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This paper aims to present dual solutions for the two-dimension copper oxide with silver (CuO–Ag) and zinc oxide with silver (ZnO–Ag) hybrid nanofluid flow past a permeable shrinking sheet in a dusty fluid with velocity slip.

The governing partial differential equations for the two dust particle phases are reduced to the pertinent ordinary differential equations using a similarity transformation. Closed-form analytical solutions for the reduced skin friction and reduced Nusselt number, as well as for the velocity and temperature profiles, were presented, both graphically and in tables, under specific non-dimensional physical parameters such as the suction parameter, Prandtl number, slip parameter and shrinking parameter, which are also presented in both figures and tables.

The results indicate that for the shrinking flow, the wall skin friction is higher in the dusty fluid when compared with the clear (viscous) fluid. In addition, the effect of the fluid–particle interaction parameter to the fluid phase can be seen more clearly in the shrinking flow. Furthermore, multiple (dual, upper and lower branch solutions) are found for the governing similarity equations and the upper branch solution expanded with higher values of the suction parameter. It can be confirmed that the lower branch solution is unstable.

In practice, the study of the stretching/shrinking flow is crucially important and useful. Both the problems of steady and unsteady flow of a dusty fluid have a wide range of possible applications in practice, such as in the centrifugal separation of particles, sedimentation and underground disposal of radioactive waste materials.

Even though the problem of dusty fluid has been broadly investigated, very limited results can be found for a shrinking sheet. Indeed, this paper has succeeded to obtain analytically dual solutions. The stability analysis can be performed by following many published papers on stretching/shrinking sheets. Finally, the critical values and plotting curves for obtaining single or dual solution are successfully presented.

The purpose of this study is to explore the effects of aerospike and hemispherical aerodisks on flow characteristics and drag reduction in supersonic flow over a blunt body. Specifically, the study aims to analyze the impact of varying the length of the cylindrical rod in the aerospike (ranging from 0.5 to 2.0 times the diameter of the blunt body) and the diameter of the hemispherical disk (ranging from 0.25 to 0.75 times the blunt body diameter). CFD simulations were conducted at a supersonic Mach number of 2 and a Reynolds number of 2.79 × 10⁶.

ICEM CFD and ANSYS CFX solver were used to generate the three-dimensional flow along with its structures. The flow structure and drag coefficient were computed using Reynolds-averaged Navier–Stokes equation model. The drag reduction mechanism was also explained using the idea of dividing streamline and density contour. The performance of the aero spike length and the effect of aero disk size on the drag are investigated.

The separating shock is located in front of the blunt body, forming an effective conical shape that reduces the pressure drag acting on the blunt body. It was observed that extending the length of the spike beyond a specific critical point did not impact the flow field characteristics and had no further influence on the enhanced performance. The optimal combination of disk and spike length was determined, resulting in a substantial reduction in drag through the introduction of the aerospike and disk.

To predict the accurate results of drag and to reduce the simulation time, a hexa grid with finer mesh structure was adopted in the simulation.

The blunt nose structures are primarily employed in the design of rockets, missiles, and re-entry capsules to withstand higher aerodynamic loads and aerodynamic heating.

For the optimized size of the aero spike, aero disk is also optimized to use the benefits of both.

The purpose of the present article is to obtain the similarity solution for the shock wave generated by a piston propagating in a self-gravitating nonideal gas under the impact of azimuthal magnetic field for adiabatic and isothermal flows.

The Lie group theoretic method given by Sophus Lie is used to obtain the similarity solution in the present article.

Similarity solution with exponential law shock path is obtained for both ideal and nonideal gas cases. The effects on the flow variables, density ratio at the shock front and shock strength by the variation of the shock Cowling number, adiabatic index of the gas, gravitational parameter and nonidealness parameter are investigated. The shock strength decreases with an increase in the shock Cowling number, nonidealness parameter and adiabatic index, whereas the strength of the shock wave increases with an increase in gravitational parameter.

Propagation of shock wave with spherical geometry in a self-gravitating nonideal gas under the impact of azimuthal magnetic field for adiabatic and isothermal flows has not been studied by any author using the Lie group theoretic method.

This study aims to investigate the rarefaction effects on flow and thermal performances of an equivalent sand-grain roughness model for aerodynamic thrust bearing.

In this study, a model of gas lubrication thrust bearing was established by modifying the wall roughness and considering rarefaction effect. The flow and lubrication characteristics of gas film were discussed based on the equivalent sand roughness model and rarefaction effect.

The boundary slip and the surface roughness effect lead to a decrease in gas film pressure and temperature, with a maximum decrease of 39.2% and 8.4%, respectively. The vortex effect present in the gas film is closely linked to the gas film’s pressure. Slip flow decreases the vortex effect, and an increase in roughness results in the development of slip flow. The increase of roughness leads to a decrease for the static and thermal characteristics.

This work uses the rarefaction effect and the equivalent sand roughness model to investigate the lubrication characteristics of gas thrust bearing. The results help to guide the selection of the surface roughness of rotor and bearing, so as to fully control the rarefaction effect and make use of it.