Computational fluid dynamic simulation of two-fluid non-Newtonian nanohemodynamics through a diseased artery with a stenosis and aneurysm

Abstract

This article presents a two-dimensional theoretical study of hemodynamics through a diseased permeable artery with a mild stenosis and an aneurysm present. The effect of metallic nanoparticles on the blood flow is considered, motivated by drug delivery (pharmacology) applications. Two different models are adopted to mimic non-Newtonian characteristics of the blood flow; the Casson (viscoplastic) fluid model is deployed in the core region and the Sisko (viscoelastic) fluid model employed in the peripheral (porous) region. The revised Buongiorno two-component nanofluid model is utilized for nanoscale effects. The blood is considered to contain a homogenous suspension of nanoparticles. The governing equations are derived by extending the Navier-Stokes equations with linear Boussinesq approximation (which simulates both heat and mass transfer). Natural (free) double-diffusive convection is considered to simulate the dual influence of thermal and solutal buoyancy forces. The conservation equations are normalised by employing appropriate non-dimensional variables. The transformed equations are solved numerically using the finite element method with the variational formulation scheme available in the FreeFEM++ code. A comprehensive mesh-independence study is included. The effect of selected parameters (thermophoresis, Brownian motion, Grashof number, thermo-solutal buoyancy ratio, Sisko parameter ratio, and permeability parameter) on velocity, temperature, nanoparticle concentration, and hemodynamic pressure have been calculated for two clinically important cases of arteries with stenosis and an aneurysm. Skin-friction coefficient, Nusselt number, volumetric flow rate, and resistance impedance of blood flow are also computed. Colour contours and graphs are employed to visualize the simulated blood flow characteristics. It is observed that by increasing the thermal buoyancy parameter, i.e. Grashof number (Gr), the nanoparticle concentration and temperature decrease, whereas velocity increases with an increment in the Brownian motion parameter (Nb). Furthermore, velocity decreases in the peripheral porous region with elevation in the Sisko material ratio (m) and permeability parameter (k’). The simulations are relevant to transport phenomena in pharmacology and nano-drug targeted delivery in haematology.

Keywords:

• Arterial stenosis
• aneurysm
• Casson fluid model
• Sisko fluid model
• nano-drugs
• porous walls
• thermophoresis
• finite-element method
• FreeFEM++

Acknowledgements

The authors are grateful to the Science and Engineering Research Board (SERB), Department of Science and Technology (DST), Govt of India for undertaking the research work under the research project File Number: ECR/2017/001053 dated on 12/03/2018.

Disclosure statement

No potential conflict of interest was reported by the author(s).