Abstract
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.