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In this article, the steady two-dimensional laminar flow of a viscous incompressible fluid in a semi-porous channel in the presence of a transverse magnetic field is considered. The homotopy perturbation method (HPM) and variational iteration method (VIM) are employed to compute an approximation to the solution of the system of differential equations governing on the problem. Velocity profiles, streamlines, and the other parameters of flow are determined. Comparisons are made between the numerical method (NM) and the results of our methods. The results reveal that these methods are very effective, simple, and can be applied to other nonlinear problems.

This study reports both MagnetoHydroDynamics (MHD) and heat generation aspects of a water-based hybrid nanofluid flow with various shapes of the nanoparticles involving Nimonic 80A and ${\mathrm{\text{Fe}}}_3{\mathrm{\text{O}}}_4$, over a moving wedge. Similarity transformations were adapted to obtain non-dimensional equations and solved using MATLAB bvp4c code. All the results and graphs were formulated after a positive outcome of our results with that available in existing literature. Nusselt number, which signifies the heat transfer rate in a flow, increased with an increase in empirical shape factors of the nanoparticle with a contrasting decrease in the drag experienced during the flow, represented by the skin friction coefficient. The velocity profile decreased at a rate of 0.75% for $M=0.6$ to $M=0.8$ due to the augmenting Lorentz forces while it augmented by 18.9% for an augmenting velocity ratio parameter from $R=0.0$ to $R=0.5$ due to the no-slip boundary conditions. Both the Nusselt number and skin friction coefficients decreased with an increase in magnetic parameter. An increase in the nanoparticle concentration resulted in an incrementing streamline value along with increasing temperature profile due to increasing thermal conductivity of the fluid flow system. The physical significance of the study involves in its applications in nuclear, steel industries, MRI scanning for its anti-corrosive and high thermal conductivity properties.

In this study, the effects of suction and buoyancy are used to analyze the Ternary hybrid nanofluid flow on a stretching sheet through a porous media. Ternary hybrid nanofluid is (Carbon nanotubes) CNT$+$Graphene$+{\mathrm{\text{Al}}}_2{\mathrm{\text{O}}}_3$ with base fluid as Water. Case-1 Buoyancy Assisting flow and Case-2 Buoyancy Opposing flow. Hybrid nanofluids have been used to speed up the heat transfer process. Nonlinear partial differential equations (PDEs) have been converted to ordinary differential equations (ODEs) using Lie group transformations. The ODE45, an algorithmic approach, has been using the aid of this built-in solver, and the resulting Ordinary differential equations were resolved. The general relationship between temperature, velocity, heat transfer rate, and shear stress on a stretchy surface is shown for a range of values of the significant factors. The temperature profiles have been rising with the impact of $\mathrm{\text{Da}},f_w$. Using streamlines to examine the flow pattern of a fluid and a method of machine learning, in terms of modern language, an artificial neural network (ANN) made up of artificial neurons or nodes is known as a neural network. A neural network is a network or circuit of genetic neurons.

The tortuosity is a very important parameter for description of fluid flow in porous media, and it has been shown that porous media in nature have the fractal characteristics. The Sierpinski carpet is an exactly self-similar fractal model, which is often used to simulate fractal porous media. In this work, the tortuosity of different generations of Sierpinski carpet is calculated and analyzed by the finite volume method. A simple linear relation between the generations and tortuosity in pore fractal model of porous media is obtained. The results are compared with the available conclusions and show a more realistic tortuosity predication for fluid flow in the two-dimensional pore fractal models of porous media.

In this research, a general solution of volume constancy differential equation is presented based on the equation of deformation field for a general process. As the Bezier method is suitable for construction of complex geometries, the solution is used in conjunction with the Bezier method to analyze the equal channel angular extrusion (ECAE) process of rectangular cross section. Thus, a generalized kinematically admissible velocity field is derived from the equation of deformation zone such that the compatibility of the surface representing the deformation zone is fulfilled. The effects of die angle, friction between the billet and die wall, and the angle of outer curved corner, on extrusion pressure are all considered in the analysis. It is found that extrusion pressure decreases with increasing both the die angle and the outer curved corner angle and with decreasing the friction coefficient. Also, the effect of die curvature on inhemogenity of strain is assessed. It is exhibited that increasing the angle of outer curved corner decreases the extrusion pressure and increases the inhomogeniety of strain field of deformation zone. A good agreement is found between the predicted and experimental results pertaining to two dies of different outer curved corner.

Appropriate mesh refinement plays a vital role in the accuracy and convergence of computational fluid dynamics solvers. This work is an extension of the previous work that further demonstrates the accuracy of the 3D adaptive mesh refinement method by comparing the accuracy measures between the ones derived from the analytical fields and those identified by the refined meshes. The adaptive mesh refinement method presented in this study is based on the law of mass conservation for three-dimensional incompressible or compressible steady fluid flows. The assessment of the performance of the adaptive mesh refinement method considers its key features such as drawing closed streamline and identification of singular points, asymptotic planes, and vortex axis. Several illustrative examples of the applications of the 3D mesh refinement method with a multi-level refinement confirm the accuracy and efficiency of the proposed method. Furthermore, the results demonstrate that the adaptive mesh refinement method can provide accurate and reliable qualitative measures of 3D computational fluid dynamics problems.

In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the gradient of the stream function associated to the fluid beneath the interface vanishes, on the wave surface, at exactly two points. Furthermore, there exists a critical layer which is bounded from above by the wave profile. Besides, we prove, without excluding the presence of stagnation points, that if the vorticity function associated to each fluid in part is real-analytic, bounded, and non-increasing, then capillary-gravity steady internal waves are a priori real-analytic. Our new method provides the real-analyticity of capillary and capillary-gravity waves with stagnation points traveling over a homogeneous rotational fluid under the same restrictions on the vorticity function.

The aim of this study is to visualize and analyze the mucous layer effects towards the nasal airflow. Mucous layer had been neglected in previous works as it is considered a very thin layer along the nasal passageway. This paper discussed the effects in nasal airflow caused by the micrometer changes of the mucous layer thickness along the nasal passageway. Differences in maximum velocities caused by the mucous layer and visualization of the nasal airflow were studied. Computational fluid dynamics (CFD) was used to study three-dimensional nasal cavity of an adult Malaysian female. Six different models with various thickness of mucous layer within the range of 5–50 μm were implemented in the analysis with mass flow rate of 7.5 and 20 L/min. Mucous layer is assumed to be uniform, solid, and also stationary for this study. The results from all the six models were compared with the model with non-mucous effects. Based on both laminar and turbulent airflow simulations, it is shown that the addition of mucous layer thickness in analysis increased the maximum velocities at the four cross sections along the nasal cavity.