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Water/Al₂O₃ nanofluid with volume fractions of 0, 0.3 and 0.06 was investigated inside a rectangular microchannel. Jet injection of nanofluid was used to enhance the heat transfer under a homogeneous magnetic field with the strengths of Ha = 0, 20 and 40. Both slip velocity and no-slip boundary conditions were used.

The laminar flow was studied using Reynolds numbers of 1, 10 and 50. The results showed that in creep motion state, the constricted cross section caused by fluid jet is not observable and the rise of axial velocity level is only because of the presence of additional size of the microchannel. By increasing the strength of the magnetic field and because of the rise of the Lorentz force, the motion of fluid layers on each other becomes limited.

Because of the limitation of sudden changes of fluid in jet injection areas, the magnetic force compresses the fluid to the bottom wall, and this behavior limits the vertical velocity gradients. In the absence of a magnetic field and under the influence of the velocity boundary layer, the fluid motion has more variations. In creeping velocities of fluid, the presence or absence of the magnetic field does not have an essential effect on Nusselt number enhancement.

In lower velocities of fluid, the effect of the jet is not significant, and the thermal boundary layer affects the entire temperature field. In this case, for Hartmann numbers of 40 and 0, changing the Nusselt number on the heated wall is similar.

This paper aims to investigate a linear and temporal stability analysis of hybrid nanofluid flow between two parallel plates filled with a porous medium and whose lower plate is fixed and the upper plate animated by a uniform rectilinear motion.

The nanofluid is composed of water as a regular fluid, silver (Ag) and alumina (Al₂O₃) as nanoparticles. The mathematical model takes into account other effects such as the magnetic field and the aspiration (injection/suction). Under the assumption of a low magnetic Reynolds number, a modified Orr–Sommerfeld-type eigenvalue differential equation governing flow stability was derived and solved numerically by Chebyshev’s spectral collocation method. The effects of parameters such as volume fraction, Darcy number, injection/suction Reynolds number, Hartmann number were analyzed.

It was found the following: the Darcy number affects the stability of the flow, the injection/suction Reynolds number has a negligible effect, the volume fraction damped disturbances and the magnetic field plays a very important role in enlarging the area of flow stability.

The originality of this work resides in the linear and temporal stability analysis of hydromagnetic Couette flow for hybrid nanofluid through porous media with small suction and injection effects.

This work aims to investigates exact solutions of the classical Glauert’s laminar wall jet mass and heat transfer under wall suction, wall contraction or dilation, and two thermal transport boundary conditions; prescribed constant surface temperature and prescribed constant surface flux in nanofluidic environment.

The flow system arranged in terms of partial dif- ferential equations is non-dimensionalized with suitable dimensionless transformation variables, and this new set of equations is reduced into ordinary differential equations via a set of similarity transformations, where they are treated analytically for closed form solutions.

Exact solutions of nanofluid flow for velocity distributions, momentum flux, wall shear stress and heat transfer boundary layers for commonly studied nanoparticles; namely copper, alumina, silver, and titanium oxide are presented. The flow behavior of alumina and titanium oxide is identical, and a similar behavior is seen for copper and silver, making two pairs of identical traits. The mathematical expressions as well as visual analysis of wall shear drag and temperature gradient which are of practical interest are analyzed. It is shown that wall stretching or shrinking, wall transpiration and velocity slip together influences the jet flow mechanism and extends the original Glauert’s jet solutions. The exact solutions for the two temperature boundary layer conditions and temperature gradients are analyzed analytically. It is found that the effect of nanopar- ticles concentration on thermal boundary layer is intense, causing temperature uplift, whereas the wall transpiration causes a decrease in thermal layers.

The analysis carried out in nanofluid environment is genuinely new and unique, as our work generalizes the Glauert’s classical regular wall jet fluid problem.

The purpose of this study is to analyze the nonhomogeneous model on the mixed convection of Al2O3–Fe3O4 Bingham plastic hybrid nanofluid in a ventilated enclosure subject to an externally imposed uniform magnetic field. Entropy generation and the pressure drop are determined to analyze the performance of the heat transfer. The significance of Joule heating arising due to the applied magnetic field on the heat transfer of the yield stress fluid is described.

The ventilation in the enclosure of heated walls is created by an opening on one vertical wall through which cold fluid is injected and another opening on the opposite vertical wall through which fluid can flow out.

This study finds that the inclusion of Fe₃O₄ nanoparticles with the Al₂O₃-viscoplastic nanofluid augments the heat transfer. This rate of enhancement in heat transfer is higher than the rate by which the entropy generation is increased as well as the enhancement in the pressure drop. The yield stress has an adverse effect on the heat transfer; however, it favors thermal mixing. The magnetic field, which is acting opposite to the direction of the inlet jet, manifests heat transfer of the viscoplastic hybrid nanofluid. The horizontal jet of cold fluid produces the optimal heat transfer.

The objective of this study is to analyze the impact of the inclined cold jet of viscoplastic electrically conducting hybrid nanofluid on heat transfer from the enclosure in the presence of a uniform magnetic field. The combined effect of hybrid nanoparticles and a magnetic field to enhance heat transfer of a viscoplastic fluid in a ventilated enclosure has not been addressed before.

This paper aims to study the magnetohydrodynamic (MHD) wall jet of a hybrid nanofluid flow over a moving surface with a thermally convective surface, wall moving with suction/injection.

On using appropriate similarity transformations, the governing equations that describe the model are converted into a system of nonlinear ordinary differential equations. These equations are solved both analytically and numerically using standard two-point boundary-value problem solvers and Chebyshev pseudospectral differentiation matrix method, respectively.

These results show that the HNF is heating/cooling with growth of the positive/negative values of the parameter measuring the velocity of the moving surface. The temperature distributions increase, where the thermal boundary layer gets thicker, as the magnetic field strengthens and with an increase in the absolute value of the Biot number.

The current findings for the HNFs are new and original. They generalize successfully the problems investigated previously by different researchers for the cases of fluids and also nanofluids.

The purpose of this study is to do a numerical analysis of the jet to a body filled with phase change material (PCM). The melting of the PCM filled body was investigated by the hot jet flow. Four different values of the Reynolds number were taken, ranging from 5 × 103 = Re = 12.5 103. Water, Al₂O₃ 1%, Al₂O₃ 2% and hybrid nanofluid (HNF; Al₂O₃–Ag mixture) were used as fluid types and the effects of fluid type on melting were investigated. At 60 °C, the jet stream was impinged on the PCM filled body at different Reynolds numbers.

Two-dimensional analysis of melting of PCM inserted A block via impinging turbulent slot jet is numerically studied. Governing equations for turbulent flow are solved by using the finite element method via analysis and system fluent R2020.

The obtained results showed that the best melting occurred when the Reynolds number increased and the HNF was used. However, the impacts of using alumina-water nanofluid were slight. At Re = 12,500, phase completion time was reduced by about 13.77% when HNF was used while this was only 3.93% with water + alumina nanofluid as compared to using only water at Re = 5,000. In future studies, HNF concentrations will change the type of nanoenhanced PCMs. In addition, the geometry and jet parameters of the PCM-filled cube can be changed.

Effects of impinging jet onto PCM filled block and control of melting via impinging hot jet of PCM. Thus, novelty of the work is to control of melting in a block by impinging hot jet and nanoparticles.

The purpose of this paper is to study the laminar boundary layer cross flow and heat transfer on a rotational stagnation-point flow over either a stretching or shrinking porous wall submerged in hybrid nanofluids. The involved boundary layers are of stream-wise type with stretching/shrinking process along the surface.

Using appropriate similarity variables the partial differential equations are reduced to ordinary (similarity) differential equations. The reduced system of equations is solved analytically (by high-order perturbed field propagation for small to moderate stretching/shrinking parameter and low-order perturbation for large stretching/shrinking parameter) and numerically using the function bvp4c from MATLAB for different values of the governing parameters.

It was found that the basic similarity equations admit dual (upper and lower branch) solutions for both stretching/shrinking surfaces. Moreover, performing a linear stability analysis, it was confirmed that the upper branch solution is realistic (physically realizable), while the lower branch solution is not physically realizable in practice. These dual solutions will be studied in the present paper.

The authors believe that all numerical results are new and original and have not been published before for the present problem.

The purpose of this study is to conduct a comparative investigation for incompressible electrically conducting nanofluid fluid through wall jet. Single-walled carbon nanotubes (SWCNTs) and multiple-walled carbon nanotubes (MWCNTs) are considered as the nanoparticles. To record the effect of Lorentz forces, a magnetic field is applied normally with the assumption that the induced magnetic field is negligible.

Boundary layer approximation is used to convert governing equations into ordinary differential equations along with appropriate boundary conditions. To obtain the results, used homotopy analysis method (HAM) has been used as an analytical technique and to validate the obtained results a famous numerical Runge–Kutta–Fehlberg method is also exploited. It has been observed that the results obtained through both of the methods are in excellent agreement with exact solution.

The Hartmann number is used as controlling parameter for velocity and temperature profile. That can be recorded as its extended values help to normalize the velocity, whereas it controls the rapid increase in temperature. The temperature profile is boosted by increasing the value of the Biot number, a physical parameter. Similarly, it also increases for an increased percentage of volume fraction of particles (SWCNTs/MWCNTs). The Hartmann number plays an important role in decreasing local skin friction coefficient. The influence of the Biot number and volume fraction of nanoparticles caused similar increasing effects on the local Nusselt number. Nanoparticles of the form SWCNT provide better heat transfer as compared to MWCNTs. Influence of the Biot number and volume fraction of nanoparticles caused similar increasing effects on the local Nusselt number. Nanoparticles of the form SWCNT provide better heat transfer as compared to MWCNTs.

To gain insight into the problem, the effects of various emerging parameters and physical quantities such as Biot number, Nusselt number and skin friction coefficient, have been explored.

This paper aims to investigate increasing heat transfer in bend tube 90° by fluid injection using nano fluid flow that was performed by expending varying Reynolds number. This paper studies the increased heat transfer in the bent tube that used some parameters to examine the effects of volume fraction, nanoparticle diameter, fluid injection, Reynolds number on heat transfer and flow in a bend pipe.

Designing curved tubes increases the thermal conductivity amount between fluid and wall. It is used the finite volume method and simple algorithms to solve the conservation equations of mass, momentum and energy. The results showed that the nanoparticles used in bent tube transfusion increase the heat transfer performance by increasing the volume fraction; it has a direct impact on enhancing the heat transfer coefficient.

Heat transfer coefficient enhanced 1.5% when volume fraction increased from 2 % to 6%, the. It is due to the impact of nanoparticles on the thermal conductivity of the fluid. The fluid is injected into the boundary layer flow due to jamming that enhances heat transfer. Curved lines used create a centrifugal force due to the bending and lack of development that increase the heat transfer.

This study has investigated the effect of injection of water into a 90° bend before and after the bend. Specific objectives are to analyze effect of injection on heat transfer of bend tube and pressure drop, evaluate best performance of mixing injection and bend in different positions and analyze effect of nano fluid volume fraction on injection.

The purpose of this study is to present a simple analytic solution to wall jet flow of nanofluids. The concept of exponentially decaying wall jet flows proposed by Glauert (1956) is considered.

A proper similarity variables are used to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then solved analytically.

Dual solutions are found and a stability analysis has been done. These solutions show that the first solution is physically realizable, whereas the second solution is not practicable.

The present results are original and new for the study of fluid flow and heat transfer over a static permeable wall, as they successfully extend the problem considered by Glauert (1956) to the case of nanofluids.