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Development of thin Casson liquid (CL) film on a heated nonlinear flat stretching surface is examined under influences of thermal radiation and transverse magnetic field. The velocity and temperature at any point of the stretching surface are assumed as the generalized nonlinear functions of the distance of that point. The analytical expressions for velocity components and temperature are obtained using long-wave approximation technique. The numerical solution for nonlinear film evolution equation is incurred by the Newton–Kantorovich method. It is found that initial non-uniform film thickness becomes flat with due course of time. It is further observed that the film thinning rate enhances for larger values of the Marangoni number and radiation parameter. It is also discovered that the rate of film thinning diminishes for the larger Hartmann number and Casson parameter.

Energy restoration is the prime issue for the researcher and they have tried to develop advanced techniques and resources for renewable energy. The nanofluid is one of the resources for the restoration of energy which depends on the dynamic thermophysical properties of metal nanoparticles. The recent study is concerned with the thin film flow of carbon nanotubes (CNTs) water-based nanofluid for the improvement of heat transfer applications. The flow of two types of CNTs nanofluid was studied, comprising single-walled carbon nanotube (SWCNT) and multi-walled carbon nanotube (MWCNT) over the surface of a thin stirring needle. The study has been carried out in the presence of a magnetic effect and viscous dissipation. The BVP 2.0 package has been used for the solution of the modeled problem. The effect of the physical constraints like Prandtl number, magnetic field and Eckert number vs the momentum and thermal boundary layers has been analyzed. The sum of the residual errors has been obtained up to the 20th order estimates to settle the strong convergence of the problem. The obtained results show that the thin film has a quick response to the increasing of heat transfer rate over the surface of a thin needle as compared to the thick boundary layers.

Nanoparticles have the capability to augment the thermal conductivity of nanofluids. For the transmission of heat, the material’s low thermal conductivity is the key problem. Therefore, to increase the thermal conductivity, researchers mixed different nanoparticles in the base fluids. In this field of study, utilizing three different particles is the most recent strategy to form a ternary hybrid nanofluid that gives us better results in terms of heat transfer. The interaction of three different kinds of nanoparticles, i.e. copper, alumina and silver, is considered with water serving as the base fluid to form a ternary hybrid nanofluid. The paper explores the behavior of ternary hybrid nanofluids on heat and mass transportation phenomena of the two-dimensional magnetohydrodynamic (MHD) micropolar flow across a porous extending surface with zero mass flux and convective conditions. The Brownian motion, thermal radiation, heat source and sink, and joule heating are taken into consideration in the temperature equation. The chemical reaction is incorporated into the concentration equation. Appropriate similarity transformations are used to transform the system of partial differential equations (PDEs) to a coupled system of ordinary differential equations (ODEs). The homotopy analysis method (HAM) is used to solve the system of the flow equations. The effects of the nanoparticle’s volume fractions and other different physical parameters on the surface drag force, Nusselt number, velocities, microrotation, temperature and concentration profiles are scrutinized through figures and tables. The outcomes of the present investigation show that the heat transfer rate is augmented with the increasing value of thermophoresis parameter. The magnetic field has augmented temperature while the opposite result is seen in velocity and microrotation profiles. With the escalating values of thermophoresis parameter, the concentration and temperature of ternary hybrid nanofluids are boosted while the increasing Brownian and chemical reaction parameters have decreased the concentration profile. The surface friction coefficient exhibited by the ternary hybrid nanofluid is higher than hybrid and conventional nanofluids.