Numerical solutions of the partial differential equations for investigating the significance of partial slip due to lateral velocity and viscous dissipation: The case of blood-gold Carreau nanofluid and dusty fluid

The dynamics of blood conveying gold nanoparticles (GNPs) are helpful to the health workers while air conveying dust particles over rockets is helpful to space scientists during the testing phase. However, little is known on the significance of thermal diffusivity in these aforementioned cases. In this report, the partial differential equation suitable to unravel the implication of increasing partial slip and viscous dissipation on the dynamics of the mixture of (i) blood and nano size of GNPs (ii) air and dust particles on an object with an increasing diameter (uhspr) is investigated. The density, zero shear rate viscosity, heat capacity, and thermal conductivity treated in this study vary with volume fraction nanoparticles. In the second case, the interaction between the solid particles and air is incorporated into the momentum equation using the Stokes drag. Transformation and parametrization of the two-dimensional nonlinear partial differential equations were obtained with the aid of suitable similarity variables. Thereafter, the numerical solutions of the corresponding boundary valued problems were obtained using the classical Runge-Kutta integration scheme together with shooting techniques and Matlab bvp5c package. Enhancement in the rate of viscous dissipation is a major factor suitable to increase the velocities of both fluids, boost temperature distribution across both fluids, and local skin friction coefficients. There exist a significant difference between the effect of partial slip on the dynamics of blood-gold nanofluid and dusty fluid.

Automated summary

The dynamics of blood conveying gold nanoparticles are beneficial to health workers, while air conveying dust particles over rockets is helpful to space scientists. The significance of thermal diffusivity in these cases is not well understood.