Understanding how fluid flow and how solutes disperse in human bodies is crucial in Biomedical Engineering. The study of blood rheology is critical as it may help in detecting, designing a treatment for some blood related diseases and understanding them better. The aims of the present thesis is to study the effect of rheological parameters on blood flow and solute dispersion in a microvessel. Firstly the impact of stress jump condition and heterogeneous reaction on velocity, temperature and concentration during Casson fluid flow through a permeable microvessel was analysed by taking the flow to be steady. We have used a two phase model where the radius of the microvessel is divided into two parts. The flow nature at the clear region is defined by non-Newtonian Casson fluid and the peripheral region is defined by Newtonian fluid. The wall of the microvessel is considered as permeable and the nature defined by Brinkman model. Secondly we analyze steady solute dispersion in Herschel-Bulkely fluid in a permeable microvessel. Due to the aggregation of red blood cells at the axial in the vessel, we have continued the two phase model. Blood in the peripheral region is taken to obey Newtonian fluid character while at the clear region obeys the non-Newtonian Herschel-Bulkely fluid character. Nature of the microvessel’s inner wall is considered to be permeable and characterised by Darcy model. The effect of blood rheological parameter, permeability parameter, pressure constant, particle volume fraction, stress jump constant, slip constant and yield stress on the process are analysed and discussed. Lastly we analyze unsteady dispersion in Herschel-Bulkely fluid through a mild stenosed artery and looking at the pulsatile flow of blood under the influence of body acceleration.

Thesis (MSc Pure and Applied Mathematics)--Botswana International University of Science and Technology, 2020