Nanofluids are extremely useful to investigators due to their greater heat transfer rates, which have significant applications in multiple industries. The primary objective of this article is to look into the effect of viscous dissipation in Sisko nano liquid flow with gold $\left(\mathrm{Au}\right)$ nanoparticles on a porous stenosis artery. Heat transfer properties were explored. Blood was utilized as a base fluid for nanoparticles. To renovate the governing nonlinear PDEs into nonlinear ODEs, appropriate transformations were used. The bvp4c-based shooting method, via MATLAB, was used to determine the numerical results of the nonlinear ODEs. Furthermore, flow forecasts for each physical quantity were explored. To demonstrate the physical influences of flow constraints versus presumed flow fields, physical explanations were used. The findings demonstrated that the velocity contour improved as the volume fraction, curvature, power law index, and material parameter upsurged. For the Prandtl number, the volume fraction of nanoparticles, the index of the power law, and the temperature profile of the nanofluid declined. Furthermore, the drag force and transfer of the heat were also investigated as explanations for influences on blood flow. Further, the Nusselt number reduced and the drag force enhanced as the curvature parameter values increased. The modeling and numerical solutions play an impressive role in predicting the cause of atherosclerosis.

The theory of symmetry has a significant influence in many research areas of mathematics. The class of symmetric functions has wide connections with other classes of functions. Among these, one is the class of convex functions, which has deep relations with the concept of symmetry. In recent years, the Schur convexity, convex geometry, probability theory on convex sets, and Schur geometric and harmonic convexities of various symmetric functions have been extensively studied topics of research in inequalities. The present attempt provides novel portmanteauHermite–Hadamard–Jensen–Mercer-type inequalities for convex functions that unify continuous and discrete versions into single forms. They come as a result of using Riemann–Liouville fractional operators with the joint implementations of the notions of majorization theory and convex functions. The obtained inequalities are in compact forms, containing both weighted and unweighted results, where by fixing the parameters, new and old versions of the discrete and continuous inequalities are obtained. Moreover, some new identities are discovered, upon employing which, the bounds for the absolute difference of the two left-most and right-most sides of the main results are established.

The non-isothermal couple stress fluid inside a reverse roll coating geometry is considered. The slip condition is considered at the surfaces of the rolls. To develop the flow equations, the mathematical modelling is performed using conservation of momentum, mass, and energy. The LAT (lubrication approximation theory) is employed to simplify the equations. The closed form solution for velocity, temperature, and pressure gradient is obtained. While the pressure and flow rate are obtained numerically. The impact of involved parameters on important physical quantities such as temperature, pressure, and pressure gradient are elaborated through graphs and in tabular form. The pressure and pressure gradient decreases for variation of the couple stress parameter and velocity ratio parameter K. While the variation of the slip parameter increases the pressure and pressure gradient inside the flow geometry. Additionally, flow rate decreases for the variation of the slip parameter as fluid starts moving rapidly along the roller surface. The most important physical quantity which is responsible for maintaining the quality of the coating and thickness is flow rate. For variation of both the couple stress parameter and the slip parameter, the flow rate decreases compared to the Newtonian case, consequently the coating thickness decreases for the variation of the discussed parameter.