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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.

In this article, the characteristics of physical model steady axisymmetric flow of cross-fluid over a stretching sheet are explored numerically. Furthermore, steady flow of nanofluid is expressed by means of Buongiorno’s model for nanoparticles. Moreover, the features of thermal radiation and chemical reaction processes with partial velocity slip condition are adopted here. Nonlinear PDEs are converted to ODEs using suitable transformation variables. The reduced systems of ODEs are resolved using an effective bvp4c scheme implemented. Numerical computation for physical parameters such as skin friction, Nusselt and Sherwood numbers are also examined. Magnetic field plays a vital role in controlling the flow of fluid and has the tendency to enhance the thermal boundary layer and concentration. Similarly, skin friction, Nusselt and Sherwood numbers depreciate by improving the values of velocity slip parameter, magnetic parameter, magnetic parameter, thermophoresis parameter in shear thickening fluids.

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 considers the steady and unsteady swirling axisymmetric flows of a homogeneous viscous incompressible fluid. The possibility of the existence of helical vortex lines on the surface of revolution homeomorphic to a torus is investigated. An example of unsteady flow in which there are helical vortex lines is given. It is proved that the existence of helical vortex lines lying on the surface of revolution homeomorphic to a torus is impossible in a steady axisymmetric flow of a viscous incompressible fluid.

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.

For the first time, a numerical solution code, based on Levenberg–Marquardt method is presented for solving non-linear problem of inverse heat transfer in axisymmetric stagnation flow impinging on a cylinder rod to determine time-dependent wall temperature by temperature distribution at a specific point in the fluid region. Also, the effect of noisy data on the final result has been studied. For this purpose, the numerical solution of the dimensionless temperature and the convective heat transfer in a radial incompressible flow on a cylinder axis is carried out as a direct problem. In the direct problem, the free stream is steady with an initial flow strain rate of k¯ . Using similarity variable and appropriate transformations, momentum and energy equations are converted into semi-similar equations. The new equation systems are then discretized using an implicit finite difference method and solved by applying the tridiagonal matrix algorithm (TDMA). The wall temperature is then estimated by applying the Levenberg–Marquardt parameter estimation approach. This technique is an iterative approach based on minimizing the least-square summation of the error values, the error being the difference between the estimated and measured temperatures. Results of the inverse analysis indicate that the Levenberg–Marquardt algorithm is an efficient and acceptably stable technique for estimating wall temperature in axisymmetric stagnation flow. The maximum value of the sensitivity coefficient is related to the estimation of polynomial wall temperature and its value is 0.1952 also the minimum value of the sensitivity coefficient is 8.62 × 10–6 which is related to the triangular wall temperature. The results show that the parameter estimation error in calculating the triangular and trapezoidal wall temperature is greater than the others because the maximum value of RMS error is obtained for these two cases, which are 0.451 and 0.479, respectively, the reason for the increase in error in estimating these functions is the existence of points where the first derivative of the function does not exist. This method also exhibits considerable stability for noisy input data.

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.