with position at different values of $R_0$ for $H=0.02cm$, $\mu =0.4$, $r_f=0.75cm$, ${\rho }_0=1.03gm/c{m}^3$, ${\rho }_f=1.05gm/c{m}^3$, $a_1=78.692$, $b_1=296.105$, $b_2=991.496$, ${\lambda }_z={\lambda }_r=1.6$, $v=8cm/s$ and $\alpha =0.8$.

Fig. 4 The pressure wave with position at different values of $H$ for $R_0=0.38cm$, $\mu =0.4$, $r_f=0.75cm$, ${\rho }_0=1.03gm/c{m}^3$, ${\rho }_f=1.05gm/c{m}^3$, $a_1=78.692$, $b_1=296.105$, $b_2=991.496$, ${\lambda }_z={\lambda }_r=1.6$, $v=8cm/s$ and $\alpha =0.8$.

Fig. 5 The pressure wave with position at different values of $\mu$ for $R_0=0.38cm$, $H=0.02cm$, $r_f=0.75cm$, ${\rho }_0=1.03gm/c{m}^3$, ${\rho }_f=1.05gm/c{m}^3$, $a_1=78.692$, $b_1=296.105$, $b_2=991.496$, ${\lambda }_z={\lambda }_r=1.6$, $v=8cm/s$ and $\alpha =0.8$.

Fig. 6 The pressure wave with position at different values of $r_f$ for $R_0=0.38cm$, $H=0.02cm$, $\mu =0.4$, ${\rho }_0=1.03gm/c{m}^3$, ${\rho }_f=1.05gm/c{m}^3$, $a_1=78.692$, $b_1=296.105$, $b_2=991.496$, ${\lambda }_z={\lambda }_r=1.6$, $v=8cm/s$ and $\alpha =0.8$.