Study of Transport of Nanoparticles with K-L Model Through a Stenosed Microvessels

This paper studies a constitutive equation for blood with the transport of nanoparticles in a stenosed microvessel. The flow of blood through a bell-shaped stenosed micro blood vessel has been investigated with an importance of permeable walls that treats blood as non-Newtonian fluid by using K-L model. This model is more appropriate than other non-Newtonian models because K-L model involve three parameters such as plasma viscosity, yield stress and one other chemical variable while casson model involves only one parameter i.e. yield stress. In the present paper, the effective longitudinal diffusion of nanoparticles has been studied in stenosed blood vessel considering the contribution of molecular and convective diffusion based on Taylor\u27s theory. Also we analyze the flow characteristics of blood such as velocity, flow rate and effective diffusion during a nanoparticle assisted drug delivery process through a stenosed permeable microvessel. An explicit expression has been derived for velocity, flow rate and effective diffusion of nanoparticles depending non-linearly on rheological parameter, stenosis height and plasma viscosity. It has been shown that for a given values of rheological parameter, stenosis height and plasma viscosity, fluid velocity is maximum at the central axis and flow rate is minimum at the axis of symmetry. Also it has concluded that the effective diffusion of nanoparticles is maximum at the vessel walls and minimum at the axis of symmetry