A novel mathematical modeling with solution for movement of fluid through ciliary caused metachronal waves in a channel.
Wasim Ullah Khan, Ali Imran, Muhammad Asif Zahoor Raja, Muhammad Shoaib, Saeed Ehsan Awan, Khadija Kausar, Yigang He
Author Information
Wasim Ullah Khan: School of Electrical Engineering and Automation, Wuhan University, Wuhan, 430072, China. kwasim814@whu.edu.cn.
Ali Imran: Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock, Pakistan.
Muhammad Asif Zahoor Raja: Future Technology Research center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, Yunlin, 64002, Taiwan, ROC.
Muhammad Shoaib: Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock, Pakistan.
Saeed Ehsan Awan: Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Kamra road, Attock, Pakistan.
Khadija Kausar: Department of Mathematics, COMSATS University Islamabad, Attock Campus, Kamra Road, Attock, Pakistan.
Yigang He: School of Electrical Engineering and Automation, Wuhan University, Wuhan, 430072, China.
In the present research, a novel mathematical model for the motion of cilia using non-linear rheological fluid in a symmetric channel is developed. The strength of analytical perturbation technique is employed for the solution of proposed physical process using mectachoronal rhythm based on Cilia induced flow for pseudo plastic nano fluid model by considering the low Reynolds number and long wave length approximation phenomena. The role of ciliary motion for the fluid transport in various animals is explained. Analytical expressions are gathered for stream function, concentration, temperature profiles, axial velocity, and pressure gradient. Whereas, transverse velocity, pressure rise per wave length, and frictional force on the wall of the tubule are investigated with aid of numerical computations and their outcomes are demonstrated graphically. A comprehensive analysis for comparison of Perturb and numerical solution is done. This analysis validates the analytical solution.
