The roll-coating analysis of viscous nanofluid using lubrication approximation theory over a flat porous sheet is investigated. We considered water-based copper (Cu) nanoparticles to discuss the roll-coating analysis. The rate of fluid entering at the roll surface is assumed equal to the rate of fluid leaving on the web surface. The resulting differential equation developed under lubrication approximation and closed-form expressions is obtained for velocity and pressure gradient. The effects of entering velocity, Reynolds number, geometric parameter, and nanoparticle volume fraction with different models on physical quantities such as pressure, pressure gradient, velocity, force, power input are calculated. Some of these effects are presented graphically. It is noted that increasing nanoparticle volume fraction increases the pressure gradient, pressure distribution and has negligible effect on the velocity profile. Model II has a greater effect on pressure and pressure gradient than model I and has an inverse effect on force and power factor.

The recent investigations ensure that the effect of an endoscope on the peristaltic flow is very important for medical diagnosis and it has many clinical applications such as gastric juice motion in the small intestine when an endoscope is inserted through it. Therefore, we have studied the problem of peristaltic flow with heat and mass transfer through the gap between coaxial inclined tubes where the inner tube is rigid and the outer tube has sinusoidal wave traveling down its wall. The inner tube fulfilled the slip condition while the outer tube has a no-slip condition. The lubrication approximation theory is utilized to simplify the normalized equations. The perturbation procedure is employed to concede the results for the pressure gradient and velocity field, whereas exact outcomes are established for the energy and concentration fields. Frictional forces and pressure rise per wavelength are calculated numerically. The impacts of embedded parameters are portrayed through graphs. It is found that fluid velocity reduces by increasing the couple stress parameter however the inverse effect is noted for the slip parameter. Furthermore, better pumping is viewed in the vertical tube as compared to the horizontal tube. A validity of perturbation solutions for velocity distribution is made with the finite element method and an admirable comparison is also noticed with previously published results.

This paper aims to inspect the mixed convective peristaltic transport of ternary hybrid nanofluids between two sinusoidally deforming lubricated curved concentric tubes. Titanium, Alumina, and copper nanoparticles are taken for the current problem with blood as a base fluid. The heat equation is also modeled in the presence of heat generation/absorption. The curved shape structure of flow geometry from the external side with a flexible complex nature of the peristaltic endoscope present inside that is similar to the endoscopy of a living organ. The governing expressions of the proposed model are followed under the long wavelength and small Reynolds number hypothesis. The exact solutions for flow fields that is, velocity, temperature, pumping phenomenon, and streamlines are attained by utilizing the separation of variable technique. Furthermore, graphs are used to examine and discuss different parameters outcomes. The outcomes reveal that liquid velocity enhances near the outer wall of the sinusoidal curved tube but it declines with the peristaltic endoscope for enhancing curvature parameter. The fluid temperature is reduced by enhancing the values of curvature parameter.

Vertical channels between two flat plates have a wide range of engineering applications, such as heat exchangers, chemical processing equipment, electronic component heat dissipation, and so on. Therefore, this analysis examines the significance of variable properties on the dynamics of Casson fluid in a vertical channel due to mixed convection when thermal radiation and Joule heating are significant. The combined effects of temperature-dependent plastic dynamics viscosity and temperature-dependent thermal conductivity are analyzed. Moreover, the evaluation of heat transfer is further supported by viscous dissipation. The nondimensional governing equations are elucidated analytically by employing the perturbation technique and numerically by Runge–Kutta method with the shooting technique. The effects of numerous dimensionless parameters on fluid flow are featured through graphs. In addition, the heat transfer rate and the skin friction coefficient are computed and scrutinized. It is reported that velocity depicts enhancing behavior for higher values of the Casson fluid and slip parameters. It has also been observed that the fluid temperature decreases with an increase in the thermal conductivity parameter.

Cilia motion is commonly located in mammalian cells of living organisms which continually grow and feature conspicuously. The ciliary apparatus is associated with cell cycle movement and proliferation, and cilia play a dynamic part in human and animal growth and everyday life. The motivation of these applications, a theoretical model is presented to examine the viscous dissipation effects on the ciliary flow of micropolar fluid through a two- two-dimensional channel under slip constraints. The flow is controlled by the metachronal wave propagation generated by cilia beating on the inner walls of the channel. The model comprises the motivational aspects of radiative flux and predicts the parametric ranges for excellent heat transfer results. The normalized equations are simplified by the lubrication hypothesis and analytical outcomes are attained by integration technique. Graphical illustrations have been utilized to explore the impressions of the derived physical parameters on the flow configurations to give each parameter a physical interpretation. Special attention is given to investigating the pumping and trapping characteristics of the micropolar fluid due to ciliary metachronism. The major outcomes disclosed that the fluid velocity upsurges for enhancing values of coupling number and micropolar parameter. The pressure gradient increased with the slip parameter, providing insights into flow control, particularly where minimizing or enhancing shear is critical. The fluid temperature is enhanced by enhancing the Brickman number however temperature is decreased by increasing the thermal radiation parameter.

Heat transmission processes have numerous industrial applications. A novel form of nanofluid known as the hybrid nanofluid that has a higher thermal exponent helps in improving the ability of regular fluids to transfer heat. This article aims to analyze the impact of hybrid nanofluid with effects like magnetohydrodynamics (MHD), Brownian motion and thermophoresis, heat generation/absorption, and chemical reaction past a permeable moving thin needle. Two assorted nanomaterials (MoS₂ and Fe₃O₄) are added in a base fluid such as ethylene glycol (EG) to access the performance of the hybrid nanofluid. Using suitable similarity variables, the governing equations of the problem are turned into customary ordinary differential equations. The resulting equations are solved analytically using the Galerkin method (GM) and dual solutions are obtained in a certain range of moving parameter λ. Due to this, a stability test is implemented to find a stable solution. With the help of a bvp4c function in Matlab software, the smallest eigenvalues are computed, where positive eigenvalues are linked with the stable solution while negative eigenvalues are linked with the unstable solution. It is concluded that only the first solution is stable while the second solution is not. The skin friction factor and heat transfer rate are reduced by growing the needle size. The magnetic field has an inverse relation with the flow field and direct relation with the temperature field. The improvement in heat generation parameter causes the fluid temperature to rise. The fluid concentration is enhanced with the increment of the chemical reaction parameter.