Influence of Hall and Ion-Slip Currents on Peristaltic Transport of Magneto-Nanofluid in an Asymmetric Channel

Abstract

Of special concern here is to examine the dual impact of Hall and ion-slip currents on a peristaltic transport of water-based nanofluid in an asymmetric channel under the influence of a strong magnetic field. The heat transfer is simulated in the presence of viscous and Ohmic dissipations. Copper-water nanofluid is considered in this simulation. The governing equations are simplified under long wavelength and small Reynolds number approximations. Closed-form solutions are obtained for stream function, axial velocity, temperature, and axial pressure gradient. The graphical analysis examines the impacts of various influential parameters on axial velocity, temperature, axial pressure gradient, pressure rise, frictional forces, heat transfer coefficient, and streamline structure. The temperature function shows a decaying behavior due to the existence of Hall and ion-slip currents. The incorporation of Hall and ion-slip currents leads to lessening the axial pressure gradient. The trapping phenomena are designed and discussed under significant governing parameters. The entrapped bolus is symmetric about the centerline for the symmetric channel whereas it slightly tends to shift in the reverse direction of the wave propagation for the asymmetric channel. This study is envisioned to shed light on conceivable applications in pharmaceutical, physiological, biological, and technological sciences.

Appendix

The following constant expressions are utilized in the results.

$$ \begin{array}{@{}rcl@{}} x_{1}&=&\frac{1}{\left( 1-\phi\right)^{2.5}\left\{(1-\phi)+\phi\left( \frac{\rho_{s}}{\rho_{f}}\right)\right\}},\\ x_{2}&=&\frac{1+\frac{3(\sigma-1)\phi}{(\sigma+2)-\left( \sigma-1\right)\phi}}{(1-\phi)+\phi\left( \frac{\rho_{s}}{\rho_{f}}\right)}, x_{3}=\frac{\frac{k_{s}+2k_{f}-2\phi(k_{f}-k_{s})}{k_{s}+2k_{f}+\phi(k_{f}-k_{s})}}{(1-\phi)+\phi \frac{(\rho c_{p})_{s}}{(\rho c_{p})_{f}}},\\ x_{4}&=&\frac{1+\frac{3(\sigma-1)\phi}{(\sigma+2)-\left( \sigma-1\right)\phi}}{(1-\phi)+\phi \frac{(\rho c_{p})_{s}}{(\rho c_{p})_{f}}}, x_{5}=\frac{1}{\left( 1-\phi\right)^{2.5}\left\{(1-\phi)+\phi \frac{(\rho c_{p})_{s}}{(\rho c_{p})_{f}}\right\}},\!\!\!\\ \alpha_{e}&=&(1+\beta_{i}\beta_{e}), y_{1}=\frac{x_{4}}{x_{3}}, y_{2}=\frac{x_{2}}{x_{1}}, y_{3}=\frac{x_{2} x_{5}}{x_{1} x_{4}},\\ y_{4}&=&\frac{x_{4}}{x_{3}}\sqrt{\frac{x_{1}}{x_{2}}}, y_{5}=\frac{x_{4}}{x_{3}}+\alpha_{e}\frac{x_{2} x_{5}}{x_{1} x_{3}},\\ A_{1}&=&-\frac{(h_{1}+h_{2})\left[F \zeta\cosh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)} +2\sinh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)}\right]} {2\left[(h_{1}-h_{2})\zeta\cosh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)} -2\sinh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)}\right]},\\ A_{2}&=&\frac{F \zeta\cosh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)} +2\sinh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)}} {(h_{1}-h_{2})\zeta\cosh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)} -2\sinh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)}},\\ A_{3}&=&\frac{(h_{1}-h_{2}+F)\sinh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)}} {(h_{1}-h_{2})\zeta\cosh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)} -2\sinh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)}},\\ A_{4}&=&-\frac{(h_{1}-h_{2}+F)\cosh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)}} {(h_{1}-h_{2})\zeta\cosh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)} -2\sinh{\frac{\zeta}{2}\left( h_{1}-h_{2}\right)}},\\ A_{5}&=&\frac{h_{1}[1-G(h_{2})]+h_{2}G(h_{1})}{h_{1}-h_{2}},\\ A_{6}&=&-\frac{1-G(h_{2})+G(h_{1})}{h_{1}-h_{2}},\\ \zeta&=&M\sqrt{\frac{y_{2}\alpha_{e}}{{\alpha_{e}^{2}}+{\beta_{e}^{2}}}} \end{array} $$

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