Non-linear convective flow of the thin film nanofluid over an inclined stretching surface

To enhance the surface properties of solids the mechanism of thin films is frequently used. Penetration, degradation, stiffness, illumination, diffusion, absorption, and electric performance are all characteristics of a bulk substance medium that a thin film can improve. In nanotechnology, thin film processing can be extremely useful. Therefore, the time-dependent nonlinearly convective stream of thin film nanoliquid over an inclined stretchable sheet with magnetic effect is investigated in current work. The features of mass and heat transport processes are explained using important factors like thermophoresis and Brownian movement. Nonlinear partial differential equations are obtained to model the time-dependent liquid film flow over an inclined surface, which are then turned into couple ordinary differential equations utilizing appropriate alterations. The results of the computation of the model problem are collected using an analytical approach Homotopy Analysis Method and presented the final finding numerically and graphically. During the flow assessment, the impact of individual flow factors such as magnetic, Brownian, and thermophoresis parameters on regular profiles (temperature, velocity, and concentration) are analyzed and found to be quite remarkable. Furthermore, the consequence of M and Nt factors on the velocity, concentration and thermal distribution leads to diminishing conduct. On the other hand, the thermal profile of the liquid film rises in response to the thermophoresis factor. The % wise variation in the skin friction, Nusselt number and Sherwood number versus physical parameters has been obtained and discussed.

Convective and Absolute Instabilities Induced by Viscous Dissipation in the Thermocapillary Convection with Through-Flow

The mixed convection in a thin liquid film flow over a horizontal plate is investigated under finite Prandtl numbers. The gas-liquid interface is considered free, non-deformable and subject to surface tension gradients and convection, while gravity is assumed negligible. Therefore, Marangoni instead of buoyancy effects appear due to the unstable temperature stratification induced by the internal heating generated by viscous dissipation. A linear and modal stability analysis of this model is then performed to identify its convective/absolute nature. This is achieved by solving the resulting differential eigenvalue problem with a shooting method. Longitudinal rolls are the most unstable at the onset of instability for most parametric conditions. Otherwise, transverse rolls are the first to become convectively unstable. Finally, longitudinal rolls are absolutely stable. A transition to absolute instability occurs through transverse rolls, but only within a limited region in parametric space.