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The purpose of this paper is the theoretical presentation of tensorial formulation with surface mobility forces and numerical verification of Reynolds thermal transpiration law in a contemporary experiment with nanoflow.

The velocity profiles in a single microchannel are calculated by solving the momentum equations and using thermal transpiration force as the boundary conditions. The mass flow rate and pressure of unstationary thermal transpiration modeling of the benchmark experiment has been achieved by the implementation of the thermal transpiration mobility force closure for the thermal momentum accommodation coefficient.

An original and easy-to-implement method has been developed to numerically prove that at the final equilibrium, i.e. zero-flow state, there is a connection between the Poiseuille flow in the center of channel and counter thermal transpiration flow on the surface. The numerical implementation of the Reynolds model of thermal transpiration has been performed, and its usefulness for the description of the benchmark experiment has been verified.

The simplified procedure requires the measurement or assumption of the helium-glass slip length.

The procedure can be very useful in the design of micro-electro-mechanical systems and nano-electro-mechanical systems, especially for accommodation pumping.

The paper discussed possible constitutive equations in the transpiration shell-like layer. The new approach can be helpful for modeling phenomena occurring at a fluid–solid phase interface at the micro- and nanoscales.

The purpose of this study is to analyze the impact of inclined magnetohydrodynamics (MHD) and thermal radiation on the flow of a ternary micropolar nanofluid on a sheet that is expanding and contracting while applying mass transpiration and velocity slip conditions to the flow. The nanofluid, which is composed of Au, Ag and Cu nanoparticles dispersed in water as the base fluid, possesses critical properties for increasing the heat transfer rate and is frequently used in manufacturing and industrial establishments.

The set of governing nonlinear partial differential equations is transformed into a set of nonlinear ordinary differential equations. The outcome of this differential equation is solved and obtained the closed-form solution and energy equation in the form of hypergeometric functions.

The velocity, micro-rotation and temperature field are investigated versus a parametric variation. The physical domains of mass suction or injection and micropolar characteristics play an important role in specifying the presence, singleness and multiplanes of exact solutions. In addition, many nondimensional characteristics of the profiles of temperature, angular velocity and velocity profiles are graphically shown with substantial consequences. Furthermore, adding nanoparticles increases the heat transfer rate of the fluid used in manufacturing and industrial establishments. The current findings may be used for better oil recovery procedures, smart materials such as magnetorheological fluids, targeted medicine administration and increased heat transmission. Concerning environmental cleanup, nanomaterial fabrication and biomedical devices, demonstrate their potential influence in a variety of disciplines.

The originality of this paper is to analyze the impact of inclined MHD at an angle with the ternary nanofluid on a micropolar fluid over an expanding and contracting sheet with thermal radiation effect.

The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al₂O₃/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties.

The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed.

The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only.

The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.

The progress of solid propellent technology appears to have been retarded by lack of development of a fundamental mechanism of burning. A study of previous work indicates that while experimental techniques used are valid, hypotheses were inadequate; and fresh hypothetical approaches are needed. There is evidence of lack of theory development in the more fundamental field of the combustion of turbulent, pre‐mixed, fuel‐rich flames as it applies to propellent burning. The roles of radiative heat transfer and a physical disintegrative mode of surface dissipation are proposed for consideration. Previous experimental techniques together with new ones are proposed to exploit these hypotheses.

This paper aims to describe a proposal for an innovative method of normal shock wave–turbulent boundary layer interaction (SBLI) and shock-induced separation control.

The concept is based on the introduction of a tangentially moving wall upstream of the shock wave and in the interaction region. The SBLI control mechanism may be implemented as a closed belt floating on an air cushion, sliding over two cylinders and forming the outer skin of the suction side of the airfoil. The presented exploratory numerical study is conducted with SPARC solver (steady 2D RANS). The effect of the moving wall is presented for the NACA 0012 airfoil operating in transonic conditions.

To assess the accuracy of obtained solutions, validation of the computational model is demonstrated against the experimental data of Harris, Ladson & Hill and Mineck & Hartwich (NASA Langley). The comparison is conducted not only for the reference (impermeable) but also for the perforated (permeable) surface NACA 0012 airfoils. Subsequent numerical analysis of SBLI control by moving wall confirms that for the selected velocity ratios, the method is able to improve the shock-upstream boundary layer and counteract flow separation, significantly increasing the airfoil aerodynamic performance.

The moving wall concept as a means of normal shock wave–turbulent boundary layer interaction and shock-induced separation control has been investigated in detail for the first time. The study quantified the necessary operational requirements of such a system and practicable aerodynamic efficiency gains and simultaneously revealed the considerable potential of this promising idea, stimulating a new direction for future investigations regarding SBLI control.

This paper aims to accentuate the behavior of second-grade hybrid Al₂O₃–Cu nanofluid flow and its thermal characteristics driven by a stretching/shrinking Riga plate.

The second-grade fluid is considered with the combination of Cu and Al₂O₃ nanoparticles. Three base fluids namely water, ethylene glycol (EG) and methanol with different Prandtl number are also examined. The formulation of the mathematical model of second-grade hybrid nanofluid complies with the boundary layer approximations. The complexity of the governing model is reduced into a simpler differential equations using the similarity transformation. The bvp4c solver is fully used to solve the reduced equations. The observation of multiple solutions is conducted for the assisting (stretching) and opposing (shrinking) cases.

The impact of suction parameter, second-grade parameter, electromagnetohydrodynamics (EMHD) parameter, velocity ratio parameter and the volumetric concentration of the alumina and copper nanoparticles are numerically analyzed on the velocity and temperature profiles, skin friction coefficient and local Nusselt number (thermal rate) of the second-grade Al₂O₃–Cu/water. The solution is unique when (static and stretching cases) while dual for a specific range of negative in the presence of suction effect. Based on the appearance of the first solution in all cases of, it is physically showed that the first solution is stable. Further examination reveals that the EMHD and suction parameters are the contributing factors for the thermal enhancement of this non-Newtonian working fluid. Meanwhile, the viscosity of the non-Newtonian fluid also plays a significant role in the fluid motion and heat transfer rate based on the finding that the EG base fluid produces the maximum heat transfer rate but the lowest critical value and skin friction coefficient.

The results are novel and contribute to the discovery of the hybrid nanoparticles’ performance in the non-Newtonian second-grade fluid. Besides, this study is beneficial to the researchers in this field and general audience from industries regarding the factors, which contributing to the thermal enhancement of the working fluid.

A novel type of heat transfer fluid known as hybrid nanofluids is used to improve the efficiency of heat exchangers. It is observed from literature evidence that hybrid nanofluids outperform single nanofluids in terms of thermal performance. This study aims to address the stagnation point flow induced by Williamson hybrid nanofluids across a vertical plate. This fluid is drenched under the influence of mixed convection in a Darcy–Forchheimer porous medium with heat source/sink and entropy generation.

By applying the proper similarity transformation, the partial differential equations that represent the leading model of the flow problem are reduced to ordinary differential equations. For the boundary value problem of the fourth-order code (bvp4c), a built-in MATLAB finite difference code is used to tackle the flow problem and carry out the dual numerical solutions.

The shear stress decreases, but the rate of heat transfer increases because of their greater influence on the permeability parameter and Weissenberg number for both solutions. The ability of hybrid nanofluids to strengthen heat transfer with the incorporation of a porous medium is demonstrated in this study.

The findings may be highly beneficial in raising the energy efficiency of thermal systems.

The originality of the research lies in the investigation of the Darcy–Forchheimer stagnation point flow of a Williamson hybrid nanofluid across a vertical plate, considering buoyancy forces, which introduces another layer of complexity to the flow problem. This aspect has not been extensively studied before. The results are verified and offer a very favorable balance with the acknowledged papers.

Since the second world war, considerable research funds and effort have been spent on developing means for controlling the ever‐increasing flood of recorded knowledge. As far as librarians and information officers are concerned, the problem can be divided up into five distinct stages, as shown in Figure 1.

This paper aims to explore on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder by adding the effect of chemical reaction, B together with the magnetic field, M.

A set of reduced ordinary differential equations from the governing equations of partial differential equations is obtained through similarities requirements. The resulting equations are solved using bvp4c in MATLAB2019a. The impact of various physical parameters such as curvature parameter, ϒ, chemical reaction rate, B, magnetic field, M and Schmidt numbers, Sc on shear stress, f′′0 local heat flux, -θ′(0) and mass transfer, -∅′(0) also for velocity, f′(η), temperature, θ(η) and concentration, ∅(η) profiles have been plotted and briefly discussed. In this work, some vital characteristics such as local skin friction, Cf, local Nusselt number, Nux and local Sherwood number, Shx are chosen for physical and numerical analysis.

The findings expose that the duality of solutions appears in a shrinking region ( ε < 0). The value of skin friction, heat transfer rate and mass transfer rate reduction for existing of M, but in contrary result obtain for larger ϒ, B and Sc. Furthermore, the hybrid nanofluid demonstrates better heat transfer compared to nanofluid.

The hybrid nanofluid has widened its applications such as in electronic cooling, manufacturing, automotive, heat exchanger, solar energy, heat pipes and biomedical, as their efficiency in the heat transfer field is better compared to nanofluid.

The findings on stagnation point flow of Ag-CuO/water over a horizontal stretching/shrinking cylinder with the effect of chemical reaction, B and magnetic field, M is new and the originality is preserved for the benefits of future researchers.

Concerns the laminar flows from a permeable heated surface which arise in fluids due to the interaction of the force of gravity and density differences caused by the simultaneous diffusion of thermal energy and of chemical species. Species concentration levels in air are assumed to be small in many processes in the atmosphere. Under the usual Boussinesque approximations, a set of non‐similar equations for combined buoyancy effects and the permeability of the surface are obtained. The resulting equations have been integrated by four distinct methods: perturbation method for small transpiration rate; asymptotic solutions for large transpiration rate; Keller‐box methods; and local non‐similarity method for any transpiration rate. Effects of various practical values of the Schmidt number, of the multiple buoyancy parameter and that of the transpiration rate of fluid through the surface on the local skin‐friction, the local Nusselt number and the local Sherwood number are shown graphically as well as in tabular form.