Amr M. Mahros, Emad H. Aly, John H. Merkin and Ioan M. Pop
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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Emad H. Aly and Abdelhalim Ebaid
The purpose of this paper is to study flow of the Marangoni boundary layer pasta surface embedded in a porous medium saturated by a hybrid nanofluid in the presence of a magnetic…
Abstract
Purpose
The purpose of this paper is to study flow of the Marangoni boundary layer pasta surface embedded in a porous medium saturated by a hybrid nanofluid in the presence of a magnetic field and thermal radiation.
Design/methodology/approach
The governing model was converted into ordinary differential equations applying proper similarity transformations. Therefore, Laplace transform was used to exactly solve the resulted equations. Hence, the influence of the velocity profile and temperature distribution was investigated under impacts of the involved parameters.
Findings
In the case of regular fluid, i.e. the solid volume fractions are zeros, the current results are in a very good agreement with those in the literature. It was found that the velocity decreases (increases) on increasing the parameters of copper-nanoparticles volume fraction, magnetic field and suction (permeability and injection). Further, the temperature increases (decreases) with an increase of the copper-nanoparticles volume fraction, magnetic field, injection and radiation (permeability and suction).
Originality/value
The current results of the Marangoni boundary layer problem for hybrid nanofluids are new, original and extend the previous problems investigated by many authors for the case of regular/nano fluids.
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Abdelhalim Ebaid, Abdulrahman F. Aljohani and Emad H. Aly
This paper aims to investigate the impacts of the gold nanoparticles on the peristaltic flow and heat transfer of blood in the presence of heat source. This element has been…
Abstract
Purpose
This paper aims to investigate the impacts of the gold nanoparticles on the peristaltic flow and heat transfer of blood in the presence of heat source. This element has been chosen because on comparing with the other common nanoparticles, gold nanoparticles are preferred due to their unique properties in absorbing the temperature when a heat source exists.
Design/methodology/approach
On simplifying the governing equations under the assumption of long-wavelength and low-Reynolds number approximations, the resulted system has been solved by applying the homotopy perturbation method. Then, detailed physical discussion has been introduced through several plots while focusing on the consequences of the current results on the treatment of cancer.
Findings
The present results revealed that the heat source has a great effect on the blood velocity, blood temperature and concentration of the gold nanoparticles within the artery/vein cavity when represented as asymmetric channel. Moreover, the accuracy of the current solutions was validated through several plots of the remainder error for each studied phenomenon.
Originality/value
The current idea gives some light on the attempts of using the gold nanoparticles in the treatment of cancer and therefore may lead to possible applications for diagnosis/therapy of the human cancer. To the best of authors’ knowledge, this is novel, very efficient and applicable.
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Emad H. Aly, Waqar Khan Usafzai, John H. Merkin and Ioan M. Pop
The steady laminar wall jet flow over a stretching/shrinking surface in the presence of lateral suction or injection with a convective boundary condition is considered.
Abstract
Purpose
The steady laminar wall jet flow over a stretching/shrinking surface in the presence of lateral suction or injection with a convective boundary condition is considered.
Design/methodology/approach
The partial differential equations for mass, momentum and energy conservation are changed to the system of ordinary differential equations through similarity solution transformations. Solutions, both numerical and asymptotic, to these similarity equations are found in some new ranges of parameters in the governing equations.
Findings
The equations are solved both asymptotically and numerically for a range of the transpiration parameter S and the flow parameter λ given in Mahros et al. (2023), thus greatly extending the range of these previous solutions. Asymptotic solutions for both large and small values of the Prandtl number σ are derived, showing good agreement with additional numerical integrations. It should be noted that in Mahros et al. (2023), only the case when σ=1 was treated. A solution for large λ when S=1 is obtained, showing a different asymptotic form to the case when S>0 in Mahros et al. (2023). Multiple solutions were seen by them for S<0 and the nature of the lower solution branch as S→0 from below is discussed. The question as to whether the lower branch solutions join as λ>0 when S<0 is resolved through obtaining an asymptotic solution λ small.
Originality/value
The accuracy of the solutions has been checked through a detailed comparison between the solutions obtained numerically and analytically, where excellent agreement has been found. This study is important for scientists working in the area of jet flows to become familiar with the flow properties and behaviour of jets.
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Emad H. Aly and Ioan Pop
The purpose of this study is to present both effective analytic and numerical solutions to MHD flow and heat transfer past a permeable stretching/shrinking sheet in a hybrid…
Abstract
Purpose
The purpose of this study is to present both effective analytic and numerical solutions to MHD flow and heat transfer past a permeable stretching/shrinking sheet in a hybrid nanofluid with suction/injection and convective boundary conditions. Water (base fluid) nanoparticles of alumina and copper were considered as a hybrid nanofluid.
Design/methodology/approach
Proper-similarity variables were applied to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. Exact analytical solutions were then presented for the dimensionless stream and temperature functions. Further, the authors introduce a very nice analytic and numerical solutions for both small and large values of the magnetic parameter.
Findings
It was found that no/unique/two equal/dual physical solutions exist for the investigated boundary value problem. The physically realizable practice of these solutions depends on the range of the governing parameters. For a stretching/shrinking sheet, it was deduced that a hybrid nanofluid works as a cooler on increasing some of the investigated parameters. Moreover, in the case of a shrinking sheet, the first solutions of hybrid nanofluid are stable and physically realizable rather than the nanofluid, while those of the second solutions are not for both hybrid nanofluid and nanofluid.
Originality/value
The present results for the hybrid nanofluids are new and original, as they successfully extend (generalize) the problems previously considered by different authors for the case of nanofluids.
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G.K. Ramesh, J.K. Madhukesh, Emad H. Aly and Ioan Pop
The purpose of this paper is to study the steady biomagnetic hybrid nanofluid (HNF) of oxytactic microorganisms taking place over a thin needle with a magnetic field using the…
Abstract
Purpose
The purpose of this paper is to study the steady biomagnetic hybrid nanofluid (HNF) of oxytactic microorganisms taking place over a thin needle with a magnetic field using the modified Buongiorno’s nanoliquid model.
Design/methodology/approach
On applying the appropriate similarity transformations, the governing partial differential equations were transformed into a set of ordinary differential equations. These equations have been then solved numerically using Runge–Kutta–Fehlberg method of fourth–fifth order programming in MAPLE software. Features of the velocity profiles, temperature distribution, reduced skin friction coefficient, reduced Nusselt number and microorganisms’ flux, for different values of the governing parameters were analyzed and discussed.
Findings
It was observed that as the needle thickness and solid volume fraction increase, the temperature rises, but the velocity field decreases. For a higher Peclet number, the motile microorganism curve increases, and for a higher Schmidt number, the concentration curve rises.
Originality/value
On applying the modified Buongiorno’s model, the present results are original and new for the study of HNF flow and heat transfer past a permeable thin needle.
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Waqar Khan Usafzai, Emad H. Aly and Ioan Pop
The purpose of this study is to investigate the simultaneous effects of normal wall transpiration, stretching strength parameter, velocity slip and nanoparticles on the flow of a…
Abstract
Purpose
The purpose of this study is to investigate the simultaneous effects of normal wall transpiration, stretching strength parameter, velocity slip and nanoparticles on the flow of a ternary hybrid nanofluid through an elastic surface. The goal is to understand the behavior of the flow field, temperature distribution, skin friction and temperature gradient under these conditions, and to explore the existence and nature of solutions under varying parameter values.
Design/methodology/approach
The analysis involves expressing the flow field, power-law temperature field, skin friction and temperature gradient in closed-form formulas. The study examines both stretching and shrinking surfaces, distinguishing between unique and dual solutions. The methodology includes deriving exact solutions for exponential and algebraic temperature and temperature rate formulas analytically by deriving the system of governing equations into ordinary differential equations.
Findings
The study reveals that for a stretching sheet, the solution is unique, whereas dual solutions are observed for a shrinking surface. Special solutions are provided for various parametric values, showing the behavior of the exponential and algebraic temperature and temperature rate, with a focus on identifying turning points that demarcate the existence and non-existence of single or multiple solutions. The solutions are represented through graphs and tables to facilitate a comprehensive qualitative analysis. The research identifies turning points that determine the presence or absence of single or multiple solutions, uncovering multiple solutions for different parameter sets. These findings are displayed graphically and in tabular form, highlighting the complex interplay between the parameters and the resulting flow behavior.
Originality/value
This analysis contributes to the field by providing new insights into the multiple solution phenomena in ternary hybrid nanofluid flows, particularly under the combined effects of normal wall transpiration, stretching strength, velocity slip and nanoparticle presence. The identification of turning points and the exact solutions for various temperature profiles are of significant value, offering a deeper understanding of the factors influencing the flow and thermal characteristics in such systems. The study’s findings have potential applications in optimizing fluid flow in engineering systems where such conditions are prevalent.
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S. Manjunatha, B. Ammani Kuttan, G.K. Ramesh, B.J. Gireesha and Emad H. Aly
The purpose of this paper is to discuss the 3D micropolar hybrid (Ag-CuO/H2O) nanofluid past rapid moving surface, where porous medium has been considered.
Abstract
Purpose
The purpose of this paper is to discuss the 3D micropolar hybrid (Ag-CuO/H2O) nanofluid past rapid moving surface, where porous medium has been considered.
Design/methodology/approach
The model of problem was represented by highly partial differential equations which were deduced by using suitable approximations (boundary layer). Then, the governing model was converted into five combined ordinary differential equations applying proper similarity transformations. Therefore, the eminent iterative Runge–Kutta–Fehlberg method (RKF45) has been applied to solve the resulting equations.
Findings
Higher values of vortex viscosity, spin gradient viscosity and micro-inertia density parameters are reduced in horizontal direction, whereas opposite behaviour is noticed for vertical direction.
Originality/value
The work has not been done in the area of hybrid micropolar nanofluid. Hence, this article culminates to probe how to improve the thermal conduction and fluid flow in 3D boundary layer flow of micropolar mixture of nanoparticles driven by rapidly moving plate with convective boundary condition.
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Waqar Khan Usafzai, Rizwan Ul Haq and Emad H. Aly
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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Waqar Khan Usafzai, Emad H. Aly and Ioan Pop
This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport…
Abstract
Purpose
This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions.
Design/methodology/approach
The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions.
Findings
The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases.
Originality/value
The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.