Dynamics of variable-viscosity nanofluid flow with heat transfer in a flexible vertical tube under propagating waves

Abstract

Background and objectives: The present investigation addresses nanofluid flow and heat transfer in a vertical tube with temperature-dependent viscosity. A Tiwari-Das type formulation is employed for the nanofluid with a viscosity modification. As geometry of the problem is flexible tube so flow equations are modeled considering cylindrical coordinates. Governing partial differential equations are simplified and converted into differential equations using non-dimensionless variables with low Reynolds number (Re ≪ 0 i.e. inertial forces are small as compared to the viscous forces) and long wavelength (δ ≪ 0 i.e. physiologically valid that length of tube is very large as compared to width of the tube) approximations. Methods results conclusions: Mathematica software is employed to evaluate the exact solutions of velocity profile, temperature profile, axial velocity profile, pressure gradient and stream function. The influence of heat source/sink parameter (β), Grashof number (Gr) and the viscosity parameter (α) and nanoparticle volume fraction (ϕ) on velocity, temperature, pressure gradient, pressure rise and wall shear stress distributions is presented graphically. Three different nanofluid suspensions are investigated-Titanium oxide-water, Copper oxide-water and Silver-water. Streamline plots are also computed to illustrate bolus dynamics and trapping phenomena which characterize peristaltic propulsion. The computations show that wall shear stress is maximum for the Silver-water nanofluid case. Furthermore the pressure rise is reduced with increasing Grashof number, heat absorption parameter and viscosity parameter in the augmented pumping region whereas the contrary response is observed in the peristaltic pumping region. Significant modification in the quantity of trapped boluses is found with different nanofluids and the size of the trapped bolus decreased in the Titanium oxide-water nanofluid case with either greater heat source or sink parameter. The study is relevant to drug delivery systems exploiting nano-particles. Keywords: Biophysics, Heat transfer, Flexible tube, Temperature-dependent viscosity, Nanoparticles, Drug delivery