The electro-osmotically modulated hemodynamic across an artery with multiple stenosis is mathematically evaluated. The non-Newtonian behaviour of blood flow is tackled by utilizing Casson fluid model for this flow problem. The blood flow is confined in such arteries due to the presence of stenosis and this theoretical analysis provides the electro-osmotic effects for blood flow through such arteries. The mathematical equations that govern this flow problem are converted into their dimensionless form by using appropriate transformations and then exact mathematical computations are performed by utilizing Mathematica software. The range of the considered parameters is given as $0.03<{\delta }_l<0.12,2<m<3.5,0.03<Q<2,0<U_{\mathrm{HS}}<3,2<B_r<2.9,0.01<S<0.025$ . The graphical results involve combine study of symmetric and non-symmetric structure for multiple stenosis. Joule heating effects are also incorporated in energy equation together with viscous effects. Streamlines are plotted for electro-kinetic parameter $m$ and flow rate $Q$ . The trapping declines in size with incrementing $m$ , for symmetric shape of stenosis. But the size of trapping increases for the non-symmetric case.

The irreversibility examination in steady flows of water based silver and copper nanofluids between two rotating disks is presented in this paper. The Darcy–Forchheimer relation is applied to the fluid flow. The two disks are kept at constant temperatures and are rotating with angular velocities. A magnetic field along radial and tangential directions is also applied. Moreover, viscous dissipation, heat generation, and Joule heating influences are taken in the nanofluid flows. The modeled problem is treated with the homotopy analysis method (HAM) and shooting techniques. The deviations in both nanofluids due to embedded factors are shown in graphs. The HAM and shooting techniques are compared and are shown with the help of figures and tables. The leading arguments of the current study are stated in the concluding section.

Peristaltic flow of hybrid nanofluid inside a duct having sinusoidally advancing boundaries and elliptic cross-section is mathematically investigated. The notable irreversibility effects are also examined in this mathematical research by considering a descriptive entropy analysis. In addition, this work provides a comparison analysis for two distinct nanofluid models: a hybrid model (Cu-Ag/water) and a phase flow model (Cu/water). A comprehensive graphical description is also provided to interpret the physical aspects of this mathematical analysis.

The second grade nanofluid flow with Cattaneo-Christov heat flux model by a stretching disk is examined in this paper. The nanofluid flow is characterized with Hall current, Brownian motion and thermophoresis influences. Entropy optimization with nonlinear thermal radiation, Joule heating and heat absorption/generation is also presented. The convergence of an analytical approach (HAM) is shown. Variation in the nanofluid flow profiles (velocities, thermal, concentration, total entropy, Bejan number) via influential parameters and number are also presented. Radial velocity, axial velocity and total entropy are enhanced with the Weissenberg number. Axial velocity, tangential velocity and Bejan number are heightened with the Hall parameter. The total entropy profile is enhanced with the Brinkman number, diffusion parameter, magnetic parameter and temperature difference. The Bejan number profile is heightened with the diffusion parameter and temperature difference. Arithmetical values of physical quantities are illustrated in Tables.