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Article
Publication date: 19 June 2019

Natalia C. Roşca, Alin V. Roşca and Ioan Pop

The purpose of this paper is to theoretically investigate the unsteady separated stagnation-point flow and heat transfer past an impermeable stretching/shrinking sheet in…

Abstract

Purpose

The purpose of this paper is to theoretically investigate the unsteady separated stagnation-point flow and heat transfer past an impermeable stretching/shrinking sheet in a copper (Cu)-water nanofluid using the mathematical nanofluid model proposed by Tiwari and Das.

Design/methodology/approach

A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary (similarity) differential equations which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters.

Findings

It is found that the solution is unique for stretching case; however, multiple (dual) solutions exist for the shrinking case.

Originality/value

The authors believe that all numerical results are new and original, and have not been published elsewhere.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 26 September 2020

Natalia C. Roşca, Alin V. Roşca, Amin Jafarimoghaddam and Ioan Pop

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 10 June 2021

Natalia C. Roșca, Alin V. Roșca and Ioan Pop

The purpose of this paper is to numerically study the problem of mixed convection flow of a hybrid nanofluid past a vertical wedge with thermal radiation effect.

Abstract

Purpose

The purpose of this paper is to numerically study the problem of mixed convection flow of a hybrid nanofluid past a vertical wedge with thermal radiation effect.

Design/methodology/approach

The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which is then solved numerically through the function bvp4c from MATLAB for different values of the governing parameters. The solutions contain a mixed convection parameter λ that has a considerable impact on the flow fields.

Findings

It is found that the solutions of the ordinary (similarity) differential equations have two branches, upper and lower branch solutions, in a certain range of the mixed convection and several other parameters. To establish which of these solutions are stable and which are not, a stability analysis has been performed. The effects of the governing parameters on the fluid flow and heat transfer characteristics are illustrated in tables and figures. It is found that dual (upper and lower branch) solutions exist for both the cases of assisting and opposing flow situations. A stability analysis has also been conducted to determine the physical meaning and stability of the dual solutions.

Practical implications

This theoretical study is significantly relevant to the applications of the heat exchangers placed in a low-velocity environment and electronic devices cooled by fans.

Originality/value

The case of mixed convection flow of a hybrid nanofluid past a vertical wedge with thermal radiation effects has not been studied before, and hence all generated numerical results are claimed to be original and novel.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 4 December 2017

Giulia Giantesio, Anna Verna, Natalia C. Roşca, Alin V. Rosca and Ioan Pop

This paper aims to study the problem of the steady plane oblique stagnation-point flow of an electrically conducting Newtonian fluid impinging on a heated vertical sheet…

Abstract

Purpose

This paper aims to study the problem of the steady plane oblique stagnation-point flow of an electrically conducting Newtonian fluid impinging on a heated vertical sheet. The temperature of the plate varies linearly with the distance from the stagnation point.

Design/methodology/approach

The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB.

Findings

An exact similarity solution of the magnetohydrodynamic (MHD) Navier–Stokes equations under the Boussinesq approximation is obtained. Numerical solutions of the relevant functions and the structure of the flow field are presented and discussed for several values of the parameters which influence the motion: the Hartmann number, the parameter describing the oblique part of the motion, the Prandtl number (Pr) and the Richardson numbers. Dual solutions exist for several values of the parameters.

Originality value

The present results are original and new for the problem of MHD mixed convection oblique stagnation-point flow of a Newtonian fluid over a vertical flat plate, with the effect of induced magnetic field and temperature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 1 October 2018

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…

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 4 October 2018

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 23 November 2020

Natalia C. Roşca, Alin V. Roşca and Ioan Pop

This paper aims to report theoretical and numerical results for the problem of laminar axisymmetric flow of hybrid nanofluid over a permeable non-linearly…

Abstract

Purpose

This paper aims to report theoretical and numerical results for the problem of laminar axisymmetric flow of hybrid nanofluid over a permeable non-linearly stretching/shrinking sheet with radiation effect.

Design/methodology/approach

The numerical solutions of the arising boundary value problem are obtained using the function bvp4c from MATLAB for different values of the governing parameters.

Findings

It is found that the solutions of the ordinary (similarity) differential equations have two branches, upper and lower branch solutions, in a certain range of the stretching/shrinking and suction parameters. To establish which of these solutions are stable and which are not, a stability analysis has been performed.

Originality/value

To the best of the authors’ knowledge, present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Mustafa et al. (2015) to the case of hybrid nanofluids.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 10 December 2019

Mohammad Ghalambaz, Natalia C. Roşca, Alin V. Roşca and Ioan Pop

This study aims to study the mixed convection flow and heat transfer of Al2O3-Cu/water hybrid nanofluid over a vertical plate. Governing equations for conservation of…

Abstract

Purpose

This study aims to study the mixed convection flow and heat transfer of Al2O3-Cu/water hybrid nanofluid over a vertical plate. Governing equations for conservation of mass, momentum and energy for the hybrid nanofluid over a vertical flat plate are introduced.

Design/methodology/approach

The similarity transformation approach is used to transform the set of partial differential equations into a set of non-dimensional ordinary differential equations. Finite-deference with collocation method is used to integrate the governing equations for the velocity and temperature profiles.

Findings

The results show that dual solutions exist for the case of opposing flow over the plate. Linear stability analysis was performed to identify a stable solution. The stability analysis shows that the lower branch of the solution is always unstable, while the upper branch of the solution is always stable. The results of boundary layer analysis are reported for the various volume fractions of composite nanoparticles and mixed convection parameter. The outcomes show that the composition of nanoparticles can notably influence the boundary layer flow and heat transfer profiles. It is also found that the trend of the variation of surface skin friction and heat transfer for each of the dual solution branches can be different. The critical values of the mixed convection parameter, λ, where the dual solution branches joint together, are also under the influence of the composition of hybrid nanoparticles. For instance, assuming a total volume fraction of 5 per cent for the mixture of Al2O3 and Cu nanoparticles, the critical value of mixing parameter of λ changes from −3.1940 to −3.2561 by changing the composition of nanofluids from Al2O3 (5 per cent) + Cu (0%) to Al2O3 (2.5%) + Cu (2.5 per cent).

Originality/value

The mixed convection stability analysis and heat transfer study of hybrid nanofluids for a stagnation-point boundary layer flow are addressed for the first time. The introduced hybrid nanofluid model and similarity solution are new and of interest in both mathematical and physical points of view.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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Article
Publication date: 3 January 2017

Natalia C. Rosca, Alin V. Rosca, John H. Merkin and Ioan Pop

The purpose of this study is to consider the effects that buoyancy arising from the combination of both thermal and concentration gradients can have on the mixed…

Abstract

Purpose

The purpose of this study is to consider the effects that buoyancy arising from the combination of both thermal and concentration gradients can have on the mixed convection boundary-layer flow near a forward stagnation point with the effect of Stefan blowing being included. Ad suitable choice for the functional forms of the outer flow and the wall temperature and concentration enables the problem to be reduced to a similarity form involving the dimensionless parameters, λ (mixed convection), κ (Stefan blowing) and N (relative strength of concentration driven buoyancy to that of thermal driven), as well as the Prandtl and Schmidt numbers. Numerical solutions to this similarity system for a range of representative parameter values indicate a finite, non-zero range of κ where there can be four solutions in opposing flow with only one solution in aiding flow. Asymptotic solutions for large values of N and κ are derived, the latter having two different structures in the opposing flow.

Design/methodology/approach

This paper sets up a similarity problem to examine the effects of Stefan blowing on a mixed convection flow with the aims of solving the equations numerically and complementing the results with appropriate asymptotic analysis.

Findings

The findings of the study include multiple solution branches, saddle-node bifurcations and singularities appearing in the solution.

Originality/value

The authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 1
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 28 April 2020

Alin V. Roşca, Natalia C. Roşca and Ioan Pop

The purpose of this study is to describe the steady mixed convection stagnation point of a hybrid nanofluid with a second-order velocity slip.

Abstract

Purpose

The purpose of this study is to describe the steady mixed convection stagnation point of a hybrid nanofluid with a second-order velocity slip.

Design/methodology/approach

Using appropriate similarity variables, the partial differential equations are transformed into ordinary (similar) differential equations, which are numerically solved using the bvp4c function in MATLAB. The numerical results are used to present graphical illustrations for the reduced skin friction, reduced Nusselt number, velocity and temperature profiles.

Findings

Dual solutions are discovered in this study. Thus, stability analysis is implemented and the first (upper branch) and second (lower branch) solutions are determined and analyzed.

Research limitations/implications

Hybrid nanofluids have many practical applications in the modern industry such as in micro-manufacturing, periodic heat exchanges process, nano drug delivery system and nuclear reactors.

Originality/value

Despite numerous studies on the mixed convection stagnation point of classical viscous fluids past a vertical plate flow, none of the researchers have focused on the effect of second-order slip velocity on hybrid nanofluids. The behavior of the flow and heat transfer has been thoroughly analyzed with the variations in governing parameters such as heat source/sink and nanoparticle volume fraction. Moreover, the use of the wall slip velocity in this hybrid nanofluid model strengthened the novelty of this study.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

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