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The utilization of solar energy is essential to all living things since the beginning of time. In addition to being a constant source of energy, solar energy (SE) can also be used to generate heat and electricity. Recent technology enables to convert the solar energy into electricity by using thermal solar heat. Solar energy is perhaps the most easily accessible and plentiful source of sustainable energy. Copper-based nanofluid has been considered as a method to improve solar collector performance by absorbing incoming solar energy directly. The goal of this research is to explore theoretically the Agrawal axisymmetric flow induced by Cu-water nanofluid over a moving permeable disk caused by solar energy. Moreover, the impacts of Maxwell velocity and Smoluchowski temperature slip are incorporated to discuss the fine points of nanofluid flow and characteristics of heat transfer. The primary partial differential equations are transformed to similarity equations by employing similarity variables and then utilizing bvp4c to resolve the set of equations numerically. The current numerical approach can produce double solutions by providing suitable initial guesses. In addition, the results revealed that the impact of solar collector efficiency enhances significantly due to nanoparticle volume fraction. The suction parameter delays the boundary layer separation. Moreover, stability analysis is performed and is found that the upper solution is stable and physically trustworthy while the lower one is unstable.

We consider the incompressible axisymmetric Navier–Stokes equations with swirl as an idealized model for tornado-like flows. Assuming an infinite vortex line which interacts with a boundary surface resembles the tornado core, we look for stationary self-similar solutions of the axisymmetric Euler and axisymmetric Navier–Stokes equations. We are particularly interested in the connection of the two problems in the zero-viscosity limit. First, we construct a class of explicit stationary self-similar solutions for the axisymmetric Euler equations. Second, we consider the possibility of discontinuous solutions and prove that there do not exist self-similar stationary Euler solutions with slip discontinuity. This nonexistence result is extended to a class of flows where there is mass input or mass loss through the vortex core. Third, we consider solutions of the Euler equations as zero-viscosity limits of solutions to Navier–Stokes. Using techniques from the theory of Riemann problems for conservation laws, we prove that, under certain assumptions, stationary self-similar solutions of the axisymmetric Navier–Stokes equations converge to stationary self-similar solutions of the axisymmetric Euler equations as ν → 0 . This allows to characterize the type of Euler solutions that arise via viscosity limits.

It is traditionally believed that in a liquid of uniform density, an axisymmetric barotropic flow with solid-body rotation is stable. Within the framework of a two-level quasi-geostrophic model, this work shows that this is not in the case of a baroclinic flow with solid-body rotation of the heton type. Such a flow has different directions of rotation at two levels. Due to the vertical velocity shift, this flow is always unstable. This paper develops a linear theory of the instability of such flows both in a model without friction and in a model with Ekman friction. It is shown that, for instability in a model with friction, the horizontal wave number of the disturbance should not exceed a certain critical value. It has been established that instability with respect to longwave disturbances in the model without friction is absolute in nature; i.e., it always exists. The development of instability may be associated with the formation of observed disturbances in the axial zone of intense atmospheric vortices.

The article presents a study of the laser conversion of methane mixtures under various conditions of the computational experiment. Such flows are characterized by sharp local changes in the gas dynamic characteristics and concentrations of the mixture components. Their dynamics and mutual transformations are described by a rigid system of Navier–Stokes equations and chemical kinetics, which imposes serious restrictions on the choice of computational algorithm. Numerical experiments are carried out using previously developed 2D code for modeling subsonic axisymmetric flows of a multicomponent medium, supplemented by moduli that take into account laser radiation and solve the equations of the chemical kinetics of methane conversion. The accuracy of the results is checked by calculating the conversion of methane under the influence of external heating of the walls. Comparison of the concentrations of the substances at the pipe outlet with the direct solution of the chemical kinetics system at different reaction temperatures shows a good agreement of the results. Computational experiments on the effect of laser radiation on the flow of a chemically active absorbing medium are completed. It is shown that the laser radiation introduced into the mixture and absorbed by ethylene changes the flow pattern and significantly increases the temperature of the gas mixture. An increase in temperature contributes to an increase in the yield of the target products (ethylene, acetylene, and hydrogen) at shorter length of the reactor, while in the absence of radiation the maximum concentrations of products appear at the reactor outlet. The effect of the initial composition of the gas mixture on the methane conversion is investigated, and it is concluded that the presence of ethylene significantly increases the formation of target products at moderate temperatures of the reactor walls in the presence of laser radiation.

A numerical investigation of the influence of the compressibility of the air flowing around a disk–cylinder–disk set with an outward-projecting disk of diameter 0.4 and a clearance between this disk and the cylinder of 0.98, close to the optimum one as to the profile drag for the movement with a transonic velocity at Mach numbers of 0–2, on the circulation air flow in the clearance and on the frontal resistance of the set has been performed. The adequacy of the numerical estimates made was substantiated by their comparison with the corresponding results of experiments in a wind tunnel. It was established that in the transonic Mach number range 0.7–0.8, the structure of a vortex in the clearance between the outward-projecting disk and the front edge of the cylinder is rearranged. Because of this, unlike the axisymmetric flow of air around a disk–cylinder–disk set optimum for an incompressible medium, normal and oblique shocks are not formed over the shear layer of the detached flow in the indicated clearance, and, at M = 0.9, a lambda-like shock is formed over the side surface of the cylinder. The wave drag of a disk–cylinder–disk set, optimum for transonic velocities, increases at a smaller rate with increase in the Mach number and appear to be smaller by almost two times compared to the wave drag of a disk–cylinder–disk set optimum for the deep subsonic velocities.

Colloidal suspensions of regular fluids and nanoparticles are known as nanofluids. They have a variety of applications in the medical field, including cell separation, drug targeting, destruction of tumor tissue, and so on. On the other hand, the dispersion of multiple nanoparticles into a regular fluid is referred to as a hybrid nanofluid. It has a variety of innovative applications such as microfluidics, heat dissipation, dynamic sealing, damping, and so on. Because of these numerous applications of nanofluids in minds, therefore, the objective of the current exploration divulged the axisymmetric radiative flow and heat transfer induced by hybrid nanofluid impinging on a porous stretchable/shrinkable rotating disc. In addition, the impact of Smoluchowski temperature and Maxwell velocity slip boundary conditions are also invoked. The hybrid nanofluid was formed by mixing the copper (Cu) and alumina (Al2O3) nanoparticles scattered in the regular (viscous) base fluid (H2O). Similarity variables are used to procure the similarity equations, and the numerical outcomes are achieved using bvp4c in MATLAB software. According to the findings, double solutions are feasible for stretching (λ>0) and shrinking cases (λ<0). The heat transfer rate is accelerated as the hybrid nanoparticles increases. The suction parameter enhances the friction factors as well as heat transfer rate. Moreover, the friction factor in the radial direction and heat transfer enrich for the first solution and moderate for the second outcome due to the augmentation δ1, while the trend of the friction factor in the radial direction is changed only in the case of stretching for both branches.

This paper deals with a simplified model taking into account the interplay of compressible, laminar, axisymmetric flow and the electrodynamical effects due to Lorentz force’s action on the combustion process in a cylindrical pipe. The combustion process with Arrhenius kinetics is modelled by a single step exothermic chemical reaction of fuel and oxidant. We analyze non-stationary PDEs with 6 unknown functions: the 3 components of velocity, density, concentration of fuel and temperature. For pressure the ideal gas law is used. For the inviscid flow approximation ADI method is used. Some numerical results are presented.

Axisymmetric base flow is investigated to understand flow physics associated with the massive flow separation at a subsonic speed. The detached-eddy simulation (DES) approach is well suited in the current separated flow with a known separation point. The upstream attached boundary layer is well represented with the Reynolds-averaged Navier–Stokes (RANS) mode, whereas the separated flow from the base is well captured in the large-eddy simulation (LES) mode. Since the spatial resolution in the LES zone impacts directly the fidelity of the DES computation, a systematic approach is applied to the computational grid. Current computational grids are designed for nearly isotropic grids in the separated region (i.e., LES zone) with much reduced anisotropy of the grid in the separating shear layer, compared to computational grids documented in literature. Current grids allow the separating shear layer to undergo the Kelvin–Helmholtz instability, resulting in a rapid shift from the RANS to LES mode right after the flow separation. In consequence, the axisymmetric base flow is well resolved in the current DES computation with good agreement to relevant experimental data including the mean base pressure and the center-line velocity in the wake. The base flow is further discussed with statistical data of the separated flow. Current DES simulation is also compared with a typical RANS simulation to emphasize the high fidelity of the computational approach.

In this paper, we examined the numerical and perturbative analysis of non-Newtonian fluid towards non-axisymmetric Homann stagnation-point flow. The Maxwell fluid model is applied to investigate the behavior of viscoelastic fluid for this particular geometry. The influence of Maxwell parameter β 1 and ratio γ on different profiles are addressed in this analysis. The governed partial differential equations are reduced to ordinary differential equations with the help of similarity transformations. The numerical and perturbative outcomes of the resulting system of differential equations are obtained by applying the shooting technique. The solution is achieved for diverse values of relaxation time parameter β 1 and ratio γ . The wall shear stress is compared to their large- γ asymptotic behaviors and displacement thicknesses are also presented. The numerical data for velocity profiles are obtained in terms of plots. It is predicted through analysis that a gradual increase in relaxation time raises wall skin friction components. On the other hand, velocity decreases which constitutes to reduce the reverse flow. Meanwhile, displacement thicknesses in x and y direction decreases. However, three-dimensional displacement thickness increases due to more viscoelastic material like Maxwell fluid than viscous fluid.

In this paper, we present the numerical results for the unsteady axisymmetric flow and heat transfer of Carreau fluid induced by time dependent permeable radially stretching surface. Numerical results are demonstrated for both shear thinning and shear thickening fluids. The time dependent non-linear PDE of the considered problem are reduced into non-linear ODE with the aid of suitable transformations. An effective numerical technique namely bvp4c function in MATLAB is employed to construct the numerical solutions of the transformed non-linear ODE for the velocity and temperature fields. Numerical computations of the local skin-friction coefficient and local Nusselt number are tabulated for steady and unsteady flows of shear thinning fluid as well as shear thickening fluid. It is worth mentioning that the magnitude of the skin friction coefficient and local Nusselt number for the steady flow is less than that for unsteady flow.