The current study deals the theoretical investigation of a viscous fluid due to metachronal waves of cilia through the curved channel with porous medium effects. Due to the complex nature of flow regime, curvilinear coordinates are used to develop constitutive equations for two-dimensional flow. Firstly, the whole system is transformed from fixed frame to wave frame of reference. Secondly, the scaling factors are used to convert the system of EOM ( equation of motion ) into the dimensionless form. To analyse the flow phenomena due to metachronal waves ( a sequence of beating of cilia from row to row ), we employed long wavelength and creeping flow approximation. Finally, the components of fluid velocity are replaced by the derivatives of stream function. Analytical solution of stream function is calculated. The influence of key physical parameters i.e. curvature parameter, porosity parameter and two distinct amplitude ratios of metachronal wave patterns on fluid transport is investigated in detail. Moreover, a dynamic association among the curved and straight channels are highlighted through graphs and discussed in detail.

The overall objective of the current analysis is to examine how electroosmotic flow combined with peristaltic pumping phenomenon could ably contribute to intracellular fluid flow. The biofluid is taken as non-Newtonian Couple stress fluid, while micro-passage is approximated as two-dimensional inclined channel comprehending complex peristaltic walls. Following a traditional approach of peristaltic fluid flow problem balance of mass and momentum is utilized. Beside channel waves, flow is also generated by Lorentz force triggered by electric and magnetic fields. To integrate electric potential term Poisson-Boltzmann and Nernst Planck equation are utilized. Finally, a sixth order BVP in term of stream function is obtained by employing creeping flow, long wavelength and Debye-Hückel assumptions. A numerical solution is calculated and analyzed by plotting fluid velocity and level curves in MATLAB 2021b. It is observed that couple stress fluid flows with greater speed (in central region of the channel) as compared to Newtonian fluid. Moreover, electro-osmotic parameter and Debye-Hückel length are assistive factors to the fluid velocity in the lower half of the passage.