In the present work, we have studied a numerical solutions of MHD stagnation point flow of nanofluid over a stretching/shrinking sheet with mass suction condition. We have used the upper convected Maxwell (UCM) fluid model for the development of momentum equation and utilized it to explore the characteristics of elasticity of this model. We used the Buongiorno nanofluid model to develop the equations for the present problem. The governing flow, energy, and concentration equations are changed into the ordinary differential equations by means of suitable transformation. The subsequent ordinary ones are solved numerically using bvp4c scheme in MATLAB. The combined results of buoyancy forces, double slip (first‐ and second‐order slip), and elasticity have been investigated, and the influence of various flow parameters such as Hartmann number, suction parameter, and stretching/shrinking parameter on the skin friction coefficient, local Nusselt number, Sherwood number, and streamlines is studied and exposed through graphs. It is found that mass suction parameter and elasticity of UCM fluid increase the range of buoyancy forces for the existence of dual solutions. Also, buoyancy force increases the range of stretching/shrinking parameter where solution exists.

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The flow of nanofluids is very important in industrial refrigeration systems. The operation of nuclear reactors and the cooling of the entire installation to improve safety and economics are entirely dependent on the application of nanofluids in water. Therefore, a model of Maxwell’s dusty nanofluid with temperature-dependent viscosity, surface suction and variable surface tension under the action of solar radiation is established. The basic equations of momentum and temperature of the dust and liquid phases are solved numerically using the MATLAB bvp4c scheme. In the current evaluation, taking into account variable surface tension and varying viscosity, the effect of dust particles is studied by immersing dust particles in a nanofluid. Qualitative and quantitative discussions are provided to focus on the effect of physical parameters on mass and heat transfer. The propagation results show that this mixing effect can significantly increase the thermal conductivity of nanofluids. With small changes in the surface tension parameters, a stronger drop in the temperature distribution is observed. The suction can significantly reduce the temperature distribution of the liquid and dust phases. The stretchability of the sheet is more conducive to temperature rise. The tables are used to explain how physical parameters affect the Nusselt number and mass transfer. The increased interaction of the liquid with nanoparticles or dust particles is intended to improve the Nusselt number. This model contains features that have not been previously studied, which stimulates demand for this model among all walks of life now and in the future.

This report is devoted to the study of the flow of MHD nanofluids through a vertical porous plate with a temperature-dependent surface tension using the Cattaneo–Christov heat flow model. The energy equation was formulated using the Cattaneo–Christov heat flux model instead of Fourier’s law of heat conduction. The Tiwari–Das model was used to take into account the concentration of nanoparticles when constructing the momentum equation. The problem is described mathematically using the boundary layer approach as a PDE, which is then converted into an ODE with the help of the transformation process. The solution finding process was completed by running the bvp4c code in MATLAB. A quantitative analysis of the influence of some newly occurring parameters on physical quantities was carried out using graphics. The addition of nanoparticles to the base fluid leads to an increase in both skin friction and thermal conductivity. The increase in thermal conductivity is the advantage, while the increase in skin friction is the disadvantage of the nanoparticle concentration. Marangoni convection has proven to be one of the most cost-effective tools available that can reduce skin friction. Marangoni convection improves the heat transfer coefficient during suction but decreases the heat transfer coefficient during the injection.

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