The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

In this paper, the boundary layer magnetohydrodynamics (MHD) flow of Williamson nanofluids over a stretching sheet with Newtonian heating in the presence of thermal radiation effect is analyzed. Using a similarity transformation, the governing equations are reduced to a set of nonlinear ordinary differential equations (ODEs). These equations are solved numerically using a shooting method. The effects of Williamson parameter, magnetic parameter, radiation parameter, Prandtl number, Lewis number, Schmidt number, heat capacities ratio, thermophoretic diffusivity and conjugate parameter on velocity, temperature and concentration fields are shown graphically and discussed. It is found that the rate of heat transfer is higher for Williamson nanofluids compared to the classical viscous fluid. Also, the comparisons with existing results are provided in the literature.

The use of hybrid nanofluid as an alternate heat transfer fluid has shown great potential, and ongoing research to improve its thermal conductivity is important. This study focuses on the impact of heat generation/ absorption on the unsteady Hiemenz flow of aqueous hybrid nanofluid containing copper and silica nanoparticles. Mathematical equations for the hybrid nanofluid model are derived using suitable similarity transformations and solved numerically using bvp4c codes in Matlab software. The results indicate that increased heat generation/absorption leads to an increase in both momentum and thermal boundary layer thickness. The effects of suction and nanoparticle concentration are also analysed and presented graphically. Additionally, a stability analysis is also performed, which discloses that the first solution produced is stable, however, the second solution is not. The findings of this study provide valuable insights into the behaviour of hybrid nanofluid in unsteady flow and can aid in the development of more efficient heat transfer fluids for various engineering applications.

The potential of hybrid nanofluid as an alternative heat transfer fluid is undoubted and the insightful research on enhancing its thermal conductivity is crucial. This study accentuates the influence of magnetic field and thermal radiation on the ethylene glycol base hybrid nanofluid with a combination of argentum and magnetite nanoparticles. The mathematical equations of the hybrid nanofluid model are derived with the suitable similarity transformations and then solved numerically with the execution of bvp4c codes in Matlab software. Graphical results show that an upsurge in magnetic parameter reduces the momentum boundary layer thickness while the higher thermal radiation enlarges the thermal boundary layer thickness. The effects of suction and nanoparticles concentration are also presented graphically. Stability analysis reveals that the first solution obtained in this study is stable, and conversely, the second solution is not.

The steady two-dimensional Homan stagnation point flow and heat transfer of water base hybrid nanofluids (Al2O3 & Cu) over a permeable radially stretching/shrinking sheet have been studied. The similarity variables are introduced to transform the partial differential equations of the model into the ordinary differential equations. Numerical findings and dual solutions have been carried out by implementing the bvp4c code through MATLAB software. The most prominent effect is illustrated in the boundary layer thickness where the velocity profile increases upon the increment of the suction intensity but decreases in the temperature profile. Besides, the reduced Nusselt number also decreases as enlarging the value of copper and alumina nanoparticle volume fraction. The analysis of the first and second solutions are presented graphically with critical values as well as the detail discussions on the effects of the other involving parameters.