Finite difference simulations for non-isothermal hydromagnetic peristaltic flow of a bio-fluid in a curved channel: Applications to physiological systems

Abstract

Owing to the fundamental significances of peristalsis phenomenon in various biological systems like circulation of blood in vessels, lungs devices, pumping of blood in heart and movement of chyme in the gastrointestinal tract, variety of research by scientist on this topic has been presented in recently years. The peristaltic pumping plays a novel role in various industrial processes like transfer of sanitary materials, the pumping equipment design of roller pumps and many more. The present article investigates numerically the theoretical aspects of heat and mass transportation in peristaltic pattern of Carreau fluid through a curved channel. The computations for axial velocity, pressure rise, temperature field, mass concentration, and stream function are carried out under low Reynolds number and long wavelength approximation in the wave frame of reference by utilizing appropriate numerical implicit finite difference technique (FDM). The implementation of numerical procedure and graphical representation of the computations are accomplished using MATLAB language. The impacts of rheological parameters of Carreau fluid, Brinkmann number, curvature parameter and Hartmann number are shown and discussed briefly. The study shows that for shear thinning of bio-materials, the velocity exhibits the boundary layer character near the boundary walls for greater Hartmann number. The interesting observations based on numerical simulations are graphically elaborated. The results show that the curvature of channel with larger value allows more heat transportation within the flow domain. On the contrary, inside the channel wall, the solutal mass concentration follows an increasing trend with decreasing the channel curvature. The temperature profile enhanced with increment of power-law index and curvature parameter. Moreover, the concentration profile increases with Brinkmann number and Hartmann number.