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, 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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Ioan Pop, Siti Suzilliana Putri Mohamed Isa, Norihan M. Arifin, Roslinda Nazar, Norfifah Bachok and Fadzilah M. Ali
The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a…
Abstract
Purpose
The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically.
Design/methodology/approach
The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined.
Findings
Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter.
Originality/value
The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.
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Dalia Sabina Cimpean and Ioan Pop
This paper aims to develop a numerical study of the steady natural convection in an inclined square porous cavity filled by a nanofluid with sinusoidal temperature distribution on…
Abstract
Purpose
This paper aims to develop a numerical study of the steady natural convection in an inclined square porous cavity filled by a nanofluid with sinusoidal temperature distribution on the side walls and adiabatic conditions on the upper and lower walls.
Design/methodology/approach
Governing equations transformed in terms of the dimensionless variables using the Darcy–Boussinesq approximation have been solved numerically using a central finite-difference scheme. The Gaus-Siedel iteration technique was used for the system of discretized equations. The two-phase nanofluid model including the Brownian diffusion and thermophoresis effects has been considered for simulation of nanofluid transport inside the cavity.
Findings
The numerical results of streamlines, isotherms and isoconcentrations are investigated and the effect of different important parameters, such as inclination angle of the cavity, amplitude ratio of the sinusoidal temperature or phase deviation, is discussed. The results obtained for no inclination of the cavity are compared and successfully validated with previous reported results of the literature. The important findings of the study are focused on the changes made by the inclination angle and the periodic thermal boundary conditions, on the heat and fluid flow.
Originality/value
The originality of the present study is given by the mathematical model presented for an inclined cavity, the numerical solution with new results for inclined cavity and the applications for design of solar energy devices such as solar collectors in which the boundary conditions vary with time because of changes in weather conditions.
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Ioan Pop, Natalia C. Roşca and Alin V. Roşca
The purpose of this paper is to study the effects of MHD, suction, second-order slip and melting on the stagnation-point and heat transfer of a nanofluid past a…
Abstract
Purpose
The purpose of this paper is to study the effects of MHD, suction, second-order slip and melting on the stagnation-point and heat transfer of a nanofluid past a stretching/shrinking sheet.
Design/methodology/approach
Using appropriate variables, the governing partial differential equations were transformed into ordinary (similarity) differential equations, which are then solved numerically using the function bvp4c from Matlab.
Findings
It is found that dual (upper and lower branch) solutions exist for some values of the governing parameters. From the stability analysis, it is found that the upper branch solution is stable, while the lower branch solution is unstable. The sample velocity, temperature and concentration profiles along both solution branches are graphically presented.
Originality/value
The results of the paper are new and original with many practical applications of nanofluids in the modern industry.
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Dalia Sabina Cimpean and Ioan Pop
This paper aims to focus on the analysis of the entropy generation in an inclined square cavity filled with a porous media saturated by a nanofluid with sinusoidal temperature…
Abstract
Purpose
This paper aims to focus on the analysis of the entropy generation in an inclined square cavity filled with a porous media saturated by a nanofluid with sinusoidal temperature distribution on the side walls, adiabatic conditions on the upper wall and a heat source at the lower wall.
Design/methodology/approach
The two-phase nanofluid model including the Brownian diffusion and thermophoresis effects has been used for simulation of nanofluid transport inside the porous cavity. The governing equations and the entropy generation owing to fluid friction, heat and mass transfer are transformed in terms of the dimensionless variables, and the results are obtained by using the finite difference method of the second-order accuracy.
Findings
The numerical results of the model are investigated, and the effect of different important parameters, such as inclination angle of the cavity, amplitude ratio of the sinusoidal temperature or phase deviation, is discussed. The results for no inclination of the cavity is compared and successfully validated with previous reported results of the literature. The important findings of the study are focused mainly on the existence of the irreversibility phenomena which are affected by the conditions of the model and the values of the studied parameters.
Originality/value
The originality of this work is given by the presented mathematical model, the numerical solution with new results for entropy generation in an inclined porous cavity filled by a nanofluid and the applications for design of electronic or energy devices.
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Ioan Pop, Natalia C. Roşca and Alin V. Roşca
The purpose of this paper is to reinvestigate the problem of multiple similarity solutions of the two-dimensional magnetohydrodynamic boundary-layer flow of an incompressible…
Abstract
Purpose
The purpose of this paper is to reinvestigate the problem of multiple similarity solutions of the two-dimensional magnetohydrodynamic boundary-layer flow of an incompressible, viscous and electrically conducting fluid past a stretching/shrinking permeable surface studied by Aly et al. (2007).
Design/methodology/approach
The transformed ordinary (similarity) differential equation was solved numerically using the function bvp4c from MATLAB. The relative tolerance was set to 10^(−10).
Findings
Dual solutions were found and a stability analysis was performed to show which solutions are stable and which are not stable. On the other hand, Aly et al. (2007) have shown that for each value of the power index and magnetic parameter in the range and for any specific values of the stretching/shrinking parameter and suction parameter the problem has only a solution.
Originality/value
The paper describes how multiple (dual) solutions for the flow reversals were obtained. The stability analysis has shown that the lower solution branches are unstable, while the upper solution branches are stable.
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Mohammad Ghalambaz, Mahmoud Sabour, Ioan Pop and Dongsheng Wen
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…
Abstract
Purpose
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.
Design/methodology/approach
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.
Findings
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.
Originality/value
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.
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Mustafa Turkyilmazoglu, Kohilavani Naganthran and Ioan Pop
The purpose of this paper is to present both an analytical and a numerical analysis of the unsteady magnetohydrodynamic (MHD) rear stagnation-point flow over off-centred…
Abstract
Purpose
The purpose of this paper is to present both an analytical and a numerical analysis of the unsteady magnetohydrodynamic (MHD) rear stagnation-point flow over off-centred deformable surfaces.
Design/methodology/approach
The numerical MATLAB solver bvp4c suitable for routine boundary value problem is used for the set of ordinary differential equations reduced from the governing partial differential equations.
Findings
Multiple solutions are found for particular eigenvalues. The physical solution is computed by the help of a linear stability analysis. The authors have succeeded in discovering the second solutions, and it is suggested that these solutions are unstable and not physically realisable in practice. The current findings add to a growing body of literature on MHD stagnation-point flow problems. It is also found that the governing parameters have different effects on the flow characteristics.
Practical implications
Even though problems of steady MHD flows have been extensively studied for stagnation-point flows, limited findings can be found on the unsteady MHD rear stagnation-point flow over off-centred deformable surfaces.
Originality/value
The originality of this work is the application of a magnetic field on a time-dependent MHD rear stagnation-point flow over off-centred deformable surfaces.
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Alessandra Borrelli, Giulia Giantesio, Maria Cristina Patria, Natalia C. Roşca, Alin V. Roşca and Ioan Pop
This paper aims to consider the influence of the temperature and of an external magnetic field on the steady oblique stagnation-point flow for a Boussinesquian nanofluid past a…
Abstract
Purpose
This paper aims to consider the influence of the temperature and of an external magnetic field on the steady oblique stagnation-point flow for a Boussinesquian nanofluid past a stretching or shrinking sheet.
Design/methodology/approach
The flow is reduced through similarity transformations to an ordinary boundary value problem, which is solved numerically in MATLAB using the bvp4c function. The behavior of the solution is discussed physically, and some analytical considerations concerning existence of the solution and the occurrence of dual solutions are drawn.
Findings
The study of the influence of an external magnetic field on the oblique stagnation-point flow of a Buongiorno's Boussinesquian nanofluid is carried out. The fluid clashes on a vertical stretching or shrinking sheet. Dual solutions appear for suitable values of the parameters.
Originality/value
The present results are new and original.