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The present study aims to address the flow and heat transfer of MgO-MWCNTs/EG hybrid nanofluid in a complex shape enclosure filled with a porous medium. The enclosure is subject to a uniform inclined magnetic field and radiation effects. The effect of the presence of a variable magnetic field on the natural convection heat transfer of hybrid nanofluids in a complex shape cavity is studied for the first time. The geometry of the cavity is an annular space with an isothermal wavy outer cold wall. Two types of the porous medium, glass ball and aluminum metal foam, are adopted for the porous space. The governing equations for mass, momentum and heat transfer of the hybrid nanofluid are introduced and transformed into non-dimensional form. The actual available thermal conductivity and dynamic viscosity data for the hybrid nanofluid are directly used for thermophysical properties of the hybrid nanofluid.

The governing equations for mass, momentum and heat transfer of hybrid nanofluid are introduced and transformed into non-dimensional form. The thermal conductivity and dynamic viscosity of the nanofluid are directly used from the experimental results available in the literature. The finite element method is used to solve the governing equations. Grid check procedure and validations were performed.

The effect of Hartmann number, Rayleigh number, Darcy number, the shape of the cavity and the type of porous medium on the thermal performance of the cavity are studied. The outcomes show that using the composite nanoparticles boosts the convective heat transfer. However, the rise of the volume fraction of nanoparticles would reduce the overall enhancement. Considering a convective dominant regime of natural convection flow with Rayleigh number of 107, the maximum enhancement ratio (Nusselt number ratio compared to the pure fluid) for the case of glass ball is about 1.17 and for the case of aluminum metal foam is about 1.15 when the volume fraction of hybrid nanoparticles is minimum as 0.2 per cent.

The effect of the presence of a variable magnetic field on the natural convection heat transfer of a new type of hybrid nanofluids, MgO-MWCNTs/EG, in a complex shape cavity is studied for the first time. The results of this paper are new and original with many practical applications of hybrid nanofluids in the modern industry.

The purpose of this paper is to investigate analytically the steady general three-dimensional stagnation-point flow of an aqueous titania-copper hybrid nanofluid past a circular cylinder that has a sinusoidal radius variation.

First, the analytic modeling of hybrid nanofluid is presented, and using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved by the well-known function bvp4c from MATLAB.

The current solution demonstrates good agreement with those of the previously published studies in the special cases of regular fluid and nanofluids. Graphical results are presented to investigate the influences of the titania and copper nanoparticle volume fractions and also the nodal/saddle indicative parameter on flow and heat transfer characteristics. Here, the thermal characteristics of hybrid nanofluid are found to be higher in comparison to the base fluid and fluid containing single nanoparticles. An important point to note is that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids.

Analytic modeling of hybrid nanofluid is the important originality of present study. Hybrid nanofluids are potential fluids that offer better heat transfer performance and thermophysical properties than convectional heat transfer fluids (oil, water and ethylene glycol) and nanofluids with single nanoparticles. In this investigation, titania (TiO₂, 50 nm), copper (Cu, 20 nm) and the hybrid of these two are separately dispersed into the water as the base fluid and analyzed.

The purpose of this study is to model and solve numerically the three-dimensional off-centered stagnation point flow and heat transfer of magnesium oxide–silver/water hybrid nanofluid impinging to a spinning disk.

The applied effective thermophysical properties of hybrid nanofluid including thermal conductivity and dynamics viscosity are according to the reported experimental relations that would be expanded by a mass-based algorithm. The single phase formulations coupled with experimental-based hybrid nanofluid model is implemented to derive the governing partial differential equations which are then transferred to a set of dimensionless ordinary differential equations (ODEs) with the use of the similarity transformation method. Afterward, the reduced ODEs are solved numerically by bvp4c function from MATLAB that is a trustworthy and efficient code according to three-stage Lobatto IIIa formula.

The effect of spinning parameter and nanoparticles masses (m_MgO, m_Ag) on the hydrodynamics and thermal boundary layers behavior and also the quantities of engineering interest are presented in tabular and graphical forms. The recent work demonstrates that the analysis of flow and heat transfer becomes more complicated when there is a non-alignment between the impinging flow and the disk axes. From computational results demonstrate that, the radial and azimuthal velocities are, respectively, the increasing and decreasing functions of the disk spinning parameter. Further, for the greater values of the spinning parameter, an overshoot of the radial velocity owing to the centrifugal forces of the spinning disk is observed. Besides, the quantities of engineering interest gently enhance with first and second nanoparticle masses, while comparing their absolute values illustrates the fact that the effect of second nanoparticle mass (m_Ag) is greater. Further, it is inferred that the second nanoparticle’s mass enhancement results in the amplification of the heat transfer; although, the high skin friction and the relevant shear stress should be controlled.

The combination of experimental thermophysical properties with theoretical modeling of the problem can be the novelty of the present work. It is evident that the experimental relations of effective thermophysical properties can be trustable and flexible in the theoretical/mathematical modeling of hybrid nanofluids flows. Besides, to the best of the authors’ knowledge, no one has ever attempted to study the present problem through a mass-based model for hybrid nanofluid.

This paper aims to study the effect of concentric hot circular cylinder inside egg-cavity porous-copper nanofluid on natural convection phenomena.

The finite element method–based Galerkin approach is applied to solve numerically the set of governing equations with appropriate boundary conditions.

The effects of different range parameters, such as Darcy number (10–3 = Da = 10–1), Rayleigh number (103 = Ra = 106), nanoparticle volume fraction (0 = ϑ = 0.06) and eccentricity (−0.3 = e = 0.1) on the fluid flow represent by stream function and heat transfer represent by temperature distribution, local and average Nusselt numbers.

A comparison between oval shape and concentric circular concentric cylinder was investigated.

In the current numerical study, heat transfer by natural convection was identified inside the new design of egg-shaped cavity as a result of the presence of a circular inside it supported by a porous medium filled with a nanofluid. After reviewing previous studies and considering the importance of heat transfer by free convection inside tubes for many applications, to the best of the authors’ knowledge, the current work is the first study that deals with a study and comparison between the common shape (concentric circular tubes) and the new shape (egg-shaped cavity).

This study aims to carry out an analysis for flow and heat transfer of a new hybrid nanofluid over a vertical flat surface embedded in a saturated porous medium with anisotropic permeability at high Rayleigh number. Here the hybrid nanofluid is considered as the working fluid, with different kinds of small particles in nanoscale being suspended.

The generalized homogenous model is introduced to describe the behaviors of hybrid nanofluid. Within the framework of the boundary layer approximations, the governing equations embodying the conservation equations of total mass, momentum and thermal energy are reduced to a set of fully coupled ordinary differential equations via relevant scaling transformations. A flow stability analysis is performed to examine the behavior of convective heat energy. Accurate solutions are obtained by means of a very efficient homotopy-based package BVPh 2.0.

Results show that the linear correlations of physical quantities among the base fluid and its suspended nanoparticles are adequate to give accurate results for simulation of behaviors of hybrid nanofluids. Heat enhancement can be also fulfilled by hybrid nanofluids. A flow stability analysis suggests the heat-related power index m > −1/3 for satisfying the increasing behavior of convective heat energy.

Free convection of a hybrid nanofluid near a vertical flat surface embedded in a saturated porous medium with anisotropic permeability is investigated for the first time. The simplified hybrid nanofluid model is proposed for describing nanofluid behaviors. The results of this proposed approach agree well with those given by the traditional hybrid nanofluid model and experiment. It is expected that, by using different combinations of various kinds of nanoparticles, the new generation of heat transfer fluids can be fabricated, which possess similar thermal-physical properties as regular nanofluids but with lower cost.

The purpose of this paper is to study the flow and heat transfer of a hybrid nanofluid, Cu–Al₂O₃/water, past a permeable stretching/shrinking sheet. The effects of Brownian motion and thermophoresis are considered here.

Similarity transformations are used to reduce the governing partial differential equations to a system of ordinary (similarity) differential equations. A MATLAB solver called the bvp4c is then used to compute the numerical solutions of equations (12) to (14) subject to the boundary conditions of equation (15). Then, the effects of various physical parameters on the flow and thermal fields of the hybrid nanofluid are analyzed.

Multiple (dual) solutions are found for the basic boundary layer equations. A stability analysis is performed to see which solutions are stable and, therefore, applicable in practice and which are not stable. Besides that, a comparison is made between the hybrid nanofluid and a traditional nanofluid, Cu/water. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than that of the other nanofluid. Thus, the hybrid nanofluid has a higher heat transfer rate than the other nanofluid. However, the increase in the shrinking parameter reduces the velocity of the hybrid nanofluid.

The present results are original and new for the study of the flow and heat transfer past a permeable stretching/shrinking sheet in Cu–Al₂O₃/water hybrid nanofluid.

This study aims to investigate the irreversibility associated with the Fe3O4–Co/kerosene hybrid-nanofluid past a wedge with nonlinear radiation and heat source.

This study reports the numerical analysis of the hybrid nanofluid model under the implications of the heat source and magnetic field over a static and moving wedge with slips. The second law of thermodynamics is applied with nonlinear thermal radiation. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved through the Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerges from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios.

The significant outcomes of the current investigation are that the velocity field uplifts for higher velocity slip and magnetic strength. Further, the heat transfer rate is reduced with the incremental values of the Eckert number, while it uplifts with thermal slip and radiation parameters. An increase in Brinkmann’s number uplifts the entropy generation rate, while that peters out the Bejan number. The results of this study are of importance involving in the assessment of the effect of some important design parameters on heat transfer and, consequently, on the optimization of industrial processes.

This study is original work that reports the hybrid nanofluid model of Fe3O4–Co/kerosene.

The purpose of this paper is to examine the axisymmetric flow and heat transfer of a hybrid nanofluid over a permeable biaxial stretching/shrinking sheet.

In this study, 0.1 solid volume fraction of alumina (Al₂O₃) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al₂O₃/water hybrid nanofluid. The hybrid nanofluid equations are converted to the similarity equations by using the similarity transformation. The bvp4c solver, which is available in the Matlab software is used for solving the similarity equations numerically. The numerical results for selected values of the parameters are presented in tabular and graphical forms, and are discussed in detail.

It is found that dual solutions exist up to a certain value of the stretching/shrinking and suction parameters. The critical value λ_c < 0 for the existence of the dual solutions decreases as nanoparticle volume fractions for copper increase. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.

The present problem is new, original with many important results for practical problems in the modern industry.

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 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.