In this paper, we show that the Max Cut problem is NP-complete on interval graphs.

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We examine the pulsating electro-osmotic nanofluid flow phenomena in a microchannel with porous walls. The combined effects of injected nanofluid velocity and ion diffusion coefficients on the electrical potential formation is considered. The novel boundary condition is introduced so as to examine the effects of electro-osmosis and frictional forces on thermal profiles and nanoparticle volume fractions of nanofluid. Being motivated by the experimental works of Kong et al. (Phys. Chem. Chem. Phys. 19 (2017) 7678), this paper aims to extend the study of ion diffusivity in terms of diffusive Reynolds number on nanofluid temperature in the pulsating pressure gradient setting. The semi-analytic differential transform method (DTM) is used to solve the physical equations, represented as coupled ordinary differential equations, with a special emphasis on the convergence of solutions, which is presented in terms of tables and graphs. The study shows that the nanofluid velocity, temperature and mass concentration are strongly influenced by the ion diffusion coefficient and the frequency of pulsating pressure gradient. The diffusive Reynolds number significantly influences the electric potential distribution. The velocity and temperature show an increasing trend in terms of diminishing sensitivity parameter. However, nanoparticle concentration increases with an enhancement of sensitivity parameter. Finally, velocity and temperature increase with a diminution of the Womersley number.

This paper aims to study the electroosmotic nanofluid flow and heat transfer phenomena in a microchannel with porous walls by paying due attention to the interaction of the injected fluid velocity and the net charge density in the base fluid on the development of zeta potential and electroosmotic slip velocity. The novelty of this study is to obtain the integral expression for electroosmotic slip velocity which is found to converge to Smoluchowski velocity when the injected fluid velocity is low and porous permeability of channel wall becomes negligible. Under a weak electric field condition, the enhancement of pressure gradient is found to increase the normalized temperature and decrease the normalized nanoparticle concentration. The bulk nanofluid temperature is found to follow an almost quadratic relationship with applied pressure gradient. Additionally, in the absence of injection velocity, we observed a new expression for Soret number as a ratio of the cross sectional nanoparticle concentration to Joule heating parameter. Finally, a comparative study on the total entropy generation is carried out to minimize the loss of thermal energy due to irreversible physical mechanisms such as heat transfer, viscous dissipation and Joule heating effects that take place during the fluid flow process in a microchannel. It is thereby observed that the total entropy generation follows a quadratic relation with the Joule heating parameter in the absence of both injection and viscous dissipation. The increment in diffusive Reynolds number reduces EDL thickness near the upper channel bed. With an increment in the applied pressure gradient, the normalized temperature increases whereas the normalized nanoparticle concentration reduces.

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