Unsteady solute dispersion in two-fluid flowing through narrow tubes: A temperature-dependent viscosity approach

Abstract

The drug delivery or transportation of nutrients to our body involves the solute dispersion process through physiological systems and hence affected by the varying nature of viscosity, heat transfer and other factors. The majority of the previous works involving the solute dispersion in fluid flow through microvessels assumed the constant blood viscosity but in treatments involving temperature variations, the blood viscosity will be affected by the change in temperature and hence it is interesting to analyze its effect on the diffusion process. The motivation of the present work is to analyze the simultaneous impact of temperature-dependent viscosity and heat transfer on the solute dispersion in a two-fluid model of blood flow through narrow tubes by adopting the solution technique proposed by Sankarasubramanian and Gill (1973). Blood is considered as Herschel-Bulkley fluid with temperature-dependent viscosity filled up in a central region of the blood vessel and an outer cell free layer of plasma encircled over the central region consists of Newtonian fluid with constant viscosity. The desired flow related information using heat transfer aspect are obtained analytically for varying viscosity model and these expressions for velocity are then used to compute the diffusion coefficients and mean concentration. The entire dispersion process described by the three main diffusion coefficients known as exchange, convective and dispersion coefficients. An important observation is that the whole diffusion process (asymptotic convection, asymptotic dispersion coefficients and mean concentration) isaffected by the temperature-dependent viscosity with temperature parameters and same observation persist for three different types of fluids like Newtonian fluid (NF), Bingham-plastic fluid (BP), Power-law fluid (PL) which are specific cases of our model. A noteworthy observation is that an enhancement in viscosity index (and hence decay in viscosity of the core region fluid) affects the fluid flow velocity and hence affects the diffusion coefficients. Further, the dominance of thermal buoyancy forces expedite the diffusion process. The outcome of the results reveal the dependence of the solute dispersion on temperature-dependent viscosity and heat transfer. The study may be applicable to drug delivery through bloodstreams in the treatments involving the temperature variations such as chemotherapy.