In current communication, the thin-film flow of Casson hybrid nanofluid consists of copper and alumina nanoparticles that dissolved in carboxymethyl cellulose (CMC) plus water over an unsteady stretching porous sheet is elucidated. Using suitable similarity variables, the resultant partial governing equations are turned into a set of nonlinear ordinary differential equations. The Keller box approach is then used to solve the transformed equations. The unknown thin-film thickness constant is determined by using the homotopy analysis approach. The thermal and velocity distributions, as well as the Nusselt number and skin friction of the fluid, are discussed for different values of relevant parameters such as thin-film thickness, nanoparticles volume fraction, and mass transition parameter. The distributions of temperature and velocity decrease when the thin-film thickness is increased. The velocity distribution is decreased by the Casson, nanoparticles volume fraction, and mass transition (injection) parameter. The temperature is enhanced by the nanoparticle's volume fraction and the Casson parameter, however, has an opposite tendency with the mass transition (injection) parameter. For the physical quantities, the skin friction has a negative function with all the parameters. The mass transition (injection) parameter increases the Nusselt number. The outcomes of the present study are useful for example in producing the smart contact lens that has been used in the biomedical field.

In recent years, hybrid nanoparticles have gained significant attention for their ability to enhance thermal conductivity in various fluid systems, making them effective heat transport catalysts. Despite advancements in thermal fluid technology, a gap remains in understanding how hybrid nanoparticles interact within non-Newtonian Jeffrey fluid systems, particularly under complex boundary conditions like Newtonian heating. The present study aims to shed light on the effect of hybrid nanoparticles (alumina and copper) incorporated into a Jeffrey fluid model on flow and heat transport, considering them as heat transport catalyst and subject to Newtonian heating to optimize thermal efficiency. An exponentially accelerated plate is used to induce the fluid flow, taking into account the effects of porosity, MHD, and thermal radiation. The examined fluid exhibits an unsteady one-dimensional flow, formulated by deriving partial differential equations, which are subsequently transformed into ordinary differential equations using suitable non-dimensional variables and the Laplace transformation. This research distinguishes itself by presenting a novel mathematical model for MHD Jeffrey hybrid nanofluid, accounting for porosity and Newtonian heating effects. The inverse of Laplace is used to generate the exact solutions for velocity and temperature profiles, which is not explored in existing literature. Graphical representations are generated using Mathcad, depicting the velocity and temperature distributions. A comparison with prior study from the literature demonstrates strong agreement between our findings and theirs. The findings indicate that the velocity and temperature profiles of the hybrid nanofluid are higher with Newtonian heating than without it. Additionally, an increase in the Grashof number, radiation, acceleration, and porosity parameters also leads to an enhanced velocity profile.

Ferrofluid is commonly used in the treatment of cancer due to its ability to be altered by a magnetic field. The present study aims to investigate the character Ferrofluid is commonly used in the treatment of cancer due to its ability to be altered by a magnetic field. The present study aims to investigate the character

Advancing hybrid ferrofluids enhances biomedical engineering and leads to better treatments for cancer and other diseases. Due to their distinctive composition, they exhibit enhanced thermal conductivity, rendering them exceptionally efficient for hyperthermia therapies, which include eliminating the growth of cancer cells at increased temperatures. This study investigates the influence of magnetism on a hybrid ferrofluid flowing past an elongation sheet. The combination of magnetite ferrite-cobalt ferrite nanoparticles (Fe_3 O_4/CoFe_2 O_4) dispersed in a water-ethylene glycol mixture, in the presence of a magnetic dipole, is analysed. The governing equations of the hybrid ferrofluid are derived using Tiwari and Das's model. Subsequently, the similarity transformation approach is applied to simplify the partial governing equations and the Keller box method is employed to solve them. The numerical results of velocity and temperature distributions for pertinent parameters, such as ferrohydrodynamics (FHD) effect and concentrations of the nanoparticles, are graphically presented. The results indicate that the FHD impact diminishes the velocity profile, but enhances the temperature field of the hybrid ferrofluid flow. The shear stress is enhanced by 90.79% and the heat transfer rate is reduced by 12.12%. The presence of hybrid nanoparticles in the fluid not only enhances the temperature distribution but also suppresses the movement of the particles. These outcomes provide insights into the interplay between magnetic fields and heat transfer, relevant to magnetic hyperthermia cancer treatment.