The FLOW of a thin film down an inclined SURFACE over topography is considered for the case of liquids with Sisko’ s model viscosity. For the first time lubrication theory is used to reduce the governing equations to a non-linear evolution equation for a current of a Sisko’ s model non-Newtonian FLUID on an inclined plane under the action of gravity and the viscous stresses. This model is solved numerically using an efficient Full Approximation Storage (FAS) multigrid algorithm. FREE SURFACE results are plotted and carefully examined near the topography for different values of power-law index np, viscosity parameter m, the aspect ratio A and for different inclination angle  of the plane with the horizontal. Number of complications and additional physical effects are discussed that enrich real situations. It is observed that the FLOWs into narrow trenches develop a capillary ridge just in front of the upstream edge of a trench followed by a small trough. For relatively small width trenches, the FREE SURFACE is almost everywhere flat as the dimensional width of the trench is much smaller than the capillary length scale. In this region, SURFACE tension dominates the solution and acts so as to stretch a membrane across the trench leading to smaller height deviations. The ridge originates from the topographic forcing which works to force FLUID upstream immediately prior to the trench before helping to accelerate it over. The upstream forcing slows down the FLUID locally and increases the layer thickness.

In this paper, a numerical model for simulation of FREE SURFACE FLUID FLOWs is presented. This method is a combination of smart genetic algorithm and FREE SURFACE FLUID FLOW tracking algorithm based on donor and acceptor elements. The specification of the new combinational method can be summarized in determining orientation vector and plane constant passing through FREE SURFACE cells. The proposed algorithm can be easily used in non-uniform grids. This numerical model has been applied to simulate some of benchmark FLOW problems and also compared with the experimental data and other researchers' results. The comparisons indicated that the described numerical model is able to make accurate predictions, and is also simple to apply for many FLUID FLOW problems.

This paper was concerned with studying the magnetohydrodynamic steady laminar FREE convection FLOW of a micropolar FLUID past a continuously moving SURFACE in the presence of heat generation and thermal radiation. Similarity transformation was employed to transform the governing partial differential equations into ordinary ones, which were then solved numerically using the finite element method. Numerical results for the dimensionless velocity, microrotation and temperature profiles were obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution. The skin friction and the rate of heat transfer were also computed and presented through tables. Favorable comparison with previously published work was performed.

This article is proposed to address the melting heat transfer of a Jeffrey FLUID in Blasius and Sakiadis FLOW caused due to a moving SURFACE. Thermal radiation and a constant FREE stream are considered in this mathematical model. The non-linear coupled dimensionless equations from the governing equations are attained by employing appropriate similarity transformations. The resulting dimensionless equations are solved by implementing RKF method. The impact of sundry emerging parameters on different FLOW fields are interpreted with the help of figures and tables. For augmented values of Deborah number, the velocity profile diminishes in the case of Blasius FLOW and the reverse behavior in the Sakiadis FLOW is observed. Moreover, the velocity of non-Newtonian liquid in case of Blasius FLOW is superior to that of the Sakiadis FLOW. The present work is demonstrated by matching with the computational results in the literature and found to be outstanding agreement.

In the present article Williamson nano FLUID FLOW over a continuously moving SURFACE is discussed when the SURFACE is heated due to the presence of hot FLUID under it. Governing equations have been developed and simplified using the suitable transformations. Mathematical analysis of various physical parameters is presented and the percentage heat transfer enhancement is discussed due to variation of these parameters. We employed Optimal homotopy analysis method to obtain the solution. It is presented that initial guess optimization will provide us one more degree of FREEdom to obtain the convergent and better solutions.

The aim of this paper is to present numerically the transport mechanism of an incompressible micropolar FLUID between two vertical walls when the motion occurs due to the buoyancy force. The governing equations in non-dimensional form are solved numerically using the Matlab software. The obtained numerical solutions for the velocity and micro-rotation profiles are displayed using the graphs for various values of the vortex viscosity parameter and material parameter. It is found that the material parameter has retarding effect on the velocity of micropolar FLUID and to make the FLOW steady state earlier for both thermal conditions. The effect of the vortex viscosity parameter is to decrease the steady state time of the velocity and micro-rotation.

The present research indicates the ability of mesh-FREE natural element numerical method in simulation of FREE-SURFACE FLOW and consistency of extended second order method of Van-Leer scheme on solving natural element method. The natural element method is based on natural neighbor interpolation. In this study, Sibson interpolation has been used. Nodal integration has been used due to inappropriateness of Gaussian point’s integration. The present method has been validated by two-dimensional heat transfer problem for the diffusion term validation and by one-dimensional dam break problem for the convective term evaluation. Simulation of FREE-SURFACE FLOW has been analyzed on non-uniform bed in the channel with a bump. The results obtained are compared with analytical results. In addition, water FLOW inside the Parshall flume is simulated and results were compared with experimental interpretations. Results of modeling and analytical solutions via normalized root mean square error (NRMSE) for temperature problems, dam break and FREE-SURFACE FLOW show NRMSE of less than 2% while 18% for Parshall flume test. In addition, the determination coefficient of numerical model for the first three tests are higher than 0.99 and 0.90 for the Parshall flume which suggests high capability of numerical model in simulation of FREE-SURFACE FLOW.