The present study highlights the flow of an incompressible nanofluid following the non-Newtonian flow. The non-Newtonian fluid behavior is characterized by the Casson prototype. The flow occupies the conical gap between the rotating/stationary surfaces of the cone and the horizontal disc. Heat and mass transfer is also considered. The novelty of the proposed mathematical model is supplemented with the impacts of a uniform magnetic field imposed vertically upon the flow together with Ohmic dissipation and chemical reactions. The constitutive equations of the Casson fluid have been interpreted along with the cylindrical coordinates. The governing partial differential equations of momentum, energy, and concentration are converted into a set of nonlinear ordinary differential equations via appropriate similarity transformations. This scheme leads to a set of coupled nonlinear ordinary equations concerning velocity, temperature, and nanoparticles concentration distributions. These equations are analytically solved by means of the Homotopy perturbation method (HPM). The theoretical findings are presented in both graphical and tabular forms. The main objective of this study is to discuss the effects of the rotations of both cone and disc and the effects of the other parameters in the two cases of rotation alternatively. Additionally, the effect of the angle between the cone and the disk is one of our interesting points because of the importance of its effect in some engineering industry applications. The rotation parameters are found to have reduction effects on both the temperature and the radial velocity of the fluid, while they have an enhancing effect on the azimuthal velocity. The effects of other parameters with these rotations are found to be qualitatively the same as some earlier published studies. To validate the current mathematical model, a comparison with the previous scientific reports is made.

The key objective of the current examination is to examine a symmetrically peristaltic movement of microorganisms in a Rabinowitsch fluid (RF). The Boussinesq approximation, buoyancy-driven flow, where the density with gravity force term is taken as a linear function of heat and concentrations, is kept in mind. The flow moves with thermophoretic particle deposition in a horizontal tube with peristalsis. The heat distribution and volume concentration are revealed by temperature radiation and chemical reaction characteristics. The originality of the existing study arises from the importance of realizing the benefits or the threats that nanoparticles, microbes, and bacteria cause in the flow inside peristaltic tubes. The results are an attempt to understand what factors perform additional advantages and or reduce damages. The controlling nonlinear partial differential equations (PDEs) are made simpler by employing the long wavelength (LWL) and low-Reynolds numeral (LRN) approximations. These equations are subjected to a set of non-dimensional transformations that result in a collection of nonlinear ordinary differential equations (ODEs). By employing the Homotopy perturbation method (HPM), the configuration of equational analytical solutions is examined. Analytical and graphical descriptions are provided for the distributions of axial speed, heat, microbes, and nanoparticles under the influence of these physical characteristics. The important findings of the current work may help to comprehend the properties of several variations in numerous biological situations. It is found that the microorganisms condensation decays with the rise of all the operational parameters. This means that the development of all these factors benefits in shrinking the existence of harmful microbes, viruses, and bacteria in the human body’s peristaltic tubes, especially in the digestive system, and large and small intestines.

This article is an analytic discussion for the motion of power-law nanofluid with heat transfer under the effect of viscous dissipation, radiation, and internal heat generation. The governing equations are discussed under the assumptions of long wavelength and low Reynolds number. The solutions for temperature and nanoparticle profiles are obtained by using homotopy perturbation method. Results for the behaviours of the axial velocity, temperature, and nanoparticles as well as the skin friction coefficient, reduced Nusselt number, and Sherwood number with other physical parameters are obtained graphically and analytically. It is found that as the power-law exponent increases, both the axial velocity and temperature increase, whereas nanoparticles decreases. These results may have applicable importance in the research discussions of nanofluid flow in channels with small diameters under the effect of different temperature distributions.

The current work scrutinizes a non-Newtonian nanofluid free convective flow induced by a rotating stretchable disc. The examination surveys the Stefan blowing and Cattaneo–Christov mass and heat fluxes, as a precise illustrative model. The innovative aspects of the ongoing project include the analysis of the border sheet nanofluid flow near a revolving disc through thermophoresis, Reiner–Rivlin prototype features, and random nanoparticle motion. The Reiner–Rivlin non-Newtonian model is considered together with the effect of an unvarying axial magnetic strength. The constitutive formulae of a Reiner–Rivlin liquid have been reproduced in the cylindrical coordinates. Through implementing the applicable relationship transformations, the controlling partial differential equations are transferred to ordinary differential equations (ODE). This procedure yields a group of coupled nonlinear ordinary differential equations in relation to speed, heat, and nanoparticle concentration profiles that are impacted by several physical characteristics. These equations are analyzed by using the homotopy perturbation method (HPM). Due to the analytical solution given by HPM, the current work enables us to take the infinity of the layer as a parameter of the problem and discuss its variation in the obtained distributions. Consequently, a physical significant graphical visualization of the data is emphasized. The rates of mass and temperature transmission are examined to understand if any of the relevant parameters may improve these rates. Additionally, the Stefan blowing causes extra particles diffusion, which enhances heat transfer and raises the nanoparticles concentration and could be useful in some medical therapies. Furthermore, the stretching of the rotating disc is concluded, which improves the fluid heat transfer.