Thermal analysis of magnetized ZnO-blood nanofluid anticipating couple stresses in vertical microchannel using differential transform method

Abstract

The widespread usage of nanoparticles in biomedicine, tissue engineering, and blood coagulation has made them indispensable in the field of blood flow. The stability and lack of toxicity of gold and zinc nanoparticles to humans have been established. The objective of this research is to derive a semi-analytical solution for the steady flow of couple-stress nanofluid within a vertical porous microchannel, using $\mathrm{ZnO}$ nanoparticles dispersed in blood. The study examines the impact of a linear radiative heat flux and magnetic field, with a focus on entropy generation. It also investigates the impact of buoyancy forces, an exponential heat source, and variations in the volume fraction and shape factor of the nanoparticles. Differential transform method is used to compute the semi-analytical solution for modelled equations while, the Runge-Kutta-Fehlberg method, combined with the shooting technique, yields the numerical solution. The results show a good level of accuracy on comparing the results by numerical method and Differential Transform Method. Outcome of the analysis shows that as radiation parameter rises, entropy production decreases near the channel walls and increases at the core of the microchannel. At the same time, the Bejan number shows the contrary behaviour, and the thermal profile decreases. Moreover, spherical-shaped nanoparticles exhibit the higher temperature and velocity, while lamina-shaped nanoparticles show the lowest values. This confirms that the shape of the nanoparticles plays a crucial role in determining the fluid’s temperature and flow behaviour.